ceph/src/boost/libs/graph_parallel/doc/html/page_rank.html

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  12 <h1 class="title"><a class="reference external" href="http://www.osl.iu.edu/research/pbgl"><img align="middle" alt="Parallel BGL" class="align-middle" src="pbgl-logo.png" /></a> PageRank</h1>
  13
  14 <!-- Copyright (C) 2004-2008 The Trustees of Indiana University.
  15 Use, modification and distribution is subject to the Boost Software
  16 License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
  17 http://www.boost.org/LICENSE_1_0.txt) -->
  18 <pre class="literal-block">
  19 namespace graph {
  20   template&lt;typename Graph, typename RankMap, typename Done&gt;
  21   inline void
  22   page_rank(const Graph&amp; g, RankMap rank_map, Done done,
  23             typename property_traits&lt;RankMap&gt;::value_type damping = 0.85);
  24
  25   template&lt;typename Graph, typename RankMap&gt;
  26   inline void
  27   page_rank(const Graph&amp; g, RankMap rank_map);
  28 }
  29 </pre>
  30 <p>The <tt class="docutils literal"><span class="pre">page_rank</span></tt> algorithm computes the ranking of vertices in a
  31 graph, based on the connectivity of a directed graph <a class="citation-reference" href="#pbmw98" id="id1">[PBMW98]</a>. The
  32 idea of PageRank is based on a random model of a Web surfer, who
  33 starts a random web page and then either follows a link from that web
  34 page (choosing from the links randomly) or jumps to a completely
  35 different web page (not necessarily linked from the current
  36 page). The PageRank of each page is the probability of the random web
  37 surfer visiting that page.</p>
  38 <div class="contents topic" id="contents">
  39 <p class="topic-title first">Contents</p>
  40 <ul class="simple">
  41 <li><a class="reference internal" href="#where-defined" id="id2">Where Defined</a></li>
  42 <li><a class="reference internal" href="#parameters" id="id3">Parameters</a></li>
  43 <li><a class="reference internal" href="#complexity" id="id4">Complexity</a><ul>
  44 <li><a class="reference internal" href="#bibliography" id="id5">Bibliography</a></li>
  45 </ul>
  46 </li>
  47 </ul>
  48 </div>
  49 <div class="section" id="where-defined">
  50 <h1><a class="toc-backref" href="#id2">Where Defined</a></h1>
  51 <p>&lt;<tt class="docutils literal"><span class="pre">boost/graph/distributed/page_rank.hpp</span></tt>&gt;</p>
  52 <p>also accessible from</p>
  53 <p>&lt;<tt class="docutils literal"><span class="pre">boost/graph/page_rank.hpp</span></tt>&gt;</p>
  54 </div>
  55 <div class="section" id="parameters">
  56 <h1><a class="toc-backref" href="#id3">Parameters</a></h1>
  57 <dl class="docutils">
  58 <dt>IN: <tt class="docutils literal"><span class="pre">Graph&amp;</span> <span class="pre">g</span></tt></dt>
  59 <dd>The graph type must be a model of <a class="reference external" href="DistributedVertexListGraph.html">Distributed Vertex List Graph</a> and
  60 <a class="reference external" href="DistributedEdgeListGraph.html">Distributed Edge List Graph</a>. The graph must be directed.</dd>
  61 <dt>OUT: <tt class="docutils literal"><span class="pre">RankMap</span> <span class="pre">rank</span></tt></dt>
  62 <dd>Stores the rank of each vertex. The type <tt class="docutils literal"><span class="pre">RankMap</span></tt> must model the
  63 <a class="reference external" href="http://www.boost.org/libs/property_map/ReadWritePropertyMap.html">Read/Write Property Map</a> concept and must be a <a class="reference external" href="distributed_property_map.html">distributed
  64 property map</a>. Its key type must be the vertex descriptor of the
  65 graph type and its value type must be a floating-point or rational
  66 type.</dd>
  67 <dt>IN: <tt class="docutils literal"><span class="pre">Done</span> <span class="pre">done</span></tt></dt>
  68 <dd><p class="first">A function object that determines when the PageRank algorithm
  69 should complete. It will be passed two parameters, the rank map and
  70 a reference to the graph, and should return <tt class="docutils literal"><span class="pre">true</span></tt> when the
  71 algorithm should terminate.</p>
  72 <p class="last"><strong>Default</strong>: <tt class="docutils literal"><span class="pre">graph::n_iterations(20)</span></tt></p>
  73 </dd>
  74 <dt>IN: <tt class="docutils literal"><span class="pre">typename</span> <span class="pre">property_traits&lt;RankMap&gt;::value_type</span> <span class="pre">damping</span></tt></dt>
  75 <dd><p class="first">The damping factor is the probability that the Web surfer will
  76 select an outgoing link from the current page instead of jumping to
  77 a random page.</p>
  78 <p class="last"><strong>Default</strong>: 0.85</p>
  79 </dd>
  80 </dl>
  81 </div>
  82 <div class="section" id="complexity">
  83 <h1><a class="toc-backref" href="#id4">Complexity</a></h1>
  84 <p>Each iteration of PageRank requires <em>O((V + E)/p)</em> time on <em>p</em>
  85 processors and performs <em>O(V)</em> communication. The number of
  86 iterations is dependent on the input to the algorithm.</p>
  87 <div class="section" id="bibliography">
  88 <h2><a class="toc-backref" href="#id5">Bibliography</a></h2>
  89 <table class="docutils citation" frame="void" id="pbmw98" rules="none">
  90 <colgroup><col class="label" /><col /></colgroup>
  91 <tbody valign="top">
  92 <tr><td class="label"><a class="fn-backref" href="#id1">[PBMW98]</a></td><td>Lawrence Page, Sergey Brin, Rajeev Motwani, and Terry
  93 Winograd. The PageRank Citation Ranking: Bringing Order to the
  94 Web. Technical report, Stanford Digital Library Technologies Project,
  95 November 1998.</td></tr>
  96 </tbody>
  97 </table>
  98 <hr class="docutils" />
  99 <p>Copyright (C) 2005 The Trustees of Indiana University.</p>
 100 <p>Authors: Douglas Gregor and Andrew Lumsdaine</p>
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