112 lines
6.1 KiB
HTML
112 lines
6.1 KiB
HTML
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
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<meta name="generator" content="Docutils 0.6: http://docutils.sourceforge.net/" />
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<title>Parallel BGL PageRank</title>
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<link rel="stylesheet" href="../../../../rst.css" type="text/css" />
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<body>
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<div class="document" id="logo-pagerank">
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<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>
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<!-- Copyright (C) 2004-2008 The Trustees of Indiana University.
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Use, modification and distribution is subject to the Boost Software
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License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt) -->
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<pre class="literal-block">
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namespace graph {
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template<typename Graph, typename RankMap, typename Done>
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inline void
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page_rank(const Graph& g, RankMap rank_map, Done done,
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typename property_traits<RankMap>::value_type damping = 0.85);
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template<typename Graph, typename RankMap>
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inline void
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page_rank(const Graph& g, RankMap rank_map);
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}
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</pre>
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<p>The <tt class="docutils literal"><span class="pre">page_rank</span></tt> algorithm computes the ranking of vertices in a
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graph, based on the connectivity of a directed graph <a class="citation-reference" href="#pbmw98" id="id1">[PBMW98]</a>. The
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idea of PageRank is based on a random model of a Web surfer, who
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starts a random web page and then either follows a link from that web
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page (choosing from the links randomly) or jumps to a completely
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different web page (not necessarily linked from the current
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page). The PageRank of each page is the probability of the random web
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surfer visiting that page.</p>
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<div class="contents topic" id="contents">
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<p class="topic-title first">Contents</p>
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<ul class="simple">
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<li><a class="reference internal" href="#where-defined" id="id2">Where Defined</a></li>
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<li><a class="reference internal" href="#parameters" id="id3">Parameters</a></li>
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<li><a class="reference internal" href="#complexity" id="id4">Complexity</a><ul>
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<li><a class="reference internal" href="#bibliography" id="id5">Bibliography</a></li>
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</ul>
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</li>
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</ul>
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</div>
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<div class="section" id="where-defined">
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<h1><a class="toc-backref" href="#id2">Where Defined</a></h1>
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<p><<tt class="docutils literal"><span class="pre">boost/graph/distributed/page_rank.hpp</span></tt>></p>
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<p>also accessible from</p>
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<p><<tt class="docutils literal"><span class="pre">boost/graph/page_rank.hpp</span></tt>></p>
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</div>
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<div class="section" id="parameters">
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<h1><a class="toc-backref" href="#id3">Parameters</a></h1>
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<dl class="docutils">
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<dt>IN: <tt class="docutils literal"><span class="pre">Graph&</span> <span class="pre">g</span></tt></dt>
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<dd>The graph type must be a model of <a class="reference external" href="DistributedVertexListGraph.html">Distributed Vertex List Graph</a> and
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<a class="reference external" href="DistributedEdgeListGraph.html">Distributed Edge List Graph</a>. The graph must be directed.</dd>
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<dt>OUT: <tt class="docutils literal"><span class="pre">RankMap</span> <span class="pre">rank</span></tt></dt>
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<dd>Stores the rank of each vertex. The type <tt class="docutils literal"><span class="pre">RankMap</span></tt> must model the
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<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
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property map</a>. Its key type must be the vertex descriptor of the
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graph type and its value type must be a floating-point or rational
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type.</dd>
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<dt>IN: <tt class="docutils literal"><span class="pre">Done</span> <span class="pre">done</span></tt></dt>
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<dd><p class="first">A function object that determines when the PageRank algorithm
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should complete. It will be passed two parameters, the rank map and
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a reference to the graph, and should return <tt class="docutils literal"><span class="pre">true</span></tt> when the
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algorithm should terminate.</p>
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<p class="last"><strong>Default</strong>: <tt class="docutils literal"><span class="pre">graph::n_iterations(20)</span></tt></p>
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</dd>
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<dt>IN: <tt class="docutils literal"><span class="pre">typename</span> <span class="pre">property_traits<RankMap>::value_type</span> <span class="pre">damping</span></tt></dt>
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<dd><p class="first">The damping factor is the probability that the Web surfer will
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select an outgoing link from the current page instead of jumping to
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a random page.</p>
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<p class="last"><strong>Default</strong>: 0.85</p>
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</dd>
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</dl>
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</div>
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<div class="section" id="complexity">
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<h1><a class="toc-backref" href="#id4">Complexity</a></h1>
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<p>Each iteration of PageRank requires <em>O((V + E)/p)</em> time on <em>p</em>
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processors and performs <em>O(V)</em> communication. The number of
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iterations is dependent on the input to the algorithm.</p>
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<div class="section" id="bibliography">
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<h2><a class="toc-backref" href="#id5">Bibliography</a></h2>
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<table class="docutils citation" frame="void" id="pbmw98" rules="none">
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<colgroup><col class="label" /><col /></colgroup>
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<tbody valign="top">
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<tr><td class="label"><a class="fn-backref" href="#id1">[PBMW98]</a></td><td>Lawrence Page, Sergey Brin, Rajeev Motwani, and Terry
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Winograd. The PageRank Citation Ranking: Bringing Order to the
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Web. Technical report, Stanford Digital Library Technologies Project,
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November 1998.</td></tr>
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</tbody>
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</table>
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<hr class="docutils" />
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<p>Copyright (C) 2005 The Trustees of Indiana University.</p>
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<p>Authors: Douglas Gregor and Andrew Lumsdaine</p>
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</div>
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</div>
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