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

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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> Connected Components Parallel Search</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 namespace graph { namespace distributed {
  20   template&lt;typename Graph, typename ComponentMap&gt;
  21   typename property_traits&lt;ComponentMap&gt;::value_type
  22   connected_components_ps(const Graph&amp; g, ComponentMap c)
  23 } }
  24 </pre>
  25 <p>The <tt class="docutils literal"><span class="pre">connected_components_ps()</span></tt> function computes the connected
  26 components of a graph by performing a breadth-first search from
  27 several sources in parallel while recording and eventually resolving
  28 the collisions.</p>
  29 <div class="contents topic" id="contents">
  30 <p class="topic-title first">Contents</p>
  31 <ul class="simple">
  32 <li><a class="reference internal" href="#where-defined" id="id1">Where Defined</a></li>
  33 <li><a class="reference internal" href="#parameters" id="id2">Parameters</a></li>
  34 <li><a class="reference internal" href="#complexity" id="id3">Complexity</a></li>
  35 <li><a class="reference internal" href="#algorithm-description" id="id4">Algorithm Description</a></li>
  36 </ul>
  37 </div>
  38 <div class="section" id="where-defined">
  39 <h1><a class="toc-backref" href="#id1">Where Defined</a></h1>
  40 <p>&lt;<tt class="docutils literal"><span class="pre">boost/graph/distributed/connected_components_parallel_search.hpp</span></tt>&gt;</p>
  41 </div>
  42 <div class="section" id="parameters">
  43 <h1><a class="toc-backref" href="#id2">Parameters</a></h1>
  44 <dl class="docutils">
  45 <dt>IN:  <tt class="docutils literal"><span class="pre">const</span> <span class="pre">Graph&amp;</span> <span class="pre">g</span></tt></dt>
  46 <dd>The graph type must be a model of <a class="reference external" href="DistributedGraph.html">Distributed Graph</a>.  The graph
  47 type must also model the <a class="reference external" href="http://www.boost.org/libs/graph/doc/IncidenceGraph.html">Incidence Graph</a> and be directed.</dd>
  48 <dt>OUT:  <tt class="docutils literal"><span class="pre">ComponentMap</span> <span class="pre">c</span></tt></dt>
  49 <dd>The algorithm computes how many connected components are in the
  50 graph, and assigns each component an integer label.  The algorithm
  51 then records to which component each vertex in the graph belongs by
  52 recording the component number in the component property map.  The
  53 <tt class="docutils literal"><span class="pre">ComponentMap</span></tt> type must be a <a class="reference external" href="distributed_property_map.html">Distributed Property Map</a>.  The
  54 value type must be the <tt class="docutils literal"><span class="pre">vertices_size_type</span></tt> of the graph.  The key
  55 type must be the graph's vertex descriptor type.</dd>
  56 </dl>
  57 </div>
  58 <div class="section" id="complexity">
  59 <h1><a class="toc-backref" href="#id3">Complexity</a></h1>
  60 <p><em>O(PN^2 + VNP)</em> work, in <em>O(N + V)</em> time, where N is the
  61 number of mappings and V is the number of local vertices.</p>
  62 </div>
  63 <div class="section" id="algorithm-description">
  64 <h1><a class="toc-backref" href="#id4">Algorithm Description</a></h1>
  65 <p>Every <em>N</em> th nodes starts a parallel search from the first vertex in
  66 their local vertex list during the first superstep (the other nodes
  67 remain idle during the first superstep to reduce the number of
  68 conflicts in numbering the components).  At each superstep, all new
  69 component mappings from remote nodes are handled.  If there is no work
  70 from remote updates, a new vertex is removed from the local list and
  71 added to the work queue.</p>
  72 <p>Components are allocated from the <tt class="docutils literal"><span class="pre">component_value_allocator</span></tt>
  73 object, which ensures that a given component number is unique in the
  74 system, currently by using the rank and number of processes to stride
  75 allocations.</p>
  76 <p>When two components are discovered to actually be the same component,
  77 a collision is recorded.  The lower component number is prefered in
  78 the resolution, so component numbering resolution is consistent.
  79 After the search has exhausted all vertices in the graph, the mapping
  80 is shared with all processes and they independently resolve the
  81 comonent mapping.  This phase can likely be significantly sped up if a
  82 clever algorithm for the reduction can be found.</p>
  83 <hr class="docutils" />
  84 <p>Copyright (C) 2009 The Trustees of Indiana University.</p>
  85 <p>Authors: Brian Barrett, Douglas Gregor, and Andrew Lumsdaine</p>
  86 </div>
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  90 Generated on: 2009-05-31 00:21 UTC.
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