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 Non-Distributed Betweenness Centrality</title> 8<link rel="stylesheet" href="../../../../rst.css" type="text/css" /> 9</head> 10<body> 11<div class="document" id="logo-non-distributed-betweenness-centrality"> 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> Non-Distributed Betweenness Centrality</h1> 13 14<!-- Copyright (C) 2004-2009 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"> 19// named parameter versions 20template<typename ProcessGroup, typename Graph, typename Param, typename Tag, typename Rest> 21void 22non_distributed_brandes_betweenness_centrality(const ProcessGroup& pg, const Graph& g, 23 const bgl_named_params<Param,Tag,Rest>& params); 24 25template<typename ProcessGroup, typename Graph, typename CentralityMap, 26 typename Buffer> 27void 28non_distributed_brandes_betweenness_centrality(const ProcessGroup& pg, const Graph& g, 29 CentralityMap centrality, Buffer sources); 30 31template<typename ProcessGroup, typename Graph, typename CentralityMap, 32 typename EdgeCentralityMap, typename Buffer> 33void 34non_distributed_brandes_betweenness_centrality(const ProcessGroup& pg, const Graph& g, 35 CentralityMap centrality, 36 EdgeCentralityMap edge_centrality_map, 37 Buffer sources); 38 39// non-named parameter versions 40template<typename ProcessGroup, typename Graph, typename CentralityMap, 41 typename EdgeCentralityMap, typename IncomingMap, typename DistanceMap, 42 typename DependencyMap, typename PathCountMap, typename VertexIndexMap, 43 typename Buffer> 44void 45non_distributed_brandes_betweenness_centrality(const ProcessGroup& pg, 46 const Graph& g, 47 CentralityMap centrality, 48 EdgeCentralityMap edge_centrality_map, 49 IncomingMap incoming, 50 DistanceMap distance, 51 DependencyMap dependency, 52 PathCountMap path_count, 53 VertexIndexMap vertex_index, 54 Buffer sources); 55 56template<typename ProcessGroup, typename Graph, typename CentralityMap, 57 typename EdgeCentralityMap, typename IncomingMap, typename DistanceMap, 58 typename DependencyMap, typename PathCountMap, typename VertexIndexMap, 59 typename WeightMap, typename Buffer> 60void 61non_distributed_brandes_betweenness_centrality(const ProcessGroup& pg, 62 const Graph& g, 63 CentralityMap centrality, 64 EdgeCentralityMap edge_centrality_map, 65 IncomingMap incoming, 66 DistanceMap distance, 67 DependencyMap dependency, 68 PathCountMap path_count, 69 VertexIndexMap vertex_index, 70 WeightMap weight_map, 71 Buffer sources); 72 73// helper functions 74template<typename Graph, typename CentralityMap> 75typename property_traits<CentralityMap>::value_type 76central_point_dominance(const Graph& g, CentralityMap centrality); 77</pre> 78<p>The <tt class="docutils literal"><span class="pre">non_distributed_betweenness_centrality()</span></tt> function computes the 79betweenness centrality of the vertices and edges in a graph. The name 80is somewhat confusing, the graph <tt class="docutils literal"><span class="pre">g</span></tt> is not a distributed graph, 81however the algorithm does run in parallel. Rather than parallelizing 82the individual shortest paths calculations that are required by 83betweenness centrality, this variant of the algorithm performs the 84shortest paths calculations in parallel with each process in <tt class="docutils literal"><span class="pre">pg</span></tt> 85calculating the shortest path from a different set of source vertices 86using the BGL's implementation of <a class="reference external" href="http://www.boost.org/libs/graph/doc/dijkstra_shortest_paths.html">Dijkstra shortest paths</a>. Each 87process accumulates into it's local centrality map and once all the 88shortest paths calculations are performed a reduction is performed to 89combine the centrality from all the processes.</p> 90<div class="contents topic" id="contents"> 91<p class="topic-title first">Contents</p> 92<ul class="simple"> 93<li><a class="reference internal" href="#where-defined" id="id1">Where Defined</a></li> 94<li><a class="reference internal" href="#parameters" id="id2">Parameters</a></li> 95<li><a class="reference internal" href="#complexity" id="id3">Complexity</a></li> 96<li><a class="reference internal" href="#algorithm-description" id="id4">Algorithm Description</a></li> 97</ul> 98</div> 99<div class="section" id="where-defined"> 100<h1><a class="toc-backref" href="#id1">Where Defined</a></h1> 101<p><<tt class="docutils literal"><span class="pre">boost/graph/distributed/betweenness_centrality.hpp</span></tt>></p> 102</div> 103<div class="section" id="parameters"> 104<h1><a class="toc-backref" href="#id2">Parameters</a></h1> 105<dl class="docutils"> 106<dt>IN: <tt class="docutils literal"><span class="pre">const</span> <span class="pre">ProcessGroup&</span> <span class="pre">pg</span></tt></dt> 107<dd>The process group over which the the processes involved in 108betweenness centrality communicate. The process group type must 109model the <a class="reference external" href="process_group.html">Process Group</a> concept.