1<?xml version="1.0" encoding="utf-8" ?> 2<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> 3<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"> 4<head> 5<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> 6<meta name="generator" content="Docutils 0.6: http://docutils.sourceforge.net/" /> 7<title>Parallel BGL PageRank</title> 8<link rel="stylesheet" href="../../../../rst.css" type="text/css" /> 9</head> 10<body> 11<div class="document" id="logo-pagerank"> 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. 15Use, modification and distribution is subject to the Boost Software 16License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at 17http://www.boost.org/LICENSE_1_0.txt) --> 18<pre class="literal-block"> 19namespace graph { 20 template<typename Graph, typename RankMap, typename Done> 21 inline void 22 page_rank(const Graph& g, RankMap rank_map, Done done, 23 typename property_traits<RankMap>::value_type damping = 0.85); 24 25 template<typename Graph, typename RankMap> 26 inline void 27 page_rank(const Graph& 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 31graph, based on the connectivity of a directed graph <a class="citation-reference" href="#pbmw98" id="id1">[PBMW98]</a>. The 32idea of PageRank is based on a random model of a Web surfer, who 33starts a random web page and then either follows a link from that web 34page (choosing from the links randomly) or jumps to a completely 35different web page (not necessarily linked from the current 36page). The PageRank of each page is the probability of the random web 37surfer 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><<tt class="docutils literal"><span class="pre">boost/graph/distributed/page_rank.hpp</span></tt>></p> 52<p>also accessible from</p> 53<p><<tt class="docutils literal"><span class="pre">boost/graph/page_rank.hpp</span></tt>></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&</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 64property map</a>. Its key type must be the vertex descriptor of the 65graph type and its value type must be a floating-point or rational 66type.</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 69should complete. It will be passed two parameters, the rank map and 70a reference to the graph, and should return <tt class="docutils literal"><span class="pre">true</span></tt> when the 71algorithm 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<RankMap>::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 76select an outgoing link from the current page instead of jumping to 77a 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> 85processors and performs <em>O(V)</em> communication. The number of 86iterations 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 93Winograd. The PageRank Citation Ranking: Bringing Order to the 94Web. Technical report, Stanford Digital Library Technologies Project, 95November 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> 101</div> 102</div> 103</div> 104<div class="footer"> 105<hr class="footer" /> 106Generated on: 2009-05-31 00:21 UTC. 107Generated by <a class="reference external" href="http://docutils.sourceforge.net/">Docutils</a> from <a class="reference external" href="http://docutils.sourceforge.net/rst.html">reStructuredText</a> source. 108 109</div> 110</body> 111</html> 112
