ceph/src/boost/libs/graph_parallel/doc/html/non_distributed_betweenness_centrality.html

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   7 <title>Parallel BGL Non-Distributed Betweenness Centrality</title>
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  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.
  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 // named parameter versions
  20 template&lt;typename ProcessGroup, typename Graph, typename Param, typename Tag, typename Rest&gt;
  21 void
  22 non_distributed_brandes_betweenness_centrality(const ProcessGroup&amp; pg, const Graph&amp; g,
  23                                                const bgl_named_params&lt;Param,Tag,Rest&gt;&amp; params);
  24
  25 template&lt;typename ProcessGroup, typename Graph, typename CentralityMap,
  26          typename Buffer&gt;
  27 void
  28 non_distributed_brandes_betweenness_centrality(const ProcessGroup&amp; pg, const Graph&amp; g,
  29                                                CentralityMap centrality, Buffer sources);
  30
  31 template&lt;typename ProcessGroup, typename Graph, typename CentralityMap,
  32          typename EdgeCentralityMap, typename Buffer&gt;
  33 void
  34 non_distributed_brandes_betweenness_centrality(const ProcessGroup&amp; pg, const Graph&amp; g,
  35                                                CentralityMap centrality,
  36                                                EdgeCentralityMap edge_centrality_map,
  37                                                Buffer sources);
  38
  39 // non-named parameter versions
  40 template&lt;typename ProcessGroup, typename Graph, typename CentralityMap,
  41          typename EdgeCentralityMap, typename IncomingMap, typename DistanceMap,
  42          typename DependencyMap, typename PathCountMap, typename VertexIndexMap,
  43          typename Buffer&gt;
  44 void
  45 non_distributed_brandes_betweenness_centrality(const ProcessGroup&amp; pg,
  46                                                const Graph&amp; 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
  56 template&lt;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&gt;
  60 void
  61 non_distributed_brandes_betweenness_centrality(const ProcessGroup&amp; pg,
  62                                                const Graph&amp; 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
  74 template&lt;typename Graph, typename CentralityMap&gt;
  75 typename property_traits&lt;CentralityMap&gt;::value_type
  76 central_point_dominance(const Graph&amp; g, CentralityMap centrality);
  77 </pre>
  78 <p>The <tt class="docutils literal"><span class="pre">non_distributed_betweenness_centrality()</span></tt> function computes the
  79 betweenness centrality of the vertices and edges in a graph.  The name
  80 is somewhat confusing, the graph <tt class="docutils literal"><span class="pre">g</span></tt> is not a distributed graph,
  81 however the algorithm does run in parallel.  Rather than parallelizing
  82 the individual shortest paths calculations that are required by
  83 betweenness centrality, this variant of the algorithm performs the
  84 shortest paths calculations in parallel with each process in <tt class="docutils literal"><span class="pre">pg</span></tt>
  85 calculating the shortest path from a different set of source vertices
  86 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
  87 process accumulates into it's local centrality map and once all the
  88 shortest paths calculations are performed a reduction is performed to
  89 combine 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>&lt;<tt class="docutils literal"><span class="pre">boost/graph/distributed/betweenness_centrality.hpp</span></tt>&gt;</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&amp;</span> <span class="pre">pg</span></tt></dt>
 107 <dd>The process group over which the the processes involved in
 108 betweenness centrality communicate.  The process group type must
 109 model 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&amp;</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
 114 supplied a <tt class="docutils literal"><span class="pre">dummy_property_map</span></tt> will be used and no vertex
 115 centrality 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
 121 not supplied a <tt class="docutils literal"><span class="pre">dummy_property_map</span></tt> will be used and no edge
 122 centrality 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
 128 part of shortest paths to that vertex.  Its key type must be the
 129 graph's vertex descriptor type and its value type must be the
 130 graph'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
 134 type.</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
 139 shortest paths portion of the algorithm.  Its key type must be the
 140 graph'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
 148 centrality calculation portion of the algorithm.  Its key type must
 149 be 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
 157 is on during the centrality calculation portion of the algorithm.
 158 Its 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
 166 descriptor type of the graph <tt class="docutils literal"><span class="pre">g</span></tt> and whose value type is an
 167 integral 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
 173 descriptor type of the graph <tt class="docutils literal"><span class="pre">g</span></tt>.  If not supplied the betweenness
 174 centrality 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
 177 algorithm.  If <tt class="docutils literal"><span class="pre">sources</span></tt> is empty a complete betweenness
 178 centrality calculation using all vertices in <tt class="docutils literal"><span class="pre">g</span></tt> will be
 179 performed.  The value type of the Buffer must be the graph's vertex
 180 descriptor 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
 188 them may be run in parallel (one per process in <tt class="docutils literal"><span class="pre">pg</span></tt>).  The
 189 reduction phase to calculate the total centrality at the end of the
 190 shortest 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
 195 non-distributed property maps.  Each process contains a separate copy
 196 of the sequential graph <tt class="docutils literal"><span class="pre">g</span></tt>.  In order for the algorithm to be
 197 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>
 198 buffer contains the vertices to use as the source of single source
 199 shortest paths calculations when approximating betweenness centrality
 200 using a subset of the vertices in the graph.  If <tt class="docutils literal"><span class="pre">sources</span></tt> is empty
 201 then a complete betweenness centrality calculation is performed using
 202 all vertices.</p>
 203 <p>In the sequential phase of the algorithm each process computes
 204 shortest paths from a subset of the vertices in the graph using the
 205 Brandes shortest paths methods from the BGL's betweenness centrality
 206 implementation.  In the parallel phase of the algorithm a reduction is
 207 performed to sum the values computed by each process for all vertices
 208 in the graph.</p>
 209 <p>Either weighted or unweighted betweenness centrality is calculated
 210 depending 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>
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