</dd> 110<dt>IN: <tt class="docutils literal"><span class="pre">const</span> <span class="pre">Graph&</span> <span class="pre">g</span></tt></dt> 111<dd>The graph type must be a model of the <a class="reference external" href="http://www.boost.org/libs/graph/doc/IncidenceGraph.html">Incidence Graph</a> concept.</dd> 112<dt>IN: <tt class="docutils literal"><span class="pre">CentralityMap</span> <span class="pre">centrality</span></tt></dt> 113<dd><p class="first">A centrality map may be supplied to the algorithm, if one is not 114supplied a <tt class="docutils literal"><span class="pre">dummy_property_map</span></tt> will be used and no vertex 115centrality information will be recorded. The key type of the 116<tt class="docutils literal"><span class="pre">CentralityMap</span></tt> must be the graph's vertex descriptor type.</p> 117<p class="last"><strong>Default</strong>: A <tt class="docutils literal"><span class="pre">dummy_property_map</span></tt>.</p> 118</dd> 119<dt>IN: <tt class="docutils literal"><span class="pre">EdgeCentralityMap</span> <span class="pre">edge_centrality_map</span></tt></dt> 120<dd><p class="first">An edge centrality map may be supplied to the algorithm, if one is 121not supplied a <tt class="docutils literal"><span class="pre">dummy_property_map</span></tt> will be used and no edge 122centrality information will be recorded. The key type of the 123<tt class="docutils literal"><span class="pre">EdgeCentralityMap</span></tt> must be the graph's vertex descriptor type.</p> 124<p class="last"><strong>Default</strong>: A <tt class="docutils literal"><span class="pre">dummy_property_map</span></tt>.</p> 125</dd> 126<dt>IN: <tt class="docutils literal"><span class="pre">IncomingMap</span> <span class="pre">incoming</span></tt></dt> 127<dd><p class="first">The incoming map contains the incoming edges to a vertex that are 128part of shortest paths to that vertex. Its key type must be the 129graph's vertex descriptor type and its value type must be the 130graph's edge descriptor type.</p> 131<dl class="last docutils"> 132<dt><strong>Default</strong>: An <tt class="docutils literal"><span class="pre">iterator_property_map</span></tt> created from a</dt> 133<dd><tt class="docutils literal"><span class="pre">std::vector</span></tt> of <tt class="docutils literal"><span class="pre">std::vector</span></tt> of the graph's edge descriptor 134type.</dd> 135</dl> 136</dd> 137<dt>IN: <tt class="docutils literal"><span class="pre">DistanceMap</span> <span class="pre">distance</span></tt></dt> 138<dd><p class="first">The distance map records the distance to vertices during the 139shortest paths portion of the algorithm. Its key type must be the 140graph's vertex descriptor type.</p> 141<dl class="last docutils"> 142<dt><strong>Default</strong>: An <tt class="docutils literal"><span class="pre">iterator_property_map</span></tt> created from a</dt> 143<dd><tt class="docutils literal"><span class="pre">std::vector</span></tt> of the value type of the <tt class="docutils literal"><span class="pre">CentralityMap</span></tt>.</dd> 144</dl> 145</dd> 146<dt>IN: <tt class="docutils literal"><span class="pre">DependencyMap</span> <span class="pre">dependency</span></tt></dt> 147<dd><p class="first">The dependency map records the dependency of each vertex during the 148centrality calculation portion of the algorithm. Its key type must 149be the graph's vertex descriptor type.</p> 150<dl class="last docutils"> 151<dt><strong>Default</strong>: An <tt class="docutils literal"><span class="pre">iterator_property_map</span></tt> created from a</dt> 152<dd><tt class="docutils literal"><span class="pre">std::vector</span></tt> of the value type of the <tt class="docutils literal"><span class="pre">CentralityMap</span></tt>.</dd> 153</dl> 154</dd> 155<dt>IN: <tt class="docutils literal"><span class="pre">PathCountMap</span> <span class="pre">path_count</span></tt></dt> 156<dd><p class="first">The path count map records the number of shortest paths each vertex 157is on during the centrality calculation portion of the algorithm. 158Its key type must be the graph's vertex descriptor type.