*: Regenerate.
[gcc.git] / libstdc++-v3 / doc / html / manual / policy_based_data_structures_test.html
index ee89d1917092ae0681c64fb50afd2c61362379b6..f62faf48b1b6f230bee696429a9c8f31981b2648 100644 (file)
@@ -1,6 +1,34 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1//EN" "http://www.w3.org/TR/xhtml11/DTD/xhtml11.dtd">
-<html xmlns="http://www.w3.org/1999/xhtml"><head><title>Testing</title><meta name="generator" content="DocBook XSL-NS Stylesheets V1.76.1"/><meta name="keywords" content="&#10;&#9;ISO C++&#10;      , &#10;&#9;policy&#10;      , &#10;&#9;container&#10;      , &#10;&#9;data&#10;      , &#10;&#9;structure&#10;      , &#10;&#9;associated&#10;      , &#10;&#9;tree&#10;      , &#10;&#9;trie&#10;      , &#10;&#9;hash&#10;      , &#10;&#9;metaprogramming&#10;      "/><meta name="keywords" content="&#10;      ISO C++&#10;    , &#10;      library&#10;    "/><meta name="keywords" content="&#10;      ISO C++&#10;    , &#10;      runtime&#10;    , &#10;      library&#10;    "/><link rel="home" href="../index.html" title="The GNU C++ Library"/><link rel="up" href="policy_data_structures.html" title="Chapter 22. Policy-Based Data Structures"/><link rel="prev" href="policy_data_structures_design.html" title="Design"/><link rel="next" href="policy_data_structures_biblio.html" title="Acknowledgments"/></head><body><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Testing</th></tr><tr><td align="left"><a accesskey="p" href="policy_data_structures_design.html">Prev</a> </td><th width="60%" align="center">Chapter 22. Policy-Based Data Structures</th><td align="right"> <a accesskey="n" href="policy_data_structures_biblio.html">Next</a></td></tr></table><hr/></div><div class="section" title="Testing"><div class="titlepage"><div><div><h2 class="title"><a id="pbds.test"/>Testing</h2></div></div></div><div class="section" title="Regression"><div class="titlepage"><div><div><h3 class="title"><a id="pbds.test.regression"/>Regression</h3></div></div></div><p>The library contains a single comprehensive regression test.
+<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><title>Testing</title><meta name="generator" content="DocBook XSL-NS Stylesheets V1.76.1"><meta name="keywords" content="
+       ISO C++
+      , 
+       policy
+      , 
+       container
+      , 
+       data
+      , 
+       structure
+      , 
+       associated
+      , 
+       tree
+      , 
+       trie
+      , 
+       hash
+      , 
+       metaprogramming
+      "><meta name="keywords" content="
+      ISO C++
+    , 
+      library
+    "><meta name="keywords" content="
+      ISO C++
+    , 
+      runtime
+    , 
+      library
+    "><link rel="home" href="../index.html" title="The GNU C++ Library"><link rel="up" href="policy_data_structures.html" title="Chapter 22. Policy-Based Data Structures"><link rel="prev" href="policy_data_structures_design.html" title="Design"><link rel="next" href="policy_data_structures_biblio.html" title="Acknowledgments"></head><body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Testing</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="policy_data_structures_design.html">Prev</a> </td><th width="60%" align="center">Chapter 22. Policy-Based Data Structures</th><td width="20%" align="right"> <a accesskey="n" href="policy_data_structures_biblio.html">Next</a></td></tr></table><hr></div><div class="section" title="Testing"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a name="pbds.test"></a>Testing</h2></div></div></div><div class="section" title="Regression"><div class="titlepage"><div><div><h3 class="title"><a name="pbds.test.regression"></a>Regression</h3></div></div></div><p>The library contains a single comprehensive regression test.
     For a given container type in this library, the test creates
     an object of the container type and an object of the
     corresponding standard type (e.g., <code class="classname">std::set</code>). It
@@ -22,9 +50,9 @@
     this library's containers and the containers' value-types are
     configured to use this allocator.</p><p>For granularity, the test is split into the
     several sources, each checking only some containers.</p><p>For more details, consult the files in
-    <code class="filename">testsuite/ext/pb_ds/regression</code>.</p></div><div class="section" title="Performance"><div class="titlepage"><div><div><h3 class="title"><a id="pbds.test.performance"/>Performance</h3></div></div></div><div class="section" title="Hash-Based"><div class="titlepage"><div><div><h4 class="title"><a id="performance.hash"/>Hash-Based</h4></div></div></div><p/><div class="section" title="Text find"><div class="titlepage"><div><div><h5 class="title"><a id="performance.hash.text_find"/>
+    <code class="filename">testsuite/ext/pb_ds/regression</code>.</p></div><div class="section" title="Performance"><div class="titlepage"><div><div><h3 class="title"><a name="pbds.test.performance"></a>Performance</h3></div></div></div><div class="section" title="Hash-Based"><div class="titlepage"><div><div><h4 class="title"><a name="performance.hash"></a>Hash-Based</h4></div></div></div><p></p><div class="section" title="Text find"><div class="titlepage"><div><div><h5 class="title"><a name="performance.hash.text_find"></a>
          Text <code class="function">find</code>
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="hash.text_find.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="hash.text_find.info"></a>
            Description
          </h6></div></div></div><p>
            This test inserts a number of values with keys from an
            </code>
          </p><p>The test checks the effect of different range-hashing
          functions, trigger policies, and cache-hashing policies.
-         </p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="hash.text_find.results"/>
+         </p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="hash.text_find.results"></a>
            Results
          </h6></div></div></div><p>The graphic below show the results for the native
          and collision-chaining hash types the the function
          applied being a text find timing test using
          <code class="function">find</code>.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_hash_text_find.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_hash_text_find.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"><col align="left" class="c4"><col align="left" class="c5"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    n_hash_map_ncah
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::tr1::unordered_map</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">cache_hash_code</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="constant">false</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    cc_hash_mod_prime_1div1_nsth_map
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mod_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_prime_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/1
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    cc_hash_mask_exp_1div2_sth_map
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">
                      cc_hash_table
                    </code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    cc_hash_mask_exp_1div1_nsth_map
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/1
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    cc_hash_mask_exp_1div2_nsth_map
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="hash.text_find.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="hash.text_find.observations"></a>
            Observations
          </h6></div></div></div><p>In this setting, the range-hashing scheme affects performance
          more than other policies. As the results show, containers using
          library's implementation. (Unfortunately, it was not possible to run
          the tests with <code class="classname">std::tr1::unordered_map</code> 's
          <code class="classname">cache_hash_code = true</code> , as it appeared to
-         malfuntion.)</p></div></div><div class="section" title="Integer find"><div class="titlepage"><div><div><h5 class="title"><a id="performance.hash.int_find"/>
+         malfuntion.)</p></div></div><div class="section" title="Integer find"><div class="titlepage"><div><div><h5 class="title"><a name="performance.hash.int_find"></a>
          Integer <code class="function">find</code>
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="hash.int_find.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="hash.int_find.info"></a>
            Description
          </h6></div></div></div><p>This test inserts a number of values with uniform
          integer keys into a container, then performs a series of finds
            </code>
          </p><p>The test checks the effect of different underlying
          hash-tables,
-         range-hashing functions, and trigger policies.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="hash.int_find.results"/>
+         range-hashing functions, and trigger policies.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="hash.int_find.results"></a>
            Results
          </h6></div></div></div><p>
            There are two sets of results for this type, one for
          </p><p>The first graphic below shows the results for the native and
          collision-chaining hash types. The function applied being a random
          integer timing test using <code class="function">find</code>.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_cc_hash_int_find.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_cc_hash_int_find.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"><col align="left" class="c4"><col align="left" class="c5"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    n_hash_map_ncah
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::tr1::unordered_map</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">cache_hash_code</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="constant">false</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    cc_hash_mod_prime_1div1_nsth_map
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mod_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_prime_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/1
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    cc_hash_mod_prime_1div2_nsth_map
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">
                      cc_hash_table
                    </code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mod_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_prime_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    cc_hash_mask_exp_1div1_nsth_map
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/1
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    cc_hash_mask_exp_1div2_nsth_map
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
                  </td></tr></tbody></table></div><p>
          </p><p>And the second graphic shows the results for the native and
          general-probe hash types. The function applied being a random
          integer timing test using <code class="function">find</code>.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_gp_hash_int_find.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_gp_hash_int_find.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"><col align="left" class="c4"><col align="left" class="c5"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    n_hash_map_ncah
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::tr1::unordered_map</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">cache_hash_code</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="constant">false</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    gp_hash_mod_quadp_prime_1div2_nsth_map
-                 </td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="4" align="left" valign="top">
                    <code class="classname">gp_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mod_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Probe_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">quadratic_probe_fn</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_prime_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    gp_hash_mask_linp_exp_1div2_nsth_map
-                 </td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="4" align="left" valign="top">
                    <code class="classname">
                      gp_hash_table
                    </code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Probe_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">linear_probe_fn</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="hash.int_find.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="hash.int_find.observations"></a>
            Observations
          </h6></div></div></div><p>In this setting, the choice of underlying hash-table affects
          performance most, then the range-hashing scheme and, only finally,
          above graphics should be noted that
          <code class="classname">std::tr1::unordered_map</code> are hard-wired
          currently to mod-based schemes.
