boost_1_45_0/libs/graph_parallel/doc/html/strong_components.html - nest-learning-thermostat/5.1.7/boost - Git at Google

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 <div class="document" id="logo-connected-components">
 <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</h1>

 <!-- Copyright (C) 2004-2008 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">
 template&lt;typename Graph, typename ComponentMap&gt;
 inline typename property_traits&lt;ComponentMap&gt;::value_type
 strong_components( const Graph&amp; g, ComponentMap c);

 namespace graph {
   template&lt;typename Graph, typename VertexComponentMap&gt;
   void
   fleischer_hendrickson_pinar_strong_components(const Graph&amp; g, VertexComponentMap r);

   template&lt;typename Graph, typename ReverseGraph,
            typename ComponentMap, typename IsoMapFR, typename IsoMapRF&gt;
   inline typename property_traits&lt;ComponentMap&gt;::value_type
   fleischer_hendrickson_pinar_strong_components(const Graph&amp; g,
                                                 ComponentMap c,
                                                 const ReverseGraph&amp; gr,
                                                 IsoMapFR fr, IsoMapRF rf);
 }
 </pre>
 <p>The <tt class="docutils literal"><span class="pre">strong_components()</span></tt> function computes the strongly connected
 components of a directed graph.  The distributed strong components
 algorithm uses the <a class="reference external" href="http://www.boost.org/libs/graph/doc/strong_components.html">sequential strong components</a> algorithm to
 identify components local to a processor.  The distributed portion of
 the algorithm is built on the <a class="reference external" href="breadth_first_search.html">distributed breadth first search</a>
 algorithm and is based on the work of Fleischer, Hendrickson, and
 Pinar <a class="citation-reference" href="#fhp00" id="id1">[FHP00]</a>. The interface is a superset of the interface to the
 BGL <a class="reference external" href="http://www.boost.org/libs/graph/doc/strong_components.html">sequential strong components</a> algorithm. The number of
 strongly-connected components in the graph is returned to all
 processes.</p>
 <p>The distributed strong components algorithm works on both <tt class="docutils literal"><span class="pre">directed</span></tt>
 and <tt class="docutils literal"><span class="pre">bidirectional</span></tt> graphs.  In the bidirectional case, a reverse
 graph adapter is used to produce the required reverse graph.  In
 the directed case, a separate graph is constructed in which all the
 edges are reversed.</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="id2">Where Defined</a></li>
 <li><a class="reference internal" href="#parameters" id="id3">Parameters</a></li>
 <li><a class="reference internal" href="#complexity" id="id4">Complexity</a></li>
 <li><a class="reference internal" href="#algorithm-description" id="id5">Algorithm Description</a></li>
 <li><a class="reference internal" href="#bibliography" id="id6">Bibliography</a></li>
 </ul>
 </div>
 <div class="section" id="where-defined">
 <h1><a class="toc-backref" href="#id2">Where Defined</a></h1>
 <p>&lt;<tt class="docutils literal"><span class="pre">boost/graph/distributed/strong_components.hpp</span></tt>&gt;</p>
 <p>also accessible from</p>
 <p>&lt;<tt class="docutils literal"><span class="pre">boost/graph/strong_components.hpp</span></tt>&gt;</p>
 </div>
 <div class="section" id="parameters">
 <h1><a class="toc-backref" href="#id3">Parameters</a></h1>
 <dl class="docutils">
 <dt>IN:  <tt class="docutils literal"><span class="pre">const</span> <span class="pre">Graph&amp;</span> <span class="pre">g</span></tt></dt>
 <dd>The graph type must be a model of <a class="reference external" href="DistributedGraph.html">Distributed Graph</a>.  The graph
 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>
 <dt>OUT:  <tt class="docutils literal"><span class="pre">ComponentMap</span> <span class="pre">c</span></tt></dt>
 <dd>The algorithm computes how many strongly connected components are in the
