[ceph.git] / ceph / src / boost / libs / graph_parallel / doc / html / page_rank.html

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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>

<!-- Copyright (C) 2004-2008 The Trustees of Indiana University.
Use, modification and distribution is subject to the Boost Software
License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt) -->
<pre class="literal-block">
namespace graph {
  template&lt;typename Graph, typename RankMap, typename Done&gt;
  inline void
  page_rank(const Graph&amp; g, RankMap rank_map, Done done,
            typename property_traits&lt;RankMap&gt;::value_type damping = 0.85);

  template&lt;typename Graph, typename RankMap&gt;
  inline void
  page_rank(const Graph&amp; g, RankMap rank_map);
}
</pre>
<p>The <tt class="docutils literal"><span class="pre">page_rank</span></tt> algorithm computes the ranking of vertices in a
graph, based on the connectivity of a directed graph <a class="citation-reference" href="#pbmw98" id="id1">[PBMW98]</a>. The
idea of PageRank is based on a random model of a Web surfer, who
starts a random web page and then either follows a link from that web
page (choosing from the links randomly) or jumps to a completely
different web page (not necessarily linked from the current
page). The PageRank of each page is the probability of the random web
surfer visiting that page.</p>
<div class="contents topic" id="contents">
<p class="topic-title first">Contents</p>
<ul class="simple">
<li><a class="reference internal" href="#where-defined" id="id2">Where Defined</a></li>
<li><a class="reference internal" href="#parameters" id="id3">Parameters</a></li>
<li><a class="reference internal" href="#complexity" id="id4">Complexity</a><ul>
<li><a class="reference internal" href="#bibliography" id="id5">Bibliography</a></li>
</ul>
</li>
</ul>
</div>
<div class="section" id="where-defined">
<h1><a class="toc-backref" href="#id2">Where Defined</a></h1>
<p>&lt;<tt class="docutils literal"><span class="pre">boost/graph/distributed/page_rank.hpp</span></tt>&gt;</p>
<p>also accessible from</p>
<p>&lt;<tt class="docutils literal"><span class="pre">boost/graph/page_rank.hpp</span></tt>&gt;</p>
</div>
<div class="section" id="parameters">
<h1><a class="toc-backref" href="#id3">Parameters</a></h1>
<dl class="docutils">
<dt>IN: <tt class="docutils literal"><span class="pre">Graph&amp;</span> <span class="pre">g</span></tt></dt>
<dd>The graph type must be a model of <a class="reference external" href="DistributedVertexListGraph.html">Distributed Vertex List Graph</a> and
<a class="reference external" href="DistributedEdgeListGraph.html">Distributed Edge List Graph</a>. The graph must be directed.</dd>
<dt>OUT: <tt class="docutils literal"><span class="pre">RankMap</span> <span class="pre">rank</span></tt></dt>
<dd>Stores the rank of each vertex. The type <tt class="docutils literal"><span class="pre">RankMap</span></tt> must model the
<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
property map</a>. Its key type must be the vertex descriptor of the
graph type and its value type must be a floating-point or rational
type.</dd>
<dt>IN: <tt class="docutils literal"><span class="pre">Done</span> <span class="pre">done</span></tt></dt>
<dd><p class="first">A function object that determines when the PageRank algorithm
should complete. It will be passed two parameters, the rank map and
a reference to the graph, and should return <tt class="docutils literal"><span class="pre">true</span></tt> when the
algorithm should terminate.</p>
<p class="last"><strong>Default</strong>: <tt class="docutils literal"><span class="pre">graph::n_iterations(20)</span></tt></p>
</dd>
<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>
<dd><p class="first">The damping factor is the probability that the Web surfer will
select an outgoing link from the current page instead of jumping to
a random page.</p>
<p class="last"><strong>Default</strong>: 0.85</p>
</dd>
</dl>
</div>
<div class="section" id="complexity">
<h1><a class="toc-backref" href="#id4">Complexity</a></h1>
<p>Each iteration of PageRank requires <em>O((V + E)/p)</em> time on <em>p</em>
processors and performs <em>O(V)</em> communication. The number of
iterations is dependent on the input to the algorithm.</p>
<div class="section" id="bibliography">
<h2><a class="toc-backref" href="#id5">Bibliography</a></h2>
<table class="docutils citation" frame="void" id="pbmw98" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id1">[PBMW98]</a></td><td>Lawrence Page, Sergey Brin, Rajeev Motwani, and Terry
Winograd. The PageRank Citation Ranking: Bringing Order to the
Web. Technical report, Stanford Digital Library Technologies Project,
November 1998.</td></tr>
</tbody>
</table>
<hr class="docutils" />
<p>Copyright (C) 2005 The Trustees of Indiana University.</p>
<p>Authors: Douglas Gregor and Andrew Lumsdaine</p>
</div>
</div>
</div>
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Commit	Line	Data
7c673cae FG	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.
	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<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
	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><<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
	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<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
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>
101	</div>
102	</div>
103	</div>
104	<div class="footer">
105	<hr class="footer" />
106	Generated on: 2009-05-31 00:21 UTC.
107	Generated 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.
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111	</html>