-         </p></div></div><div class="section" title="Integer Subscript find"><div class="titlepage"><div><div><h5 class="title"><a id="performance.hash.int_subscript_find"/>
+         </p></div></div><div class="section" title="Integer Subscript find"><div class="titlepage"><div><div><h5 class="title"><a name="performance.hash.int_subscript_find"></a>
          Integer Subscript <code class="function">find</code>
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="hash.int_subscript_find.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="hash.int_subscript_find.info"></a>
            Description
          </h6></div></div></div><p>This test inserts a number of values with uniform
          integer keys into a container, then performs a series of finds
              performance/ext/pb_ds/random_int_subscript_find_timing.cc
            </code>
          </p><p>The test checks the effect of different underlying
-         hash-tables, range-hashing functions, and trigger policies.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="hash.int_subscript_find.results"/>
+         hash-tables, range-hashing functions, and trigger policies.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="hash.int_subscript_find.results"></a>
            Results
          </h6></div></div></div><p>
            There are two sets of results for this type, one for
          and collision-chaining hash types, using as the function
          applied an integer subscript timing test with
          <code class="function">find</code>.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_cc_hash_int_subscript_find.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_cc_hash_int_subscript_find.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"><col align="left" class="c4"><col align="left" class="c5"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    n_hash_map_ncah
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::tr1::unordered_map</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">cache_hash_code</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="constant">false</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    cc_hash_mod_prime_1div1_nsth_map
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mod_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_prime_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/1
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    cc_hash_mod_prime_1div2_nsth_map
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mod_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_prime_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    cc_hash_mask_exp_1div1_nsth_map
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/1
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    cc_hash_mask_exp_1div2_nsth_map
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
                  </td></tr></tbody></table></div><p>
          </p><p>And the second graphic shows the results for the native and
          general-probe hash types. The function applied being a random
          integer timing test using <code class="function">find</code>.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_gp_hash_int_subscript_find.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_gp_hash_int_subscript_find.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"><col align="left" class="c4"><col align="left" class="c5"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    n_hash_map_ncah
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::tr1::unordered_map</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">cache_hash_code</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="constant">false</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    gp_hash_mod_quadp_prime_1div2_nsth_map
-                 </td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="4" align="left" valign="top">
                    <code class="classname">gp_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mod_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Probe_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">quadratic_probe_fn</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_prime_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    gp_hash_mask_linp_exp_1div2_nsth_map
-                 </td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="4" align="left" valign="top">
                    <code class="classname">
                      gp_hash_table
                    </code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Probe_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">linear_probe_fn</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="hash.int_subscript_find.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="hash.int_subscript_find.observations"></a>
            Observations
          </h6></div></div></div><p>This test shows similar results to Hash-Based
-         Integer <code class="classname">find</code> Find Timing test.</p></div></div><div class="section" title="Integer Subscript insert"><div class="titlepage"><div><div><h5 class="title"><a id="performance.hash.int_subscript_insert"/>
+         Integer <code class="classname">find</code> Find Timing test.</p></div></div><div class="section" title="Integer Subscript insert"><div class="titlepage"><div><div><h5 class="title"><a name="performance.hash.int_subscript_insert"></a>
          Integer Subscript <code class="function">insert</code>
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="hash.int_subscript_insert.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="hash.int_subscript_insert.info"></a>
            Description
          </h6></div></div></div><p>This test inserts a number of values with uniform i.i.d.
          integer keys into a container, using
              performance/ext/pb_ds/random_int_subscript_insert_timing.cc
            </code>
          </p><p>The test checks the effect of different underlying
-         hash-tables.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="hash.int_subscript_insert.results"/>
+         hash-tables.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="hash.int_subscript_insert.results"></a>
            Results
          </h6></div></div></div><p>
            There are two sets of results for this type, one for
          and collision-chaining hash types, using as the function
          applied an integer subscript timing test with
          <code class="function">insert</code>.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_cc_hash_int_subscript_insert.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_cc_hash_int_subscript_insert.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"><col align="left" class="c4"><col align="left" class="c5"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    n_hash_map_ncah
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::tr1::unordered_map</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">cache_hash_code</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="constant">false</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    cc_hash_mod_prime_1div1_nsth_map
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mod_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_prime_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/1
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    cc_hash_mod_prime_1div2_nsth_map
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mod_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_prime_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    cc_hash_mask_exp_1div1_nsth_map
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/1
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    cc_hash_mask_exp_1div2_nsth_map
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
                  </td></tr></tbody></table></div><p>
          </p><p>And the second graphic shows the results for the native and
          general-probe hash types. The function applied being a random
          integer timing test using <code class="function">find</code>.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_gp_hash_int_subscript_insert.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_gp_hash_int_subscript_insert.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"><col align="left" class="c4"><col align="left" class="c5"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    n_hash_map_ncah
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::tr1::unordered_map</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">cache_hash_code</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="constant">false</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    gp_hash_mod_quadp_prime_1div2_nsth_map
-                 </td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="4" align="left" valign="top">
                    <code class="classname">gp_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mod_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Probe_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">quadratic_probe_fn</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_prime_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    gp_hash_mask_linp_exp_1div2_nsth_map
-                 </td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="4" align="left" valign="top">
                    <code class="classname">
                      gp_hash_table
                    </code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Probe_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">linear_probe_fn</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="hash.int_subscript_insert.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="hash.int_subscript_insert.observations"></a>
            Observations
          </h6></div></div></div><p>In this setting, as in Hash-Based Text
          <code class="function">find</code> Find Timing test and Hash-Based
          Integer <code class="function">find</code> Find Timing test , the choice
          of underlying hash-table underlying hash-table affects performance
          most, then the range-hashing scheme, and
-         finally any other policies.</p><p>There are some differences, however:</p><div class="orderedlist"><ol class="orderedlist"><li class="listitem"><p>In this setting, probing tables function sometimes more
+         finally any other policies.</p><p>There are some differences, however:</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><p>In this setting, probing tables function sometimes more
            efficiently than collision-chaining tables.
            This is explained shortly.</p></li><li class="listitem"><p>The performance graphs have a "saw-tooth" shape. The
            average insert time rises and falls. As values are inserted
            <code class="function">find</code> Find Timing Test and Hash-Based
            Integer <code class="function">find</code> Find Timing Test.
            Unsurprisingly, however, containers with lower α<sub>max</sub> perform worse in this case,
-         since more re-hashes are performed.</p></div></div><div class="section" title="Integer find with Skewed-Distribution"><div class="titlepage"><div><div><h5 class="title"><a id="performance.hash.zlob_int_find"/>
+         since more re-hashes are performed.</p></div></div><div class="section" title="Integer find with Skewed-Distribution"><div class="titlepage"><div><div><h5 class="title"><a name="performance.hash.zlob_int_find"></a>
          Integer <code class="function">find</code> with Skewed-Distribution
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="hash.zlob_int_find.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="hash.zlob_int_find.info"></a>
            Description
          </h6></div></div></div><p>This test inserts a number of values with a markedly
          non-uniform integer keys into a container, then performs
              performance/ext/pb_ds/hash_zlob_random_int_find_timing.cc
            </code>
          </p><p>The test checks the effect of different range-hashing
-         functions and trigger policies.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="hash.zlob_int_find.results"/>
+         functions and trigger policies.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="hash.zlob_int_find.results"></a>
            Results
          </h6></div></div></div><p>The graphic below show the results for the native, collision-chaining, and general-probing hash types.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_hash_zlob_int_find.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_hash_zlob_int_find.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"><col align="left" class="c4"><col align="left" class="c5"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    n_hash_map_ncah
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::tr1::unordered_map</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">cache_hash_code</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="constant">false</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    cc_hash_mod_prime_1div1_nsth_map
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mod_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_prime_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/1
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    cc_hash_mask_exp_1div1_nsth_map
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">
                      cc_hash_table
                    </code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/1
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    gp_hash_mod_quadp_prime_1div2_nsth_map
-                 </td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="4" align="left" valign="top">
                    <code class="classname">gp_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mod_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Probe_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">quadratic_probe_fn</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_prime_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="hash.zlob_int_find.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="hash.zlob_int_find.observations"></a>
            Observations
          </h6></div></div></div><p>In this setting, the distribution of keys is so skewed that
          the underlying hash-table type affects performance marginally.
          performance is bad, a χ<sup>2</sup> test can be used
          to check how to transform it into a more uniform
          distribution.</p><p>For this reason, this library's default range-hashing
-         function is mask-based.</p></div></div><div class="section" title="Erase Memory Use"><div class="titlepage"><div><div><h5 class="title"><a id="performance.hash.erase_mem"/>
+         function is mask-based.</p></div></div><div class="section" title="Erase Memory Use"><div class="titlepage"><div><div><h5 class="title"><a name="performance.hash.erase_mem"></a>
          Erase Memory Use
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="hash.erase_mem.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="hash.erase_mem.info"></a>
            Description
          </h6></div></div></div><p>This test inserts a number of uniform integer keys
          into a container, then erases all keys except one. It measures
              performance/ext/pb_ds/hash_random_int_erase_mem_usage.cc
            </code>
          </p><p>The test checks how containers adjust internally as their
-         logical size decreases.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="hash.erase_mem.results"/>
+         logical size decreases.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="hash.erase_mem.results"></a>
            Results
          </h6></div></div></div><p>The graphic below show the results for the native, collision-chaining, and general-probing hash types.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_hash_int_erase_mem.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_hash_int_erase_mem.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"><col align="left" class="c4"><col align="left" class="c5"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    n_hash_map_ncah
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::tr1::unordered_map</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">cache_hash_code</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="constant">false</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    cc_hash_mod_prime_1div1_nsth_map
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mod_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_prime_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/1
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    cc_hash_mask_exp_1div2_nsth_map
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">
                      cc_hash_table
                    </code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="5" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="5" align="left">
                    gp_hash_mask_linp_exp_1div2_nsth_set
-                 </td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="4" align="left" valign="top">
                    <code class="classname">gp_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Probe_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">linear_probe_fn</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="hash.erase_mem.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="hash.erase_mem.observations"></a>
            Observations
          </h6></div></div></div><p>The standard's hash-based containers act very differently than trees in
          this respect. When erasing numerous keys from an standard
          depending on whether the container is tree-based or hash-based.