 graph, and assigns each component an integer label.  The algorithm
 then records to which component each vertex in the graph belongs by
 recording the component number in the component property map.  The
 <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
 value type must be the <tt class="docutils literal"><span class="pre">vertices_size_type</span></tt> of the graph.  The key
 type must be the graph's vertex descriptor type.</dd>
 <dt>UTIL:  <tt class="docutils literal"><span class="pre">VertexComponentMap</span> <span class="pre">r</span></tt></dt>
 <dd>The algorithm computes a mapping from each vertex to the
 representative of the strong component, stored in this property map.
 The <tt class="docutils literal"><span class="pre">VertexComponentMap</span></tt> type must be a <a class="reference external" href="distributed_property_map.html">Distributed Property Map</a>.
 The value and key types must be the vertex descriptor of the graph.</dd>
 <dt>IN: <tt class="docutils literal"><span class="pre">const</span> <span class="pre">ReverseGraph&amp;</span> <span class="pre">gr</span></tt></dt>
 <dd><p class="first">The reverse (or transpose) graph of <tt class="docutils literal"><span class="pre">g</span></tt>, such that for each
 directed edge <em>(u, v)</em> in <tt class="docutils literal"><span class="pre">g</span></tt> there exists a directed edge
 <em>(fr(v), fr(u))</em> in <tt class="docutils literal"><span class="pre">gr</span></tt> and for each edge <em>(v', u')</em> in <em>gr</em>
 there exists an edge <em>(rf(u'), rf(v'))</em> in <tt class="docutils literal"><span class="pre">g</span></tt>. The functions
 <em>fr</em> and <em>rf</em> map from vertices in the graph to the reverse graph
 and vice-verse, and are represented as property map arguments. The
 concept requirements on this graph type are equivalent to those on
 the <tt class="docutils literal"><span class="pre">Graph</span></tt> type, but the types need not be the same.</p>
 <p class="last"><strong>Default</strong>: Either a <tt class="docutils literal"><span class="pre">reverse_graph</span></tt> adaptor over the original
 graph (if the graph type is bidirectional, i.e., models the
 <a class="reference external" href="http://www.boost.org/libs/graph/doc/BidirectionalGraph.html">Bidirectional Graph</a> concept) or a <a class="reference external" href="distributed_adjacency_list.html">distributed adjacency list</a>
 constructed from the input graph.</p>
 </dd>
 <dt>IN: <tt class="docutils literal"><span class="pre">IsoMapFR</span> <span class="pre">fr</span></tt></dt>
 <dd><p class="first">A property map that maps from vertices in the input graph <tt class="docutils literal"><span class="pre">g</span></tt> to
 vertices in the reversed graph <tt class="docutils literal"><span class="pre">gr</span></tt>. The type <tt class="docutils literal"><span class="pre">IsoMapFR</span></tt> must
 model the <a class="reference external" href="http://www.boost.org/libs/property_map/ReadablePropertyMap.html">Readable Property Map</a> concept and have the graph's
 vertex descriptor as its key type and the reverse graph's vertex
 descriptor as its value type.</p>
 <p class="last"><strong>Default</strong>: An identity property map (if the graph type is
 bidirectional) or a distributed <tt class="docutils literal"><span class="pre">iterator_property_map</span></tt> (if the
 graph type is directed).</p>
 </dd>
 <dt>IN: <tt class="docutils literal"><span class="pre">IsoMapRF</span> <span class="pre">rf</span></tt></dt>
 <dd><p class="first">A property map that maps from vertices in the reversed graph <tt class="docutils literal"><span class="pre">gr</span></tt>
 to vertices in the input graph <tt class="docutils literal"><span class="pre">g</span></tt>. The type <tt class="docutils literal"><span class="pre">IsoMapRF</span></tt> must
 model the <a class="reference external" href="http://www.boost.org/libs/property_map/ReadablePropertyMap.html">Readable Property Map</a> concept and have the reverse
 graph's vertex descriptor as its key type and the graph's vertex
 descriptor as its value type.</p>
