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- <title>Parallel BGL Non-Distributed Betweenness Centrality</title>
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- <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>
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