          This is a fundamental consequence of the standard's interface for
          associative containers, and it is not due to a specific
-         implementation.</p></div></div></div><div class="section" title="Branch-Based"><div class="titlepage"><div><div><h4 class="title"><a id="performance.branch"/>Branch-Based</h4></div></div></div><p/><div class="section" title="Text insert"><div class="titlepage"><div><div><h5 class="title"><a id="performance.branch.text_insert"/>
+         implementation.</p></div></div></div><div class="section" title="Branch-Based"><div class="titlepage"><div><div><h4 class="title"><a name="performance.branch"></a>Branch-Based</h4></div></div></div><p></p><div class="section" title="Text insert"><div class="titlepage"><div><div><h5 class="title"><a name="performance.branch.text_insert"></a>
          Text <code class="function">insert</code>
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="branch.text_insert.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="branch.text_insert.info"></a>
            Description
          </h6></div></div></div><p>This test inserts a number of values with keys from an arbitrary
          text ([ wickland96thirty ]) into a container
            <code class="filename">
              performance/ext/pb_ds/tree_text_insert_timing.cc
            </code>
-         </p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="branch.text_insert.results"/>
+         </p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="branch.text_insert.results"></a>
            Results
          </h6></div></div></div><p>The three graphics below show the results for the native
          tree and this library's node-based trees, the native tree and
          and this library's PATRICIA-trie, respectively.
          </p><p>The graphic immediately below shows the results for the
          native tree type and several node-based tree types.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_tree_text_insert_node.png" style="text-align: middle"/></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_tree_text_insert_node.png" align="middle"></div><p>
              The abbreviated names in the legend of the graphic above are
              instantiated with the types in the following table.
-           </p></div><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+           </p></div><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_map
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::map</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    splay_tree_map
-                 </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">splay_tree_tag</code>
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">Node_update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    rb_tree_map
-                 </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rb_tree_tag</code>
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">Node_update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
                  </td></tr></tbody></table></div><p>The graphic below shows the results for the
          native tree type and a vector-based tree type.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_tree_text_insert_vector.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_tree_text_insert_vector.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_map
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::map</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    ov_tree_map
-                 </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">ov_tree_tag</code>
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">Node_update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
                  </td></tr></tbody></table></div><p>The graphic below shows the results for the
          native tree type and a PATRICIA trie type.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_tree_text_insert_trie.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_tree_text_insert_trie.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_map
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::map</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    pat_trie_map
-                 </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">pat_trie_tag</code>
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">Node_update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="branch.text_insert.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="branch.text_insert.observations"></a>
            Observations
          </h6></div></div></div><p>Observing the first graphic implies that for this setting, a splay tree
          (<code class="classname">tree</code> with <code class="classname">Tag
          encountered, a new "hash-table" is built A large fan-out PATRICIA
          trie, however, doe does well in look-ups (see Branch-Based
          Text <code class="function">find</code> Find Timing Test). It may be
-         beneficial in semi-static settings.</p></div></div><div class="section" title="Text find"><div class="titlepage"><div><div><h5 class="title"><a id="performance.branch.text_find"/>
+         beneficial in semi-static settings.</p></div></div><div class="section" title="Text find"><div class="titlepage"><div><div><h5 class="title"><a name="performance.branch.text_find"></a>
          Text <code class="function">find</code>
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="branch.text_find.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="branch.text_find.info"></a>
            Description
          </h6></div></div></div><p>This test inserts a number of values with keys from an
          arbitrary text ([wickland96thirty]) into
              performance/ext/pb_ds/text_find_timing.cc
            </code>
          </p><p>The test checks the effect of different underlying
-         data structures.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="branch.text_find.results"/>
+         data structures.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="branch.text_find.results"></a>
            Results
          </h6></div></div></div><p>The graphic immediately below shows the results for the
          native tree type and several other tree types.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_tree_text_find.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_tree_text_find.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_map
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::map</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    splay_tree_map
-                 </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">splay_tree_tag</code>
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    rb_tree_map
-                 </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rb_tree_tag</code>
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    ov_tree_map
-                 </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">ov_tree_tag</code>
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    pat_trie_map
-                 </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">pat_trie_tag</code>
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="branch.text_find.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="branch.text_find.observations"></a>
            Observations
          </h6></div></div></div><p>For this setting, a splay tree (<code class="classname">tree</code>
          with <code class="classname">Tag
          </code> = <code class="classname">splay_tree_tag</code>) does not do
-         well. This is possibly due to two reasons:</p><div class="orderedlist"><ol class="orderedlist"><li class="listitem"><p>A splay tree is not guaranteed to be balanced [motwani95random]. If a
+         well. This is possibly due to two reasons:</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><p>A splay tree is not guaranteed to be balanced [motwani95random]. If a
            splay tree contains n nodes, its average root-leaf
            path can be m &gt;&gt; log(n).</p></li><li class="listitem"><p>Assume a specific root-leaf search path has length
            m, and the search-target node has distance m'
          by a sub-trie. A large-fan-out PATRICIA trie does not do well on
          modifications (see Tree-Based and Trie-Based
          Text Insert Timing Test). Therefore, it is possibly beneficial in
-         semi-static settings.</p></div></div><div class="section" title="Text find with Locality-of-Reference"><div class="titlepage"><div><div><h5 class="title"><a id="performance.branch.text_lor_find"/>
+         semi-static settings.</p></div></div><div class="section" title="Text find with Locality-of-Reference"><div class="titlepage"><div><div><h5 class="title"><a name="performance.branch.text_lor_find"></a>
          Text <code class="function">find</code> with Locality-of-Reference
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="branch.text_lor_find.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="branch.text_lor_find.info"></a>
            Description
          </h6></div></div></div><p>This test inserts a number of values with keys from an
          arbitrary text ([ wickland96thirty ]) into
              performance/ext/pb_ds/tree_text_lor_find_timing.cc
            </code>
          </p><p>The test checks the effect of different underlying
-         data structures in a locality-of-reference setting.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="branch.text_lor_find.results"/>
+         data structures in a locality-of-reference setting.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="branch.text_lor_find.results"></a>
            Results
          </h6></div></div></div><p>The graphic immediately below shows the results for the
          native tree type and several other tree types.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_tree_text_lor_find.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_tree_text_lor_find.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_map
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::map</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    splay_tree_map
-                 </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">splay_tree_tag</code>
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    rb_tree_map
-                 </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rb_tree_tag</code>
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    ov_tree_map
-                 </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">ov_tree_tag</code>
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    pat_trie_map
-                 </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">pat_trie_tag</code>
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="branch.text_lor_find.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="branch.text_lor_find.observations"></a>
            Observations
          </h6></div></div></div><p>For this setting, an ordered-vector tree
          (<code class="classname">tree</code> with <code class="classname">Tag</code>
          tree all share approximately the same performance.</p><p>A splay tree (<code class="classname">tree</code>
          with <code class="classname">Tag</code> = <code class="classname">splay_tree_tag</code>) does
          much better, since each (successful) find "bubbles" the
-         corresponding node to the root of the tree.</p></div></div><div class="section" title="split and join"><div class="titlepage"><div><div><h5 class="title"><a id="performance.branch.split_join"/>
+         corresponding node to the root of the tree.</p></div></div><div class="section" title="split and join"><div class="titlepage"><div><div><h5 class="title"><a name="performance.branch.split_join"></a>
          <code class="function">split</code> and <code class="function">join</code>
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="branch.split_join.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="branch.split_join.info"></a>
            Description
          </h6></div></div></div><p>This test a container, inserts into a number of values, splits
          the container at the median, and joins the two containers. (If the
          implication, this test checks the most efficient way to erase a
          sub-sequence from a tree-like-based container, since this can
          always be performed by a small sequence of splits and joins.