 <p class="last"><strong>Default</strong>: An identity property map (if the graph type is
 bidirectional) or a distributed <tt class="docutils literal"><span class="pre">iterator_property_map</span></tt> (if the
 graph type is directed).</p>
 </dd>
 </dl>
 </div>
 <div class="section" id="complexity">
 <h1><a class="toc-backref" href="#id4">Complexity</a></h1>
 <p>The local phase of the algorithm is <em>O(V + E)</em>.  The parallel phase of
 the algorithm requires at most <em>O(V)</em> supersteps each containing two
 breadth first searches which are <em>O(V + E)</em> each.</p>
 </div>
 <div class="section" id="algorithm-description">
 <h1><a class="toc-backref" href="#id5">Algorithm Description</a></h1>
 <p>Prior to executing the sequential phase of the algorithm, each process
 identifies any completely local strong components which it labels and
 removes from the vertex set considered in the parallel phase of the
 algorithm.</p>
 <p>The parallel phase of the distributed strong components algorithm
 consists of series of supersteps.  Each superstep starts with one
 or more vertex sets which are guaranteed to completely contain
 any remaining strong components.  A <a class="reference external" href="breadth_first_search.html">distributed breadth first search</a>
 is performed starting from the first vertex in each vertex set.
 All of these breadth first searches are performed in parallel by having
 each processor call <tt class="docutils literal"><span class="pre">breadth_first_search()</span></tt> with a different starting
 vertex, and if necessary inserting additional vertices into the
 <tt class="docutils literal"><span class="pre">distributed</span> <span class="pre">queue</span></tt> used for breadth first search before invoking
 the algorithm.  A second <a class="reference external" href="breadth_first_search.html">distributed breadth first search</a> is
 performed on the reverse graph in the same fashion.  For each initial
 vertex set, the successor set (the vertices reached in the forward
 breadth first search), and the predecessor set (the vertices reached
 in the backward breadth first search) is computed.  The intersection
 of the predecessor and successor sets form a strongly connected
 component which is labeled as such.  The remaining vertices in the
 initial vertex set are partitioned into three subsets each guaranteed
 to completely contain any remaining strong components.  These three sets
 are the vertices in the predecessor set not contained in the identified
 strongly connected component, the vertices in the successor set not
 in the strongly connected component, and the remaing vertices in the
 initial vertex set not in the predecessor or successor sets.  Once
 new vertex sets are identified, the algorithm begins a new superstep.
 The algorithm halts when no vertices remain.</p>
 <p>To boost performance in sparse graphs when identifying small components,
 when less than a given portion of the initial number of vertices
 remain in active vertex sets, a filtered graph adapter is used
 to limit the graph seen by the breadth first search algorithm to the
 active vertices.</p>
 </div>
 <div class="section" id="bibliography">
 <h1><a class="toc-backref" href="#id6">Bibliography</a></h1>
 <table class="docutils citation" frame="void" id="fhp00" rules="none">
 <colgroup><col class="label" /><col /></colgroup>
 <tbody valign="top">
 <tr><td class="label"><a class="fn-backref" href="#id1">[FHP00]</a></td><td>Lisa Fleischer, Bruce Hendrickson, and Ali Pinar. On
 Identifying Strongly Connected Components in Parallel. In Parallel and
 Distributed Processing (IPDPS), volume 1800 of Lecture Notes in
 Computer Science, pages 505--511, 2000. Springer.</td></tr>
 </tbody>
 </table>
 <hr class="docutils" />
 <p>Copyright (C) 2004, 2005 The Trustees of Indiana University.</p>
 <p>Authors: Nick Edmonds, Douglas Gregor, and Andrew Lumsdaine</p>
 <!--  -->
 </div>
 </div>
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 <hr class="footer" />
 Generated on: 2009-05-31 00:21 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.

