<?xml version="1.0" encoding="utf-8" ?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <meta name="generator" content="Docutils 0.6: http://docutils.sourceforge.net/" /> <title>Parallel BGL Non-Distributed Betweenness Centrality</title> <link rel="stylesheet" href="../../../../rst.css" type="text/css" /> </head> <body> <div class="document" id="logo-non-distributed-betweenness-centrality"> <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> <!-- Copyright (C) 2004-2009 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"> // named parameter versions template<typename ProcessGroup, typename Graph, typename Param, typename Tag, typename Rest> void non_distributed_brandes_betweenness_centrality(const ProcessGroup& pg, const Graph& g, const bgl_named_params<Param,Tag,Rest>& params); template<typename ProcessGroup, typename Graph, typename CentralityMap, typename Buffer> void non_distributed_brandes_betweenness_centrality(const ProcessGroup& pg, const Graph& g, CentralityMap centrality, Buffer sources); template<typename ProcessGroup, typename Graph, typename CentralityMap, typename EdgeCentralityMap, typename Buffer> void non_distributed_brandes_betweenness_centrality(const ProcessGroup& pg, const Graph& g, CentralityMap centrality, EdgeCentralityMap edge_centrality_map, Buffer sources); // non-named parameter versions template<typename ProcessGroup, typename Graph, typename CentralityMap, typename EdgeCentralityMap, typename IncomingMap, typename DistanceMap, typename DependencyMap, typename PathCountMap, typename VertexIndexMap, typename Buffer> void non_distributed_brandes_betweenness_centrality(const ProcessGroup& pg, const Graph& g, CentralityMap centrality, EdgeCentralityMap edge_centrality_map, IncomingMap incoming, DistanceMap distance, DependencyMap dependency, PathCountMap path_count, VertexIndexMap vertex_index, Buffer sources); template<typename ProcessGroup, typename Graph, typename CentralityMap, typename EdgeCentralityMap, typename IncomingMap, typename DistanceMap, typename DependencyMap, typename PathCountMap, typename VertexIndexMap, typename WeightMap, typename Buffer> void non_distributed_brandes_betweenness_centrality(const ProcessGroup& pg, const Graph& g, CentralityMap centrality, EdgeCentralityMap edge_centrality_map, IncomingMap incoming, DistanceMap distance, DependencyMap dependency, PathCountMap path_count, VertexIndexMap vertex_index, WeightMap weight_map, Buffer sources); // helper functions template<typename Graph, typename CentralityMap> typename property_traits<CentralityMap>::value_type central_point_dominance(const Graph& g, CentralityMap centrality); </pre> <p>The <tt class="docutils literal"><span class="pre">non_distributed_betweenness_centrality()</span></tt> function computes the betweenness centrality of the vertices and edges in a graph. The name is somewhat confusing, the graph <tt class="docutils literal"><span class="pre">g</span></tt> is not a distributed graph, however the algorithm does run in parallel. Rather than parallelizing the individual shortest paths calculations that are required by betweenness centrality, this variant of the algorithm performs the shortest paths calculations in parallel with each process in <tt class="docutils literal"><span class="pre">pg</span></tt> calculating the shortest path from a different set of source vertices using 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 process accumulates into it's local centrality map and once all the shortest paths calculations are performed a reduction is performed to combine the centrality from all the processes.</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="id1">Where Defined</a></li> <li><a class="reference internal" href="#parameters" id="id2">Parameters</a></li> <li><a class="reference internal" href="#complexity" id="id3">Complexity</a></li> <li><a class="reference internal" href="#algorithm-description" id="id4">Algorithm Description</a></li> </ul> </div> <div class="section" id="where-defined"> <h1><a class="toc-backref" href="#id1">Where Defined</a></h1> <p><<tt class="docutils literal"><span class="pre">boost/graph/distributed/betweenness_centrality.hpp</span></tt>></p> </div> <div class="section" id="parameters"> <h1><a class="toc-backref" href="#id2">Parameters</a></h1> <dl class="docutils"> <dt>IN: <tt class="docutils literal"><span class="pre">const</span> <span class="pre">ProcessGroup&</span> <span class="pre">pg</span></tt></dt> <dd>The process group over which the the processes involved in betweenness centrality communicate. The process group type must model the <a class="reference external" href="process_group.html">Process Group</a> concept.</dd> <dt>IN: <tt class="docutils literal"><span class="pre">const</span> <span class="pre">Graph&</span> <span class="pre">g</span></tt></dt> <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> <dt>IN: <tt class="docutils literal"><span class="pre">CentralityMap</span> <span class="pre">centrality</span></tt></dt> <dd><p class="first">A centrality map may be supplied to the algorithm, if one is not supplied a <tt class="docutils literal"><span class="pre">dummy_property_map</span></tt> will be used and no vertex centrality information will be recorded. The key type of the <tt class="docutils literal"><span class="pre">CentralityMap</span></tt> must be the graph's vertex descriptor type.</p> <p class="last"><strong>Default</strong>: A <tt class="docutils literal"><span class="pre">dummy_property_map</span></tt>.</p> </dd> <dt>IN: <tt class="docutils literal"><span class="pre">EdgeCentralityMap</span> <span class="pre">edge_centrality_map</span></tt></dt> <dd><p class="first">An edge centrality map may be supplied to the algorithm, if one is not supplied a <tt class="docutils literal"><span class="pre">dummy_property_map</span></tt> will be used and no edge centrality information will be recorded. The key type of the <tt class="docutils literal"><span class="pre">EdgeCentralityMap</span></tt> must be the graph's vertex descriptor type.