-         </p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="branch.split_join.results"/>
+         </p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="branch.split_join.results"></a>
            Results
          </h6></div></div></div><p>The graphic immediately below shows the results for the
          native tree type and several other tree types.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_tree_split_join.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_tree_split_join.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_set
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::set</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    splay_tree_set
-                 </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">splay_tree_tag</code>
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    rb_tree_set
-                 </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rb_tree_tag</code>
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    ov_tree_set
-                 </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">ov_tree_tag</code>
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    pat_trie_map
-                 </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">pat_trie_tag</code>
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="branch.split_join.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="branch.split_join.observations"></a>
            Observations
          </h6></div></div></div><p>In this test, the native red-black trees must be split and
          joined externally, through a sequence of <code class="function">erase</code> and
          via <code class="classname">container_traits</code>).</p><p>It is important to note that <code class="function">split</code> and
          <code class="function">join</code> are not esoteric methods - they are the most
          efficient means of erasing a contiguous range of values from a
-         tree based container.</p></div></div><div class="section" title="Order-Statistics"><div class="titlepage"><div><div><h5 class="title"><a id="performance.branch.order_statistics"/>
+         tree based container.</p></div></div><div class="section" title="Order-Statistics"><div class="titlepage"><div><div><h5 class="title"><a name="performance.branch.order_statistics"></a>
          Order-Statistics
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="branch.order_statistics.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="branch.order_statistics.info"></a>
            Description
          </h6></div></div></div><p>This test creates a container, inserts random integers into the
          the container, and then checks the order-statistics of the
              performance/ext/pb_ds/tree_order_statistics_timing.cc
            </code>
          </p><p>The test checks the performance difference of policies based
-         on node-invariant as opposed to a external functions.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="branch.order_statistics.results"/>
+         on node-invariant as opposed to a external functions.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="branch.order_statistics.results"></a>
            Results
          </h6></div></div></div><p>The graphic immediately below shows the results for the
          native tree type and several other tree types.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_tree_order_statistics.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_tree_order_statistics.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_set
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::set</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    splay_tree_ost_set
-                 </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">splay_tree_tag</code>
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">tree_order_statistics_node_update</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    rb_tree_ost_set
-                 </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rb_tree_tag</code>
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">tree_order_statistics_node_update</code>
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="branch.order_statistics.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="branch.order_statistics.observations"></a>
            Observations
          </h6></div></div></div><p>In this test, the native red-black tree can support
          order-statistics queries only externally, by performing a
          tree (<code class="classname">tree</code>
          with <code class="classname">Tag =</code> <code class="classname">rb_tree_tag</code> ) is
          logarithmic in the number of elements. Consequently, the splay
-         tree has worse performance than the red-black tree.</p></div></div></div><div class="section" title="Multimap"><div class="titlepage"><div><div><h4 class="title"><a id="performance.multimap"/>Multimap</h4></div></div></div><p/><div class="section" title="Text find with Small Secondary-to-Primary Key Ratios"><div class="titlepage"><div><div><h5 class="title"><a id="performance.multimap.text_find_small"/>
+         tree has worse performance than the red-black tree.</p></div></div></div><div class="section" title="Multimap"><div class="titlepage"><div><div><h4 class="title"><a name="performance.multimap"></a>Multimap</h4></div></div></div><p></p><div class="section" title="Text find with Small Secondary-to-Primary Key Ratios"><div class="titlepage"><div><div><h5 class="title"><a name="performance.multimap.text_find_small"></a>
          Text <code class="function">find</code> with Small Secondary-to-Primary Key Ratios 
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_find_small.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="multimap.text_find_small.info"></a>
            Description
          </h6></div></div></div><p>This test inserts a number of pairs into a container. The
          first item of each pair is a string from an arbitrary text
              performance/ext/pb_ds/multimap_text_find_timing_small.cc
            </code>
          </p><p>The test checks the find-time scalability of different
-         "multimap" designs.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_find_small.results"/>
+         "multimap" designs.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="multimap.text_find_small.results"></a>
            Results
          </h6></div></div></div><p>The graphic below show the results for "multimaps" which
          use a tree-based container for primary keys.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_find_small_s2p_tree.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_multimap_text_find_small_s2p_tree.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"><col align="left" class="c4"><col align="left" class="c5"><col align="left" class="c6"><col align="left" class="c7"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    n_mmap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::multimap</code>
-                 </td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="6" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_lu_mtf_set
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rb_tree_tag</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Mapped</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">list_update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Update_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">lu_move_to_front_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
-                 </td></tr><tr><td rowspan="5" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="5" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rb_tree_tag</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">Mapped</code>
-                 </td><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
                  </td></tr></tbody></table></div><p>The graphic below show the results for "multimaps" which
          use a hash-based container for primary keys.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_find_small_s2p_hash.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_multimap_text_find_small_s2p_hash.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"><col align="left" class="c4"><col align="left" class="c5"><col align="left" class="c6"><col align="left" class="c7"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    n_hash_mmap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::tr1::unordered_multimap</code>
-                 </td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="6" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_lu_mtf_set
-                 </td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="4" align="left" valign="top">
                    <code class="classname">
                      cc_hash_table
                    </code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Mapped</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">list_update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Update_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">lu_move_to_front_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
-                 </td></tr><tr><td rowspan="6" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="6" align="left" valign="top">
                    <code class="classname">
                      cc_hash_table
                    </code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">Mapped</code>
-                 </td><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_find_small.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="multimap.text_find_small.observations"></a>
            Observations
          </h6></div></div></div><p>See Observations::Mapping-Semantics
-         Considerations.</p></div></div><div class="section" title="Text find with Large Secondary-to-Primary Key Ratios"><div class="titlepage"><div><div><h5 class="title"><a id="performance.multimap.text_find_large"/>
+         Considerations.</p></div></div><div class="section" title="Text find with Large Secondary-to-Primary Key Ratios"><div class="titlepage"><div><div><h5 class="title"><a name="performance.multimap.text_find_large"></a>
          Text <code class="function">find</code> with Large Secondary-to-Primary Key Ratios 
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_find_large.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="multimap.text_find_large.info"></a>
            Description
          </h6></div></div></div><p>This test inserts a number of pairs into a container. The
          first item of each pair is a string from an arbitrary text
              performance/ext/pb_ds/multimap_text_find_timing_large.cc
            </code>
          </p><p>The test checks the find-time scalability of different
-         "multimap" designs.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_find_large.results"/>
+         "multimap" designs.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="multimap.text_find_large.results"></a>
            Results
          </h6></div></div></div><p>The graphic below show the results for "multimaps" which
          use a tree-based container for primary keys.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_find_large_s2p_tree.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_multimap_text_find_large_s2p_tree.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"><col align="left" class="c4"><col align="left" class="c5"><col align="left" class="c6"><col align="left" class="c7"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    n_mmap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::multimap</code>
-                 </td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="6" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_lu_mtf_set
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rb_tree_tag</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Mapped</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">list_update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Update_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">lu_move_to_front_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
-                 </td></tr><tr><td rowspan="5" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="5" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rb_tree_tag</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">Mapped</code>
-                 </td><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
                  </td></tr></tbody></table></div><p>The graphic below show the results for "multimaps" which
          use a hash-based container for primary keys.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_find_large_s2p_hash.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_multimap_text_find_large_s2p_hash.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"><col align="left" class="c4"><col align="left" class="c5"><col align="left" class="c6"><col align="left" class="c7"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    n_hash_mmap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::tr1::unordered_multimap</code>
-                 </td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="6" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_lu_mtf_set
-                 </td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="4" align="left" valign="top">
                    <code class="classname">
                      cc_hash_table
                    </code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Mapped</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">list_update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Update_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">lu_move_to_front_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
-                 </td></tr><tr><td rowspan="6" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="6" align="left" valign="top">
                    <code class="classname">
                      cc_hash_table
                    </code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">Mapped</code>
-                 </td><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_find_large.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="multimap.text_find_large.observations"></a>
            Observations
          </h6></div></div></div><p>See Observations::Mapping-Semantics
-         Considerations.</p></div></div><div class="section" title="Text insert with Small Secondary-to-Primary Key Ratios"><div class="titlepage"><div><div><h5 class="title"><a id="performance.multimap.text_insert_small"/>
+         Considerations.</p></div></div><div class="section" title="Text insert with Small Secondary-to-Primary Key Ratios"><div class="titlepage"><div><div><h5 class="title"><a name="performance.multimap.text_insert_small"></a>
          Text <code class="function">insert</code> with Small
          Secondary-to-Primary Key Ratios
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_small.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="multimap.text_insert_small.info"></a>
            Description
          </h6></div></div></div><p>This test inserts a number of pairs into a container. The
          first item of each pair is a string from an arbitrary text
              performance/ext/pb_ds/multimap_text_insert_timing_small.cc
            </code>
          </p><p>The test checks the insert-time scalability of different
-         "multimap" designs.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_small.results"/>
+         "multimap" designs.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="multimap.text_insert_small.results"></a>
            Results
          </h6></div></div></div><p>The graphic below show the results for "multimaps" which
          use a tree-based container for primary keys.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_insert_small_s2p_tree.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_multimap_text_insert_small_s2p_tree.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"><col align="left" class="c4"><col align="left" class="c5"><col align="left" class="c6"><col align="left" class="c7"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    n_mmap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::multimap</code>
-                 </td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="6" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_lu_mtf_set
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rb_tree_tag</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Mapped</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">list_update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Update_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">lu_move_to_front_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
-                 </td></tr><tr><td rowspan="5" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="5" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rb_tree_tag</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">Mapped</code>
-                 </td><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
                  </td></tr></tbody></table></div><p>The graphic below show the results for "multimaps" which
          use a hash-based container for primary keys.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_find_small_s2p_hash.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_multimap_text_find_small_s2p_hash.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"><col align="left" class="c4"><col align="left" class="c5"><col align="left" class="c6"><col align="left" class="c7"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    n_hash_mmap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::tr1::unordered_multimap</code>
-                 </td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="6" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_lu_mtf_set
-                 </td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="4" align="left" valign="top">
                    <code class="classname">
                      cc_hash_table