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	<title>Parallel BGL Connected Components</title>
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	<body>
	<div class="document" id="logo-connected-components">
	<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</h1>

	<!-- Copyright (C) 2004-2008 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">
	template<typename Graph, typename ComponentMap>
	inline typename property_traits<ComponentMap>::value_type
	strong_components( const Graph& g, ComponentMap c);

	namespace graph {
	template<typename Graph, typename VertexComponentMap>
	void
	fleischer_hendrickson_pinar_strong_components(const Graph& g, VertexComponentMap r);

	template<typename Graph, typename ReverseGraph,
	typename ComponentMap, typename IsoMapFR, typename IsoMapRF>
	inline typename property_traits<ComponentMap>::value_type
	fleischer_hendrickson_pinar_strong_components(const Graph& g,
	ComponentMap c,
	const ReverseGraph& gr,
	IsoMapFR fr, IsoMapRF rf);
	}
	</pre>
	<p>The <tt class="docutils literal"><span class="pre">strong_components()</span></tt> function computes the strongly connected
	components of a directed graph. The distributed strong components
	algorithm uses the <a class="reference external" href="http://www.boost.org/libs/graph/doc/strong_components.html">sequential strong components</a> algorithm to
	identify components local to a processor. The distributed portion of
	the algorithm is built on the <a class="reference external" href="breadth_first_search.html">distributed breadth first search</a>
	algorithm and is based on the work of Fleischer, Hendrickson, and
	Pinar <a class="citation-reference" href="#fhp00" id="id1">[FHP00]</a>. The interface is a superset of the interface to the
	BGL <a class="reference external" href="http://www.boost.org/libs/graph/doc/strong_components.html">sequential strong components</a> algorithm. The number of
	strongly-connected components in the graph is returned to all
	processes.</p>
	<p>The distributed strong components algorithm works on both <tt class="docutils literal"><span class="pre">directed</span></tt>
	and <tt class="docutils literal"><span class="pre">bidirectional</span></tt> graphs. In the bidirectional case, a reverse
	graph adapter is used to produce the required reverse graph. In
	the directed case, a separate graph is constructed in which all the
	edges are reversed.</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="id2">Where Defined</a></li>
	<li><a class="reference internal" href="#parameters" id="id3">Parameters</a></li>
	<li><a class="reference internal" href="#complexity" id="id4">Complexity</a></li>
	<li><a class="reference internal" href="#algorithm-description" id="id5">Algorithm Description</a></li>
	<li><a class="reference internal" href="#bibliography" id="id6">Bibliography</a></li>
	</ul>
	</div>
	<div class="section" id="where-defined">
	<h1><a class="toc-backref" href="#id2">Where Defined</a></h1>
	<p><<tt class="docutils literal"><span class="pre">boost/graph/distributed/strong_components.hpp</span></tt>></p>
	<p>also accessible from</p>
	<p><<tt class="docutils literal"><span class="pre">boost/graph/strong_components.hpp</span></tt>></p>
	</div>
	<div class="section" id="parameters">
	<h1><a class="toc-backref" href="#id3">Parameters</a></h1>
	<dl class="docutils">
	<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 <a class="reference external" href="DistributedGraph.html">Distributed Graph</a>. The graph
	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>
	<dt>OUT: <tt class="docutils literal"><span class="pre">ComponentMap</span> <span class="pre">c</span></tt></dt>
	<dd>The algorithm computes how many strongly connected components are in the
	graph, and assigns each component an integer label. The algorithm
	then records to which component each vertex in the graph belongs by
	recording the component number in the component property map. The
	<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
	value type must be the <tt class="docutils literal"><span class="pre">vertices_size_type</span></tt> of the graph. The key
	type must be the graph's vertex descriptor type.</dd>
	<dt>UTIL: <tt class="docutils literal"><span class="pre">VertexComponentMap</span> <span class="pre">r</span></tt></dt>
	<dd>The algorithm computes a mapping from each vertex to the
	representative of the strong component, stored in this property map.
	The <tt class="docutils literal"><span class="pre">VertexComponentMap</span></tt> type must be a <a class="reference external" href="distributed_property_map.html">Distributed Property Map</a>.
	The value and key types must be the vertex descriptor of the graph.</dd>
	<dt>IN: <tt class="docutils literal"><span class="pre">const</span> <span class="pre">ReverseGraph&</span> <span class="pre">gr</span></tt></dt>
	<dd><p class="first">The reverse (or transpose) graph of <tt class="docutils literal"><span class="pre">g</span></tt>, such that for each
	directed edge <em>(u, v)</em> in <tt class="docutils literal"><span class="pre">g</span></tt> there exists a directed edge
	<em>(fr(v), fr(u))</em> in <tt class="docutils literal"><span class="pre">gr</span></tt> and for each edge <em>(v', u')</em> in <em>gr</em>
	there exists an edge <em>(rf(u'), rf(v'))</em> in <tt class="docutils literal"><span class="pre">g</span></tt>. The functions
	<em>fr</em> and <em>rf</em> map from vertices in the graph to the reverse graph
	and vice-verse, and are represented as property map arguments. The
	concept requirements on this graph type are equivalent to those on
	the <tt class="docutils literal"><span class="pre">Graph</span></tt> type, but the types need not be the same.</p>
	<p class="last"><strong>Default</strong>: Either a <tt class="docutils literal"><span class="pre">reverse_graph</span></tt> adaptor over the original
	graph (if the graph type is bidirectional, i.e., models the
