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<title>Parallel BGL s-t Connectivity</title>
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<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> s-t Connectivity</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
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<pre class="literal-block">
namespace graph { namespace distributed {
  template&lt;typename DistributedGraph, typename ColorMap&gt;
  inline bool
  st_connected(const DistributedGraph&amp; g,
               typename graph_traits&lt;DistributedGraph&gt;::vertex_descriptor s,
               typename graph_traits&lt;DistributedGraph&gt;::vertex_descriptor t,
               ColorMap color)

  template&lt;typename DistributedGraph&gt;
  inline bool
  st_connected(const DistributedGraph&amp; g,
               typename graph_traits&lt;DistributedGraph&gt;::vertex_descriptor s,
               typename graph_traits&lt;DistributedGraph&gt;::vertex_descriptor t)

  template&lt;typename DistributedGraph, typename ColorMap, typename OwnerMap&gt;
  bool
  st_connected(const DistributedGraph&amp; g,
               typename graph_traits&lt;DistributedGraph&gt;::vertex_descriptor s,
               typename graph_traits&lt;DistributedGraph&gt;::vertex_descriptor t,
               ColorMap color, OwnerMap owner)
} }
</pre>
<p>The <tt class="docutils literal"><span class="pre">st_connected()</span></tt> function determines whether there exists a path
from <tt class="docutils literal"><span class="pre">s</span></tt> to <tt class="docutils literal"><span class="pre">t</span></tt> in a graph <tt class="docutils literal"><span class="pre">g</span></tt>.  If a path exists the function
returns <tt class="docutils literal"><span class="pre">true</span></tt>, otherwise it returns <tt class="docutils literal"><span class="pre">false</span></tt>.</p>
<p>This algorithm is currently <em>level-synchronized</em>, meaning that all
vertices in a given level of the search tree will be processed
(potentially in parallel) before any vertices from a successive level
in the tree are processed.  This is not necessary for the correctness
of the algorithm but rather is an implementation detail.  This
algorithm could be rewritten fully-asynchronously using triggers which
would remove the level-synchronized behavior.</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>&lt;<tt class="docutils literal"><span class="pre">boost/graph/distributed/st_connected.hpp</span></tt>&gt;</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">DistributedGraph&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>.</dd>
</dl>
<p>IN:  <tt class="docutils literal"><span class="pre">vertex_descriptor</span> <span class="pre">s</span></tt></p>
<p>IN:  <tt class="docutils literal"><span class="pre">vertex_descriptor</span> <span class="pre">t</span></tt></p>
<dl class="docutils">
<dt>UTIL/OUT: <tt class="docutils literal"><span class="pre">color_map(ColorMap</span> <span class="pre">color)</span></tt></dt>
<dd>The color map must be a <a class="reference external" href="distributed_property_map.html">Distributed Property Map</a> with the same
process group as the graph <tt class="docutils literal"><span class="pre">g</span></tt> whose colors must monotonically
darken (white -&gt; gray/green -&gt; black). The default value is a
distributed <tt class="docutils literal"><span class="pre">two_bit_color_map</span></tt>.</dd>
<dt>IN:  <tt class="docutils literal"><span class="pre">OwnerMap</span> <span class="pre">owner</span></tt></dt>
<dd>The owner map must map from vertices to the process that owns them
as described in the <a class="reference external" href="GlobalDescriptor.html">GlobalDescriptor</a> concept.</dd>
<dt>OUT:  <tt class="docutils literal"><span class="pre">bool</span></tt></dt>
<dd>The algorithm returns <tt class="docutils literal"><span class="pre">true</span></tt> if a path from <tt class="docutils literal"><span class="pre">s</span></tt> to <tt class="docutils literal"><span class="pre">t</span></tt> is
found, and false otherwise.</dd>
</dl>
</div>
<div class="section" id="complexity">
<h1><a class="toc-backref" href="#id3">Complexity</a></h1>
<p>This algorithm performs <em>O(V + E)</em> work in <em>d/2 + 1</em> BSP supersteps,
where <em>d</em> is the shortest distance from <tt class="docutils literal"><span class="pre">s</span></tt> to <tt class="docutils literal"><span class="pre">t</span></tt>. Over all
supersteps, <em>O(E)</em> messages of constant size will be transmitted.</p>
</div>
<div class="section" id="algorithm-description">
<h1><a class="toc-backref" href="#id4">Algorithm Description</a></h1>
<p>The algorithm consists of two simultaneous breadth-first traversals
from <tt class="docutils literal"><span class="pre">s</span></tt> and <tt class="docutils literal"><span class="pre">t</span></tt> respectively.  The algorithm utilizes a single
queue for both traversals with the traversal from <tt class="docutils literal"><span class="pre">s</span></tt> being denoted
by a <tt class="docutils literal"><span class="pre">gray</span></tt> entry in the color map and the traversal from <tt class="docutils literal"><span class="pre">t</span></tt>
being denoted by a <tt class="docutils literal"><span class="pre">green</span></tt> entry.  The traversal method is similar
to breadth-first search except that no visitor event points are
called.  When any process detects a collision in the two traversals
(by attempting to set a <tt class="docutils literal"><span class="pre">gray</span></tt> vertex to <tt class="docutils literal"><span class="pre">green</span></tt> or vice-versa),
it signals all processes to terminate on the next superstep and all
processes return <tt class="docutils literal"><span class="pre">true</span></tt>.  If the queues on all processes are empty
and no collision is detected then all processes terminate and return
<tt class="docutils literal"><span class="pre">false</span></tt>.</p>
<hr class="docutils" />
<p>Copyright (C) 2009 The Trustees of Indiana University.</p>
<p>Authors: Nick Edmonds and Andrew Lumsdaine</p>
</div>
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Generated on: 2009-05-31 00:21 UTC.
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