                    </code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Mapped</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">list_update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Update_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">lu_move_to_front_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
-                 </td></tr><tr><td rowspan="6" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="6" align="left" valign="top">
                    <code class="classname">
                      cc_hash_table
                    </code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">Mapped</code>
-                 </td><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_small.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="multimap.text_insert_small.observations"></a>
            Observations
          </h6></div></div></div><p>See Observations::Mapping-Semantics
-         Considerations.</p></div></div><div class="section" title="Text insert with Small Secondary-to-Primary Key Ratios"><div class="titlepage"><div><div><h5 class="title"><a id="performance.multimap.text_insert_large"/>
+         Considerations.</p></div></div><div class="section" title="Text insert with Small Secondary-to-Primary Key Ratios"><div class="titlepage"><div><div><h5 class="title"><a name="performance.multimap.text_insert_large"></a>
          Text <code class="function">insert</code> with Small
          Secondary-to-Primary Key Ratios
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_large.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="multimap.text_insert_large.info"></a>
            Description
          </h6></div></div></div><p>This test inserts a number of pairs into a container. The
          first item of each pair is a string from an arbitrary text
              performance/ext/pb_ds/multimap_text_insert_timing_large.cc
            </code>
          </p><p>The test checks the insert-time scalability of different
-         "multimap" designs.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_large.results"/>
+         "multimap" designs.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="multimap.text_insert_large.results"></a>
            Results
          </h6></div></div></div><p>The graphic below show the results for "multimaps" which
          use a tree-based container for primary keys.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_insert_large_s2p_tree.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_multimap_text_insert_large_s2p_tree.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"><col align="left" class="c4"><col align="left" class="c5"><col align="left" class="c6"><col align="left" class="c7"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    n_mmap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::multimap</code>
-                 </td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="6" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_lu_mtf_set
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rb_tree_tag</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Mapped</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">list_update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Update_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">lu_move_to_front_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
-                 </td></tr><tr><td rowspan="5" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="5" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rb_tree_tag</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">Mapped</code>
-                 </td><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
                  </td></tr></tbody></table></div><p>The graphic below show the results for "multimaps" which
          use a hash-based container for primary keys.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_find_large_s2p_hash.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_multimap_text_find_large_s2p_hash.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"><col align="left" class="c4"><col align="left" class="c5"><col align="left" class="c6"><col align="left" class="c7"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    n_hash_mmap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::tr1::unordered_multimap</code>
-                 </td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="6" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_lu_mtf_set
-                 </td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="4" align="left" valign="top">
                    <code class="classname">
                      cc_hash_table
                    </code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Mapped</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">list_update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Update_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">lu_move_to_front_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
-                 </td></tr><tr><td rowspan="6" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="6" align="left" valign="top">
                    <code class="classname">
                      cc_hash_table
                    </code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">Mapped</code>
-                 </td><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_large.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="multimap.text_insert_large.observations"></a>
            Observations
          </h6></div></div></div><p>See Observations::Mapping-Semantics
-         Considerations.</p></div></div><div class="section" title="Text insert with Small Secondary-to-Primary Key Ratios Memory Use"><div class="titlepage"><div><div><h5 class="title"><a id="performance.multimap.text_insert_mem_small"/>
+         Considerations.</p></div></div><div class="section" title="Text insert with Small Secondary-to-Primary Key Ratios Memory Use"><div class="titlepage"><div><div><h5 class="title"><a name="performance.multimap.text_insert_mem_small"></a>
          Text <code class="function">insert</code> with Small
          Secondary-to-Primary Key Ratios Memory Use
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_mem_small.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="multimap.text_insert_mem_small.info"></a>
            Description
          </h6></div></div></div><p>This test inserts a number of pairs into a container. The
          first item of each pair is a string from an arbitrary text
              performance/ext/pb_ds/multimap_text_insert_mem_usage_small.cc
            </code>
          </p><p>The test checks the memory scalability of different
-         "multimap" designs.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_mem_small.results"/>
+         "multimap" designs.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="multimap.text_insert_mem_small.results"></a>
            Results
          </h6></div></div></div><p>The graphic below show the results for "multimaps" which
          use a tree-based container for primary keys.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_insert_mem_small_s2p_tree.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_multimap_text_insert_mem_small_s2p_tree.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"><col align="left" class="c4"><col align="left" class="c5"><col align="left" class="c6"><col align="left" class="c7"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    n_mmap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::multimap</code>
-                 </td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="6" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_lu_mtf_set
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rb_tree_tag</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Mapped</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">list_update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Update_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">lu_move_to_front_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
-                 </td></tr><tr><td rowspan="5" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="5" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rb_tree_tag</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">Mapped</code>
-                 </td><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
                  </td></tr></tbody></table></div><p>The graphic below show the results for "multimaps" which
          use a hash-based container for primary keys.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_find_large_s2p_hash.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_multimap_text_find_large_s2p_hash.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"><col align="left" class="c4"><col align="left" class="c5"><col align="left" class="c6"><col align="left" class="c7"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    n_hash_mmap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::tr1::unordered_multimap</code>
-                 </td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="6" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_lu_mtf_set
-                 </td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="4" align="left" valign="top">
                    <code class="classname">
                      cc_hash_table
                    </code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Mapped</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">list_update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Update_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">lu_move_to_front_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
-                 </td></tr><tr><td rowspan="6" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="6" align="left" valign="top">
                    <code class="classname">
                      cc_hash_table
                    </code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">Mapped</code>
-                 </td><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_mem_small.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="multimap.text_insert_mem_small.observations"></a>
            Observations
          </h6></div></div></div><p>See Observations::Mapping-Semantics
-         Considerations.</p></div></div><div class="section" title="Text insert with Small Secondary-to-Primary Key Ratios Memory Use"><div class="titlepage"><div><div><h5 class="title"><a id="performance.multimap.text_insert_mem_large"/>
+         Considerations.</p></div></div><div class="section" title="Text insert with Small Secondary-to-Primary Key Ratios Memory Use"><div class="titlepage"><div><div><h5 class="title"><a name="performance.multimap.text_insert_mem_large"></a>
          Text <code class="function">insert</code> with Small
          Secondary-to-Primary Key Ratios Memory Use
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_mem_large.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="multimap.text_insert_mem_large.info"></a>
            Description
          </h6></div></div></div><p>This test inserts a number of pairs into a container. The
          first item of each pair is a string from an arbitrary text
              performance/ext/pb_ds/multimap_text_insert_mem_usage_large.cc
            </code>
          </p><p>The test checks the memory scalability of different
-         "multimap" designs.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_mem_large.results"/>
+         "multimap" designs.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="multimap.text_insert_mem_large.results"></a>
            Results
          </h6></div></div></div><p>The graphic below show the results for "multimaps" which
          use a tree-based container for primary keys.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_insert_mem_large_s2p_tree.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_multimap_text_insert_mem_large_s2p_tree.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"><col align="left" class="c4"><col align="left" class="c5"><col align="left" class="c6"><col align="left" class="c7"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    n_mmap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::multimap</code>
-                 </td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="6" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_lu_mtf_set
-                 </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rb_tree_tag</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Mapped</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">list_update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Update_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">lu_move_to_front_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
-                 </td></tr><tr><td rowspan="5" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="5" align="left" valign="top">
                    <code class="classname">tree</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rb_tree_tag</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Node_Update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">null_node_update</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">Mapped</code>
-                 </td><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
                  </td></tr></tbody></table></div><p>The graphic below show the results for "multimaps" which
          use a hash-based container for primary keys.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_multimap_text_find_large_s2p_hash.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_multimap_text_find_large_s2p_hash.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/><col style="text-align: left" class="c7"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"><col align="left" class="c4"><col align="left" class="c5"><col align="left" class="c6"><col align="left" class="c7"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    n_hash_mmap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::tr1::unordered_multimap</code>
-                 </td><td colspan="6" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="6" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_lu_mtf_set
-                 </td></tr><tr><td rowspan="4" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="4" align="left" valign="top">
                    <code class="classname">
                      cc_hash_table
                    </code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left">
                    <code class="classname">Mapped</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">list_update</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Update_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">lu_move_to_front_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr style="background-color: #B0B0B0"><td colspan="7" style="text-align: left">
+                 </td><td colspan="2" align="left"> </td></tr><tr bgcolor="#B0B0B0"><td colspan="7" align="left">
                    rb_tree_mmap_cc_hash_mask_exp_1div2_nsth_set
-                 </td></tr><tr><td rowspan="6" style="text-align: left" valign="top">
+                 </td></tr><tr><td rowspan="6" align="left" valign="top">
                    <code class="classname">
                      cc_hash_table
                    </code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="4" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="4" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="3" align="left" valign="top">
                    <code class="classname">Mapped</code>
-                 </td><td rowspan="3" style="text-align: left" valign="top">
+                 </td><td rowspan="3" align="left" valign="top">
                    <code class="classname">cc_hash_table</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Comb_Hash_Fn</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">direct_mask_range_hashing</code>
-                 </td><td colspan="2" style="text-align: left"> </td></tr><tr><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td colspan="2" align="left"> </td></tr><tr><td rowspan="2" align="left" valign="top">
                    <code class="classname">Resize_Policy</code>
-                 </td><td rowspan="2" style="text-align: left" valign="top">
+                 </td><td rowspan="2" align="left" valign="top">
                    <code class="classname">hash_standard_resize_policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Size_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_exponential_size_policy</code>
-                 </td></tr><tr><td style="text-align: left" valign="top">
+                 </td></tr><tr><td align="left" valign="top">
                    <code class="classname">Trigger_Policy</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">hash_load_check_resize_trigger</code> with
                    α<sub>min</sub> = 1/8 and α<sub>max</sub> = 1/2
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="multimap.text_insert_mem_large.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="multimap.text_insert_mem_large.observations"></a>
            Observations
          </h6></div></div></div><p>See Observations::Mapping-Semantics
-         Considerations.</p></div></div></div><div class="section" title="Priority Queue"><div class="titlepage"><div><div><h4 class="title"><a id="performance.priority_queue"/>Priority Queue</h4></div></div></div><div class="section" title="Text push"><div class="titlepage"><div><div><h5 class="title"><a id="performance.priority_queue.text_push"/>
+         Considerations.</p></div></div></div><div class="section" title="Priority Queue"><div class="titlepage"><div><div><h4 class="title"><a name="performance.priority_queue"></a>Priority Queue</h4></div></div></div><div class="section" title="Text push"><div class="titlepage"><div><div><h5 class="title"><a name="performance.priority_queue.text_push"></a>
          Text <code class="function">push</code>
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_push.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.text_push.info"></a>
            Description
          </h6></div></div></div><p>This test inserts a number of values with keys from an
          arbitrary text ([ wickland96thirty ]) into
            </code>
          </p><p>The test checks the effect of different underlying data
          structures.