</p> 159<dl class="last docutils"> 160<dt><strong>Default</strong>: An <tt class="docutils literal"><span class="pre">iterator_property_map</span></tt> created from a</dt> 161<dd><tt class="docutils literal"><span class="pre">std::vector</span></tt> of the graph's degree size type.</dd> 162</dl> 163</dd> 164<dt>IN: <tt class="docutils literal"><span class="pre">VertexIndexMap</span> <span class="pre">vertex_index</span></tt></dt> 165<dd><p class="first">A model of <a class="reference external" href="http://www.boost.org/libs/property_map/ReadablePropertyMap.html">Readable Property Map</a> whose key type is the vertex 166descriptor type of the graph <tt class="docutils literal"><span class="pre">g</span></tt> and whose value type is an 167integral type. The property map should map from vertices to their 168(local) indices in the range <em>[0, num_vertices(g))</em>.</p> 169<p class="last"><strong>Default</strong>: <tt class="docutils literal"><span class="pre">get(vertex_index,</span> <span class="pre">g)</span></tt></p> 170</dd> 171<dt>IN: <tt class="docutils literal"><span class="pre">WeightMap</span> <span class="pre">weight_map</span></tt></dt> 172<dd>A model of <a class="reference external" href="http://www.boost.org/libs/property_map/ReadablePropertyMap.html">Readable Property Map</a> whose key type is the edge 173descriptor type of the graph <tt class="docutils literal"><span class="pre">g</span></tt>. If not supplied the betweenness 174centrality calculation will be unweighted.</dd> 175<dt>IN: <tt class="docutils literal"><span class="pre">Buffer</span> <span class="pre">sources</span></tt></dt> 176<dd><p class="first">A model of <a class="reference external" href="http://www.boost.org/libs/graph/doc/Buffer.html">Buffer</a> containing the starting vertices for the 177algorithm. If <tt class="docutils literal"><span class="pre">sources</span></tt> is empty a complete betweenness 178centrality calculation using all vertices in <tt class="docutils literal"><span class="pre">g</span></tt> will be 179performed. The value type of the Buffer must be the graph's vertex 180descriptor type.</p> 181<p class="last"><strong>Default</strong>: An empty <tt class="docutils literal"><span class="pre">boost::queue</span></tt> of int.</p> 182</dd> 183</dl> 184</div> 185<div class="section" id="complexity"> 186<h1><a class="toc-backref" href="#id3">Complexity</a></h1> 187<p>Each of the shortest paths calculations is <em>O(V log V)</em> and each of 188them may be run in parallel (one per process in <tt class="docutils literal"><span class="pre">pg</span></tt>). The 189reduction phase to calculate the total centrality at the end of the 190shortest paths phase is <em>O(V log V)</em>.</p> 191</div> 192<div class="section" id="algorithm-description"> 193<h1><a class="toc-backref" href="#id4">Algorithm Description</a></h1> 194<p>The algorithm uses a non-distributed (sequential) graph, as well as 195non-distributed property maps. Each process contains a separate copy 196of the sequential graph <tt class="docutils literal"><span class="pre">g</span></tt>. In order for the algorithm to be 197correct, these copies of <tt class="docutils literal"><span class="pre">g</span></tt> must be identical. The <tt class="docutils literal"><span class="pre">sources</span></tt> 198buffer contains the vertices to use as the source of single source 199shortest paths calculations when approximating betweenness centrality 200using a subset of the vertices in the graph. If <tt class="docutils literal"><span class="pre">sources</span></tt> is empty 201then a complete betweenness centrality calculation is performed using 202all vertices.</p> 203<p>In the sequential phase of the algorithm each process computes 204shortest paths from a subset of the vertices in the graph using the 205Brandes shortest paths methods from the BGL's betweenness centrality 206implementation. In the parallel phase of the algorithm a reduction is 207performed to sum the values computed by each process for all vertices 208in the graph.</p> 209<p>Either weighted or unweighted betweenness centrality is calculated 210depending on whether a <tt class="docutils literal"><span class="pre">WeightMap</span></tt> is passed.</p> 211<hr class="docutils" /> 212<p>Copyright (C) 2009 The Trustees of Indiana University.</p> 213<p>Authors: Nick Edmonds and Andrew Lumsdaine</p> 214</div> 215</div> 216<div class="footer"> 217<hr class="footer" /> 218Generated on: 2009-05-31 00:22 UTC. 219Generated 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. 220 221</div> 222</body> 223</html> 224