	<a class="reference external" href="http://www.boost.org/libs/graph/doc/BidirectionalGraph.html">Bidirectional Graph</a> concept) or a <a class="reference external" href="distributed_adjacency_list.html">distributed adjacency list</a>
	constructed from the input graph.</p>
	</dd>
	<dt>IN: <tt class="docutils literal"><span class="pre">IsoMapFR</span> <span class="pre">fr</span></tt></dt>
	<dd><p class="first">A property map that maps from vertices in the input graph <tt class="docutils literal"><span class="pre">g</span></tt> to
	vertices in the reversed graph <tt class="docutils literal"><span class="pre">gr</span></tt>. The type <tt class="docutils literal"><span class="pre">IsoMapFR</span></tt> must
	model the <a class="reference external" href="http://www.boost.org/libs/property_map/ReadablePropertyMap.html">Readable Property Map</a> concept and have the graph's
	vertex descriptor as its key type and the reverse graph's vertex
	descriptor as its value type.</p>
	<p class="last"><strong>Default</strong>: An identity property map (if the graph type is
	bidirectional) or a distributed <tt class="docutils literal"><span class="pre">iterator_property_map</span></tt> (if the
	graph type is directed).</p>
	</dd>
	<dt>IN: <tt class="docutils literal"><span class="pre">IsoMapRF</span> <span class="pre">rf</span></tt></dt>
	<dd><p class="first">A property map that maps from vertices in the reversed graph <tt class="docutils literal"><span class="pre">gr</span></tt>
	to vertices in the input graph <tt class="docutils literal"><span class="pre">g</span></tt>. The type <tt class="docutils literal"><span class="pre">IsoMapRF</span></tt> must
	model the <a class="reference external" href="http://www.boost.org/libs/property_map/ReadablePropertyMap.html">Readable Property Map</a> concept and have the reverse
	graph's vertex descriptor as its key type and the graph's vertex
	descriptor as its value type.</p>
	<p class="last"><strong>Default</strong>: An identity property map (if the graph type is
	bidirectional) or a distributed <tt class="docutils literal"><span class="pre">iterator_property_map</span></tt> (if the
	graph type is directed).</p>
	</dd>
	</dl>
	</div>
	<div class="section" id="complexity">
	<h1><a class="toc-backref" href="#id4">Complexity</a></h1>
	<p>The local phase of the algorithm is <em>O(V + E)</em>. The parallel phase of
	the algorithm requires at most <em>O(V)</em> supersteps each containing two
	breadth first searches which are <em>O(V + E)</em> each.</p>
	</div>
	<div class="section" id="algorithm-description">
	<h1><a class="toc-backref" href="#id5">Algorithm Description</a></h1>
	<p>Prior to executing the sequential phase of the algorithm, each process
	identifies any completely local strong components which it labels and
	removes from the vertex set considered in the parallel phase of the
	algorithm.</p>
	<p>The parallel phase of the distributed strong components algorithm
	consists of series of supersteps. Each superstep starts with one
	or more vertex sets which are guaranteed to completely contain
	any remaining strong components. A <a class="reference external" href="breadth_first_search.html">distributed breadth first search</a>
	is performed starting from the first vertex in each vertex set.
	All of these breadth first searches are performed in parallel by having
	each processor call <tt class="docutils literal"><span class="pre">breadth_first_search()</span></tt> with a different starting
	vertex, and if necessary inserting additional vertices into the
	<tt class="docutils literal"><span class="pre">distributed</span> <span class="pre">queue</span></tt> used for breadth first search before invoking
	the algorithm. A second <a class="reference external" href="breadth_first_search.html">distributed breadth first search</a> is
	performed on the reverse graph in the same fashion. For each initial
	vertex set, the successor set (the vertices reached in the forward
	breadth first search), and the predecessor set (the vertices reached
	in the backward breadth first search) is computed. The intersection
	of the predecessor and successor sets form a strongly connected
	component which is labeled as such. The remaining vertices in the
	initial vertex set are partitioned into three subsets each guaranteed
	to completely contain any remaining strong components. These three sets
	are the vertices in the predecessor set not contained in the identified
	strongly connected component, the vertices in the successor set not
	in the strongly connected component, and the remaing vertices in the
	initial vertex set not in the predecessor or successor sets. Once
	new vertex sets are identified, the algorithm begins a new superstep.
	The algorithm halts when no vertices remain.</p>
	<p>To boost performance in sparse graphs when identifying small components,
	when less than a given portion of the initial number of vertices
	remain in active vertex sets, a filtered graph adapter is used
	to limit the graph seen by the breadth first search algorithm to the
	active vertices.</p>
	</div>
	<div class="section" id="bibliography">
	<h1><a class="toc-backref" href="#id6">Bibliography</a></h1>
	<table class="docutils citation" frame="void" id="fhp00" rules="none">
	<colgroup><col class="label" /><col /></colgroup>
	<tbody valign="top">
	<tr><td class="label"><a class="fn-backref" href="#id1">[FHP00]</a></td><td>Lisa Fleischer, Bruce Hendrickson, and Ali Pinar. On
	Identifying Strongly Connected Components in Parallel. In Parallel and
	Distributed Processing (IPDPS), volume 1800 of Lecture Notes in
	Computer Science, pages 505--511, 2000. Springer.</td></tr>
	</tbody>
	</table>
	<hr class="docutils" />
	<p>Copyright (C) 2004, 2005 The Trustees of Indiana University.</p>
	<p>Authors: Nick Edmonds, Douglas Gregor, and Andrew Lumsdaine</p>
	<!-- -->
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	</div>
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	Generated on: 2009-05-31 00:21 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.

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