-         </p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_push.results"/>
+         </p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.text_push.results"></a>
            Results
          </h6></div></div></div><p>The two graphics below show the results for the native
          priority_queues and this library's priority_queues.
          native priority_queue type instantiated with different underlying
          container types versus several different versions of library's
          priority_queues.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_priority_queue_text_push.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_priority_queue_text_push.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_pq_vector
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Sequence</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">std::vector</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_pq_deque
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Sequence</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">std::deque</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    binary_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">binary_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    binomial_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">binomial_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    rc_binomial_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rc_binomial_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    thin_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">thin_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    pairing_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">pairing_heap_tag</code>
                  </td></tr></tbody></table></div><p>The graphic below shows the results for the binary-heap
          based native priority queues and this library's pairing-heap
          priority_queue data structures.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_pairing_priority_queue_text_push.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_pairing_priority_queue_text_push.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_pq_vector
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Sequence</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">std::vector</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_pq_deque
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Sequence</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">std::deque</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    thin_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">thin_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    pairing_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">pairing_heap_tag</code>
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_push.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.text_push.observations"></a>
            Observations
          </h6></div></div></div><p>Pairing heaps (<code class="classname">priority_queue</code> with
          <code class="classname">Tag</code> = <code class="classname">pairing_heap_tag</code>)
          operation, and the deque implementation is possibly hampered by
          its need to manipulate a relatively-complex type (deques
          support a O(1) <code class="function">push_front</code>, even though it is
-         not used by <code class="classname">std::priority_queue</code>.)</p></div></div><div class="section" title="Text push and pop"><div class="titlepage"><div><div><h5 class="title"><a id="performance.priority_queue.text_push_pop"/>
+         not used by <code class="classname">std::priority_queue</code>.)</p></div></div><div class="section" title="Text push and pop"><div class="titlepage"><div><div><h5 class="title"><a name="performance.priority_queue.text_push_pop"></a>
          Text <code class="function">push</code> and <code class="function">pop</code>
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_push_pop.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.text_push_pop.info"></a>
            Description
          </h6></div></div></div><p>This test inserts a number of values with keys from an
          arbitrary text ([ wickland96thirty ]) into
            </code>
          </p><p>The test checks the effect of different underlying data
          structures.
-         </p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_push_pop.results"/>
+         </p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.text_push_pop.results"></a>
            Results
          </h6></div></div></div><p>The two graphics below show the results for the native
          priority_queues and this library's priority_queues.
          native priority_queue type instantiated with different underlying
          container types versus several different versions of library's
          priority_queues.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_priority_queue_text_push_pop.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_priority_queue_text_push_pop.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_pq_vector
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Sequence</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">std::vector</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_pq_deque
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Sequence</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">std::deque</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    binary_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">binary_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    binomial_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">binomial_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    rc_binomial_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rc_binomial_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    thin_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">thin_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    pairing_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">pairing_heap_tag</code>
                  </td></tr></tbody></table></div><p>The graphic below shows the results for the native priority
          queues and this library's pairing-heap priority_queue data
          structures.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_pairing_priority_queue_text_push_pop.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_pairing_priority_queue_text_push_pop.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_pq_vector
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::priority_queue</code> adapting <code class="classname">std::vector</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Sequence</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">std::vector</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_pq_deque
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Sequence</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">std::deque</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    pairing_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">pairing_heap_tag</code>
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_push_pop.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.text_push_pop.observations"></a>
            Observations
          </h6></div></div></div><p>These results are very similar to Priority Queue Text
          <code class="function">push</code> Timing Test. As stated there, pairing heaps
          of <code class="function">push</code> operations, pairing heaps are better
          in this case. See Priority Queue Random
          Integer <code class="function">push</code> and <code class="function">pop</code>
-         Timing Test for a case which is different.</p></div></div><div class="section" title="Integer push"><div class="titlepage"><div><div><h5 class="title"><a id="performance.priority_queue.int_push"/>
+         Timing Test for a case which is different.</p></div></div><div class="section" title="Integer push"><div class="titlepage"><div><div><h5 class="title"><a name="performance.priority_queue.int_push"></a>
          Integer <code class="function">push</code>
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.int_push.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.int_push.info"></a>
            Description
          </h6></div></div></div><p>This test inserts a number of values with integer keys
          into a container using <code class="function">push</code>. It
            </code>
          </p><p>The test checks the effect of different underlying data
          structures.
-         </p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.int_push.results"/>
+         </p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.int_push.results"></a>
            Results
          </h6></div></div></div><p>The two graphics below show the results for the native
          priority_queues and this library's priority_queues.
          native priority_queue type instantiated with different underlying
          container types versus several different versions of library's
          priority_queues.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_priority_queue_int_push.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_priority_queue_int_push.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_pq_vector
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Sequence</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">std::vector</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_pq_deque
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Sequence</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">std::deque</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    binary_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">binary_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    binomial_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">binomial_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    rc_binomial_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rc_binomial_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    thin_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">thin_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    pairing_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">pairing_heap_tag</code>
                  </td></tr></tbody></table></div><p>The graphic below shows the results for the binary-heap
          based native priority queues and this library's
          priority_queue data structures.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_binary_priority_queue_int_push.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_binary_priority_queue_int_push.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_pq_vector
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::priority_queue</code> adapting <code class="classname">std::vector</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Sequence</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">std::vector</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_pq_deque
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Sequence</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">std::deque</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    binary_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">binary_heap_tag</code>
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.int_push.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.int_push.observations"></a>
            Observations
          </h6></div></div></div><p>Binary heaps are the most suited for sequences of
          <code class="function">push</code> and <code class="function">pop</code> operations of primitive types
          such types in arrays, they outperform even pairing heaps. (See
          Priority
          Queue Text <code class="function">push</code> Timing Test for the case of
-         non-primitive types.)</p></div></div><div class="section" title="Integer push"><div class="titlepage"><div><div><h5 class="title"><a id="performance.priority_queue.int_push_pop"/>
+         non-primitive types.)</p></div></div><div class="section" title="Integer push"><div class="titlepage"><div><div><h5 class="title"><a name="performance.priority_queue.int_push_pop"></a>
          Integer <code class="function">push</code>
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.int_push_pop.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.int_push_pop.info"></a>
            Description
          </h6></div></div></div><p>This test inserts a number of values with integer keys
          into a container using <code class="function">push</code> , then removes them
            </code>
          </p><p>The test checks the effect of different underlying data
          structures.
-         </p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.int_push_pop.results"/>
+         </p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.int_push_pop.results"></a>
            Results
          </h6></div></div></div><p>The graphic immediately below shows the results for the
          native priority_queue type instantiated with different underlying
          container types versus several different versions of library's
          priority_queues.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_priority_queue_int_push_pop.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_priority_queue_int_push_pop.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_pq_vector
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Sequence</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">std::vector</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_pq_deque
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Sequence</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">std::deque</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    binary_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">binary_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    binomial_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">binomial_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    rc_binomial_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rc_binomial_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    thin_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">thin_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    pairing_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">pairing_heap_tag</code>
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.int_push_pop.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.int_push_pop.observations"></a>
            Observations
          </h6></div></div></div><p>Binary heaps are the most suited for sequences of
          <code class="function">push</code> and <code class="function">pop</code> operations of primitive types
          types.)</p><p>At first glance it seems that the standard's vector-based
          priority queue is approximately on par with this
          library's corresponding priority queue. There are two
-         differences however:</p><div class="orderedlist"><ol class="orderedlist"><li class="listitem"><p>The standard's priority queue does not downsize the underlying
+         differences however:</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><p>The standard's priority queue does not downsize the underlying
            vector (or deque) as the priority queue becomes smaller
            (see Priority Queue
            Text <code class="function">pop</code> Memory Use Test). It is therefore
            the number of
            <code class="function">pop</code> operations is at most that of <code class="function">push</code>
            operations, the test here is the "best" for the standard's
-           priority queue.</p></li></ol></div></div></div><div class="section" title="Text pop Memory Use"><div class="titlepage"><div><div><h5 class="title"><a id="performance.priority_queue.text_pop"/>
+           priority queue.</p></li></ol></div></div></div><div class="section" title="Text pop Memory Use"><div class="titlepage"><div><div><h5 class="title"><a name="performance.priority_queue.text_pop"></a>
          Text <code class="function">pop</code> Memory Use
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_pop.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.text_pop.info"></a>
            Description
          </h6></div></div></div><p>This test inserts a number of values with keys from an
          arbitrary text ([ wickland96thirty ]) into
            </code>
          </p><p>The test checks the effect of different underlying data
          structures.
-         </p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_pop.results"/>
+         </p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.text_pop.results"></a>
            Results
          </h6></div></div></div><p>The graphic immediately below shows the results for the
          native priority_queue type instantiated with different underlying
          container types versus several different versions of library's
          priority_queues.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_priority_queue_text_pop_mem.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_priority_queue_text_pop_mem.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_pq_vector
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Sequence</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">std::vector</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_pq_deque
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Sequence</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">std::deque</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    binary_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">binary_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    binomial_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">binomial_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    rc_binomial_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rc_binomial_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    thin_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">thin_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    pairing_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">pairing_heap_tag</code>
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_pop.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.text_pop.observations"></a>
            Observations
          </h6></div></div></div><p>The priority queue implementations (excluding the standard's) use
          memory proportionally to the number of values they hold:
          impede performance compared to the standard's priority
          queues.</p><p>See Hash-Based Erase
          Memory Use Test for a similar phenomenon regarding priority
-         queues.</p></div></div><div class="section" title="Text join"><div class="titlepage"><div><div><h5 class="title"><a id="performance.priority_queue.text_join"/>
+         queues.</p></div></div><div class="section" title="Text join"><div class="titlepage"><div><div><h5 class="title"><a name="performance.priority_queue.text_join"></a>
          Text <code class="function">join</code>
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_join.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.text_join.info"></a>
            Description
          </h6></div></div></div><p>This test inserts a number of values with keys from an
          arbitrary text ([ wickland96thirty ]) into
            </code>
          </p><p>The test checks the effect of different underlying data
          structures.