</p> <p class="last"><strong>Default</strong>: A <tt class="docutils literal"><span class="pre">dummy_property_map</span></tt>.</p> </dd> <dt>IN: <tt class="docutils literal"><span class="pre">IncomingMap</span> <span class="pre">incoming</span></tt></dt> <dd><p class="first">The incoming map contains the incoming edges to a vertex that are part of shortest paths to that vertex. Its key type must be the graph's vertex descriptor type and its value type must be the graph's edge descriptor type.</p> <dl class="last docutils"> <dt><strong>Default</strong>: An <tt class="docutils literal"><span class="pre">iterator_property_map</span></tt> created from a</dt> <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 type.</dd> </dl> </dd> <dt>IN: <tt class="docutils literal"><span class="pre">DistanceMap</span> <span class="pre">distance</span></tt></dt> <dd><p class="first">The distance map records the distance to vertices during the shortest paths portion of the algorithm. Its key type must be the graph's vertex descriptor type.</p> <dl class="last docutils"> <dt><strong>Default</strong>: An <tt class="docutils literal"><span class="pre">iterator_property_map</span></tt> created from a</dt> <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> </dl> </dd> <dt>IN: <tt class="docutils literal"><span class="pre">DependencyMap</span> <span class="pre">dependency</span></tt></dt> <dd><p class="first">The dependency map records the dependency of each vertex during the centrality calculation portion of the algorithm. Its key type must be the graph's vertex descriptor type.</p> <dl class="last docutils"> <dt><strong>Default</strong>: An <tt class="docutils literal"><span class="pre">iterator_property_map</span></tt> created from a</dt> <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> </dl> </dd> <dt>IN: <tt class="docutils literal"><span class="pre">PathCountMap</span> <span class="pre">path_count</span></tt></dt> <dd><p class="first">The path count map records the number of shortest paths each vertex is on during the centrality calculation portion of the algorithm. Its key type must be the graph's vertex descriptor type.</p> <dl class="last docutils"> <dt><strong>Default</strong>: An <tt class="docutils literal"><span class="pre">iterator_property_map</span></tt> created from a</dt> <dd><tt class="docutils literal"><span class="pre">std::vector</span></tt> of the graph's degree size type.</dd> </dl> </dd> <dt>IN: <tt class="docutils literal"><span class="pre">VertexIndexMap</span> <span class="pre">vertex_index</span></tt></dt> <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 descriptor type of the graph <tt class="docutils literal"><span class="pre">g</span></tt> and whose value type is an integral type. The property map should map from vertices to their (local) indices in the range <em>[0, num_vertices(g))</em>.</p> <p class="last"><strong>Default</strong>: <tt class="docutils literal"><span class="pre">get(vertex_index,</span> <span class="pre">g)</span></tt></p> </dd> <dt>IN: <tt class="docutils literal"><span class="pre">WeightMap</span> <span class="pre">weight_map</span></tt></dt> <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 descriptor type of the graph <tt class="docutils literal"><span class="pre">g</span></tt>. If not supplied the betweenness centrality calculation will be unweighted.</dd> <dt>IN: <tt class="docutils literal"><span class="pre">Buffer</span> <span class="pre">sources</span></tt></dt> <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 algorithm. If <tt class="docutils literal"><span class="pre">sources</span></tt> is empty a complete betweenness centrality calculation using all vertices in <tt class="docutils literal"><span class="pre">g</span></tt> will be performed. The value type of the Buffer must be the graph's vertex descriptor type.</p> <p class="last"><strong>Default</strong>: An empty <tt class="docutils literal"><span class="pre">boost::queue</span></tt> of int.</p> </dd> </dl> </div> <div class="section" id="complexity"> <h1><a class="toc-backref" href="#id3">Complexity</a></h1> <p>Each of the shortest paths calculations is <em>O(V log V)</em> and each of them may be run in parallel (one per process in <tt class="docutils literal"><span class="pre">pg</span></tt>). The reduction phase to calculate the total centrality at the end of the shortest paths phase is <em>O(V log V)</em>.</p> </div> <div class="section" id="algorithm-description"> <h1><a class="toc-backref" href="#id4">Algorithm Description</a></h1> <p>The algorithm uses a non-distributed (sequential) graph, as well as non-distributed property maps. Each process contains a separate copy of the sequential graph <tt class="docutils literal"><span class="pre">g</span></tt>. In order for the algorithm to be correct, 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> buffer contains the vertices to use as the source of single source shortest paths calculations when approximating betweenness centrality using a subset of the vertices in the graph. If <tt class="docutils literal"><span class="pre">sources</span></tt> is empty then a complete betweenness centrality calculation is performed using all vertices.</p> <p>In the sequential phase of the algorithm each process computes shortest paths from a subset of the vertices in the graph using the Brandes shortest paths methods from the BGL's betweenness centrality implementation. In the parallel phase of the algorithm a reduction is performed to sum the values computed by each process for all vertices in the graph.</p> <p>Either weighted or unweighted betweenness centrality is calculated depending on whether a <tt class="docutils literal"><span class="pre">WeightMap</span></tt> is passed.</p> <hr class="docutils" /> <p>Copyright (C) 2009 The Trustees of Indiana University.</p> <p>Authors: Nick Edmonds and Andrew Lumsdaine</p> </div> </div> <div class="footer"> <hr class="footer" /> Generated on: 2009-05-31 00:22 UTC. 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. </div> </body> </html>