-         </p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_join.results"/>
+         </p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.text_join.results"></a>
            Results
          </h6></div></div></div><p>The graphic immediately below shows the results for the
          native priority_queue type instantiated with different underlying
          container types versus several different versions of library's
          priority_queues.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_priority_queue_text_join.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_priority_queue_text_join.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_pq_vector
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Sequence</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">std::vector</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_pq_deque
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Sequence</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">std::deque</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    binary_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">binary_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    binomial_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">binomial_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    rc_binomial_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rc_binomial_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    thin_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">thin_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    pairing_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">pairing_heap_tag</code>
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_join.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.text_join.observations"></a>
            Observations
          </h6></div></div></div><p>In this test the node-based heaps perform <code class="function">join</code> in
          either logarithmic or constant time. The binary heap requires
          and <code class="function">size()</code> (since they are enough to expose
          the underlying array), but this is impossible for
          a <code class="classname">std::deque</code>-based standard priority queue.
-         Without heapify, the cost is super-linear.</p></div></div><div class="section" title="Text modify Up"><div class="titlepage"><div><div><h5 class="title"><a id="performance.priority_queue.text_modify_up"/>
+         Without heapify, the cost is super-linear.</p></div></div><div class="section" title="Text modify Up"><div class="titlepage"><div><div><h5 class="title"><a name="performance.priority_queue.text_modify_up"></a>
          Text <code class="function">modify</code> Up
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_modify_up.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.text_modify_up.info"></a>
            Description
          </h6></div></div></div><p>This test inserts a number of values with keys from an
          arbitrary text ([ wickland96thirty ]) into
          arbitrary value larger (in the sense of the priority queue's
          comparison functor) corresponds to decrease-key in standard graph
          algorithms [clrs2001].
-         </p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_modify_up.results"/>
+         </p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.text_modify_up.results"></a>
            Results
          </h6></div></div></div><p>The two graphics below show the results for the native
          priority_queues and this library's priority_queues.
          native priority_queue type instantiated with different underlying
          container types versus several different versions of library's
          priority_queues.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_priority_queue_text_modify_up.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_priority_queue_text_modify_up.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_pq_vector
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Sequence</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">std::vector</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_pq_deque
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Sequence</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">std::deque</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    binary_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">binary_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    binomial_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">binomial_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    rc_binomial_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rc_binomial_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    thin_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">thin_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    pairing_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">pairing_heap_tag</code>
                  </td></tr></tbody></table></div><p>The graphic below shows the results for the
          native priority queues and this library's pairing and thin heap
          priority_queue data structures.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_pairing_priority_queue_text_modify_up_thin.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_pairing_priority_queue_text_modify_up_thin.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    thin_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">thin_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    pairing_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">pairing_heap_tag</code>
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_modify_up.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.text_modify_up.observations"></a>
            Observations
          </h6></div></div></div><p>As noted above, increasing an arbitrary value (in the sense of
          the priority queue's comparison functor) is very common in
          finding the appropriate value, then use the range-type iterator
          for the <code class="function">modify</code> operation.</p><p>The explanation for the standard's priority queues' performance
          is similar to that in Priority Queue Text
-         <code class="function">join</code> Timing Test.</p></div></div><div class="section" title="Text modify Down"><div class="titlepage"><div><div><h5 class="title"><a id="performance.priority_queue.text_modify_down"/>
+         <code class="function">join</code> Timing Test.</p></div></div><div class="section" title="Text modify Down"><div class="titlepage"><div><div><h5 class="title"><a name="performance.priority_queue.text_modify_down"></a>
          Text <code class="function">modify</code> Down
-       </h5></div></div></div><p/><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_modify_down.info"/>
+       </h5></div></div></div><p></p><div class="section" title="Description"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.text_modify_down.info"></a>
            Description
          </h6></div></div></div><p>This test inserts a number of values with keys from an
          arbitrary text ([ wickland96thirty ]) into
              performance/ext/pb_ds/priority_queue_text_modify_down_timing.cc
            </code>
          </p><p>The main purpose of this test is to contrast Priority Queue
-         Text <code class="classname">modify</code> Up Timing Test.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_modify_down.results"/>
+         Text <code class="classname">modify</code> Up Timing Test.</p></div><div class="section" title="Results"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.text_modify_down.results"></a>
            Results
          </h6></div></div></div><p>The two graphics below show the results for the native
          priority_queues and this library's priority_queues.
          native priority_queue type instantiated with different underlying
          container types versus several different versions of library's
          priority_queues.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_priority_queue_text_modify_down.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_priority_queue_text_modify_down.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_pq_vector
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Sequence</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">std::vector</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    n_pq_deque
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">std::priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Sequence</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">std::deque</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    binary_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">binary_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    binomial_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">binomial_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    rc_binomial_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">rc_binomial_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    thin_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">thin_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    pairing_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">pairing_heap_tag</code>
                  </td></tr></tbody></table></div><p>The graphic below shows the results for the
          native priority queues and this library's pairing and thin heap
          priority_queue data structures.
-         </p><div class="informalfigure"><div class="mediaobject" style="text-align: center"><img src="../images/pbds_pairing_priority_queue_text_modify_down_thin.png" style="text-align: middle"/></div></div><p>
+         </p><div class="informalfigure"><div class="mediaobject" align="center"><img src="../images/pbds_pairing_priority_queue_text_modify_down_thin.png" align="middle"></div></div><p>
            The abbreviated names in the legend of the graphic above are
            instantiated with the types in the following table.
-         </p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/></colgroup><thead><tr><th style="text-align: left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th style="text-align: left"><span class="emphasis"><em>Parameter</em></span></th><th style="text-align: left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+         </p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"></colgroup><thead><tr><th align="left"><span class="emphasis"><em>Name/Instantiating Type</em></span></th><th align="left"><span class="emphasis"><em>Parameter</em></span></th><th align="left"><span class="emphasis"><em>Details</em></span></th></tr></thead><tbody><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    thin_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">thin_heap_tag</code>
-                 </td></tr><tr style="background-color: #B0B0B0"><td colspan="3" style="text-align: left">
+                 </td></tr><tr bgcolor="#B0B0B0"><td colspan="3" align="left">
                    pairing_heap
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">Tag</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    <code class="classname">pairing_heap_tag</code>
-                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a id="priority_queue.text_modify_down.observations"/>
+                 </td></tr></tbody></table></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h6 class="title"><a name="priority_queue.text_modify_down.observations"></a>
            Observations
          </h6></div></div></div><p>Most points in these results are similar to Priority Queue
          Text <code class="function">modify</code> Up Timing Test.</p><p>It is interesting to note, however, that as opposed to that
          (in the sense of the priority queue's comparison functor), and
          so Priority Queue
          Text <code class="classname">modify</code> Up Timing Test - is more interesting
-         than this test.</p></div></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h4 class="title"><a id="pbds.test.performance.observations"/>Observations</h4></div></div></div><div class="section" title="Associative"><div class="titlepage"><div><div><h5 class="title"><a id="observations.associative"/>Associative</h5></div></div></div><div class="section" title="Underlying Data-Structure Families"><div class="titlepage"><div><div><h6 class="title"><a id="observations.associative.underlying"/>
+         than this test.</p></div></div></div><div class="section" title="Observations"><div class="titlepage"><div><div><h4 class="title"><a name="pbds.test.performance.observations"></a>Observations</h4></div></div></div><div class="section" title="Associative"><div class="titlepage"><div><div><h5 class="title"><a name="observations.associative"></a>Associative</h5></div></div></div><div class="section" title="Underlying Data-Structure Families"><div class="titlepage"><div><div><h6 class="title"><a name="observations.associative.underlying"></a>
            Underlying Data-Structure Families
          </h6></div></div></div><p>In general, hash-based containers have better timing performance
          than containers based on different underlying-data structures. The
          order-preservation, or the ability to utilize node invariants. If
          memory-use is the major factor, an ordered-vector tree gives
          optimal results (albeit with high modificiation costs), and a
-         list-based container gives reasonable results.</p></div><div class="section" title="Hash-Based Containers"><div class="titlepage"><div><div><h6 class="title"><a id="observations.associative.hash"/>
+         list-based container gives reasonable results.</p></div><div class="section" title="Hash-Based Containers"><div class="titlepage"><div><div><h6 class="title"><a name="observations.associative.hash"></a>
            Hash-Based Containers
          </h6></div></div></div><p>Hash-based containers are typically either collision
          chaining or probing. Collision-chaining
          useful also in multithreaded applications where each thread
          manipulates a hash-based container: in the standard, allocators have
          class-wise semantics (see [meyers96more] - Item 10); a
-         probing container might incur less contention in this case.</p></div><div class="section" title="Hash Policies"><div class="titlepage"><div><div><h6 class="title"><a id="observations.associative.hash_policies"/>
+         probing container might incur less contention in this case.</p></div><div class="section" title="Hash Policies"><div class="titlepage"><div><div><h6 class="title"><a name="observations.associative.hash_policies"></a>
            Hash Policies
          </h6></div></div></div><p>In hash-based containers, the range-hashing scheme seems to
          affect performance more than other considerations. In most
          function.</p><p>An orthogonal consideration is the trigger policy. This
          presents difficult tradeoffs. E.g., different load
          factors in a load-check trigger policy yield a
-         space/amortized-cost tradeoff.</p></div><div class="section" title="Branch-Based Containers"><div class="titlepage"><div><div><h6 class="title"><a id="observations.associative.branch"/>
+         space/amortized-cost tradeoff.</p></div><div class="section" title="Branch-Based Containers"><div class="titlepage"><div><div><h6 class="title"><a name="observations.associative.branch"></a>
            Branch-Based Containers
          </h6></div></div></div><p>In general, there are several families of tree-based
          underlying data structures: balanced node-based trees
          maintaining such trees is higher than that of balanced trees.
          Moderate-fan-out trees might be useful for sequences where each
          element has a limited number of choices, e.g., DNA
-         strings.</p></div><div class="section" title="Mapping-Semantics"><div class="titlepage"><div><div><h6 class="title"><a id="observations.associative.mapping_semantics"/>
+         strings.</p></div><div class="section" title="Mapping-Semantics"><div class="titlepage"><div><div><h6 class="title"><a name="observations.associative.mapping_semantics"></a>
            Mapping-Semantics
          </h6></div></div></div><p>Different mapping semantics were discussed in the introduction and design sections.Here
          the focus will be on the case where a keys can be composed into
          primary keys and secondary keys. (In the case where some keys
          are completely identical, it is trivial that one should use an
          associative container mapping values to size types.) In this
-         case there are (at least) five possibilities:</p><div class="orderedlist"><ol class="orderedlist"><li class="listitem"><p>Use an associative container that allows equivalent-key
+         case there are (at least) five possibilities:</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><p>Use an associative container that allows equivalent-key
            values (such as <code class="classname">std::multimap</code>)</p></li><li class="listitem"><p>Use a unique-key value associative container that maps
            each primary key to some complex associative container of
            secondary keys, say a tree-based or hash-based container.
          but with very high constants; using 1 with a tree-based
          container, the cost is Θ(nlog(mn)). Using 2, 3,
          and 4, the expected cost is Θ(n), but typically
-         with far lower costs than 1. 5 is similar to 1.</p></div></div><div class="section" title="Priority_Queue"><div class="titlepage"><div><div><h5 class="title"><a id="observations.priority_queue"/>Priority_Queue</h5></div></div></div><div class="section" title="Complexity"><div class="titlepage"><div><div><h6 class="title"><a id="observations.priority_queue.complexity"/>Complexity</h6></div></div></div><p>The following table shows the complexities of the different
+         with far lower costs than 1. 5 is similar to 1.</p></div></div><div class="section" title="Priority_Queue"><div class="titlepage"><div><div><h5 class="title"><a name="observations.priority_queue"></a>Priority_Queue</h5></div></div></div><div class="section" title="Complexity"><div class="titlepage"><div><div><h6 class="title"><a name="observations.priority_queue.complexity"></a>Complexity</h6></div></div></div><p>The following table shows the complexities of the different
          underlying data structures in terms of orders of growth. It is
          interesting to note that this table implies something about the
          constants of the operations as well (see Amortized <code class="function">push</code>
-         and <code class="function">pop</code> operations).</p><div class="informaltable"><table border="1"><colgroup><col style="text-align: left" class="c1"/><col style="text-align: left" class="c2"/><col style="text-align: left" class="c3"/><col style="text-align: left" class="c4"/><col style="text-align: left" class="c5"/><col style="text-align: left" class="c6"/></colgroup><thead><tr><th style="text-align: left"> </th><th style="text-align: left"><span class="emphasis"><em><code class="function">push</code></em></span></th><th style="text-align: left"><span class="emphasis"><em><code class="function">pop</code></em></span></th><th style="text-align: left"><span class="emphasis"><em><code class="function">modify</code></em></span></th><th style="text-align: left"><span class="emphasis"><em><code class="function">erase</code></em></span></th><th style="text-align: left"><span class="emphasis"><em><code class="function">join</code></em></span></th></tr></thead><tbody><tr><td style="text-align: left">
+         and <code class="function">pop</code> operations).</p><div class="informaltable"><table border="1"><colgroup><col align="left" class="c1"><col align="left" class="c2"><col align="left" class="c3"><col align="left" class="c4"><col align="left" class="c5"><col align="left" class="c6"></colgroup><thead><tr><th align="left"> </th><th align="left"><span class="emphasis"><em><code class="function">push</code></em></span></th><th align="left"><span class="emphasis"><em><code class="function">pop</code></em></span></th><th align="left"><span class="emphasis"><em><code class="function">modify</code></em></span></th><th align="left"><span class="emphasis"><em><code class="function">erase</code></em></span></th><th align="left"><span class="emphasis"><em><code class="function">join</code></em></span></th></tr></thead><tbody><tr><td align="left">
                    <code class="classname">std::priority_queue</code>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(n) worst
                    Θ(log(n)) amortized
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(log(n)) Worst
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(n log(n)) Worst
                    <sub>[std note 1]</sub>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(n log(n))
                    <sub>[std note 2]</sub>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(n log(n))
                    <sub>[std note 1]</sub>
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
                    &lt;<code class="classname">Tag</code> =
                    <code class="classname">pairing_heap_tag</code>&gt;
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    O(1)
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(n) worst
                    Θ(log(n)) amortized
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(n) worst
                    Θ(log(n)) amortized
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(n) worst
                    Θ(log(n)) amortized
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    O(1)
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
                    &lt;<code class="classname">Tag</code> =
                    <code class="classname">binary_heap_tag</code>&gt;
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(n) worst
                    Θ(log(n)) amortized
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(n) worst
                    Θ(log(n)) amortized
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(n)
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(n)
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(n)
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
                    &lt;<code class="classname">Tag</code> =
                    <code class="classname">binomial_heap_tag</code>&gt;
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(log(n)) worst
                    O(1) amortized
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(log(n))
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(log(n))
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(log(n))
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(log(n))
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>
                    &lt;<code class="classname">Tag</code> =
                    <code class="classname">rc_binomial_heap_tag</code>&gt;
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    O(1)
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(log(n))
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(log(n))
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(log(n))
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(log(n))
-                 </td></tr><tr><td style="text-align: left">
+                 </td></tr><tr><td align="left">
                    <code class="classname">priority_queue</code>&lt;<code class="classname">Tag</code> =
                    <code class="classname">thin_heap_tag</code>&gt;
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    O(1)
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(n) worst
                    Θ(log(n)) amortized
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(log(n)) worst
                    O(1) amortized,
                    or Θ(log(n)) amortized
                    <sub>[thin_heap_note]</sub>
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(n) worst
                    Θ(log(n)) amortized
-                 </td><td style="text-align: left">
+                 </td><td align="left">
                    Θ(n)
                  </td></tr></tbody></table></div><p>[std note 1] This
          is not a property of the algorithm, but rather due to the fact
          of the priority queue's comparison functor), then the amortized
          time is O(1), but if II) it decreases it, then the
          amortized time is the same as the worst case time. Note that
-         for most algorithms, I) is important and II) is not.</p></div><div class="section" title="Amortized push and pop operations"><div class="titlepage"><div><div><h6 class="title"><a id="observations.priority_queue.amortized_ops"/>
+         for most algorithms, I) is important and II) is not.</p></div><div class="section" title="Amortized push and pop operations"><div class="titlepage"><div><div><h6 class="title"><a name="observations.priority_queue.amortized_ops"></a>
            Amortized <code class="function">push</code>
            and <code class="function">pop</code> operations
          </h6></div></div></div><p>In many cases, a priority queue is needed primarily for
          terms of constants.</p><p>As the table shows, the "least constrained" underlying
          data structures are binary heaps and pairing heaps.
          Consequently, it is not surprising that they perform best in
-         terms of amortized constants.</p><div class="orderedlist"><ol class="orderedlist"><li class="listitem"><p>Pairing heaps seem to perform best for non-primitive
+         terms of amortized constants.</p><div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><p>Pairing heaps seem to perform best for non-primitive
            types (e.g., <code class="classname">std::string</code>s), as shown by
            Priority
            Queue Text <code class="function">push</code> Timing Test and Priority
            Queue Random Integer <code class="function">push</code> Timing Test and
            Priority
            Queue Random Integer <code class="function">push</code> and <code class="function">pop</code> Timing
-           Test.</p></li></ol></div></div><div class="section" title="Graph Algorithms"><div class="titlepage"><div><div><h6 class="title"><a id="observations.priority_queue.graphs"/>
+           Test.</p></li></ol></div></div><div class="section" title="Graph Algorithms"><div class="titlepage"><div><div><h6 class="title"><a name="observations.priority_queue.graphs"></a>
            Graph Algorithms
          </h6></div></div></div><p>In some graph algorithms, a decrease-key operation is
          required [clrs2001];
          as well. It is difficult to find an a-priori characterization of
          graphs in which the actual number of <code class="function">modify</code>
          operations will dwarf the number of <code class="function">push</code> and
-         <code class="function">pop</code> operations.</p></div></div></div></div></div><div class="navfooter"><hr/><table width="100%" summary="Navigation footer"><tr><td align="left"><a accesskey="p" href="policy_data_structures_design.html">Prev</a> </td><td align="center"><a accesskey="u" href="policy_data_structures.html">Up</a></td><td align="right"> <a accesskey="n" href="policy_data_structures_biblio.html">Next</a></td></tr><tr><td align="left" valign="top">Design </td><td align="center"><a accesskey="h" href="../index.html">Home</a></td><td align="right" valign="top"> Acknowledgments</td></tr></table></div></body></html>
+         <code class="function">pop</code> operations.</p></div></div></div></div></div><div class="navfooter"><hr><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="policy_data_structures_design.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="policy_data_structures.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="policy_data_structures_biblio.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Design </td><td width="20%" align="center"><a accesskey="h" href="../index.html">Home</a></td><td width="40%" align="right" valign="top"> Acknowledgments</td></tr></table></div></body></html>