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    <title>Boost Graph Library: McGregor Common Subgraphs</title>
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    <br />
    <h1>
      <tt>mcgregor_common_subgraphs</tt>
    </h1>
    <pre>
<em class="comment">// named parameter version</em>
template &lt;typename GraphFirst,
          typename GraphSecond,
          typename SubGraphCallback,
          typename Param,
          typename Tag,
          typename Rest&gt;
  void mcgregor_common_subgraphs
  (const GraphFirst&amp; graph1,
   const GraphSecond&amp; graph2,
   SubGraphCallback user_callback,
   bool only_connected_subgraphs,
   const bgl_named_params<Param, Tag, Rest>& params);

<em class="comment">// non-named parameter version</em>
template &lt;typename GraphFirst,
          typename GraphSecond,
          typename <a href="../../property_map/doc/ReadablePropertyMap.html">VertexIndexMapFirst</a>,
          typename <a href="../../property_map/doc/ReadablePropertyMap.html">VertexIndexMapSecond</a>,
          typename <a href="http://www.sgi.com/tech/stl/BinaryFunction.html">EdgeEquivalencePredicate</a>,
          typename <a href="http://www.sgi.com/tech/stl/BinaryFunction.html">VertexEquivalencePredicate</a>,
          typename SubGraphCallback&gt;
  void mcgregor_common_subgraphs
  (const GraphFirst&amp; graph1,
   const GraphSecond&amp; graph2,
   const VertexIndexMapFirst vindex_map1,
   const VertexIndexMapSecond vindex_map2,
   EdgeEquivalencePredicate edges_equivalent,
   VertexEquivalencePredicate vertices_equivalent,
   bool only_connected_subgraphs,
   SubGraphCallback user_callback);
    </pre>

    <p>
      This algorithm finds all common subgraphs
      between <tt>graph1</tt> and <tt>graph2</tt> and outputs them
      to <tt>user_callback</tt>.  The <tt>edges_equivalent</tt>
      and <tt>vertices_equivalent</tt> predicates are used to
      determine edges and vertex equivalence between the two graphs.
      To use property maps for equivalence, look at
      the <tt><a href="#make_property_map_equivalent">make_property_map_equivalent</a></tt>
      function.  By
      default, <tt><a href="#always_equivalent">always_equivalent</a></tt>
      is used, which returns true for any pair of edges or vertices.
    </p>
    <p>
      McGregor's algorithm does a depth-first search on the space of
      possible common subgraphs.  At each level, every unvisited pair
      of vertices from <tt>graph1</tt> and <tt>graph2</tt> are checked
      to see if they can extend the current subgraph.  This is done in
      three steps (assume <tt>vertex1</tt> is
      from <tt>graph1</tt> and <tt>vertex2</tt> is
      from <tt>graph2</tt>):
      <ol>
        <li>
          Verify that the <tt>vertex1</tt> and <tt>vertex2</tt> are
          equivalent using the <tt>vertices_equivalent</tt> predicate.
        </li>
        <li>
          For every vertex pair
          (<tt>existing_vertex1</tt>, <tt>existing_vertex2</tt>) in
          the current subgraph, ensure that any edges
          between <tt>vertex1</tt> and <tt>existing_vertex1</tt>
          in <tt>graph1</tt> and between <tt>vertex2</tt>
          and <tt>existing_vertex2</tt> in <tt>graph2</tt> match
          (i.e. either both exist of both don't exist).  If both edges
          exist, they are checked for equivalence using
          the <tt>edges_equivalent</tt> predicate.
        </li>
        <li>
          Lastly (and optionally), make sure that the new subgraph
          vertex has at least one edge connecting it to the existing
          subgraph.  When the <tt>only_connected_subgraphs</tt>
          parameter is false, this step is skipped.
        </li>
      </ol>
    </p>

    <h3>Where Defined</h3>
    <a href="../../../boost/graph/mcgregor_common_subgraphs.hpp"><tt>boost/graph/mcgregor_common_subgraphs.hpp</tt></a>
    <p>
      All functions are defined in the boost namespace.
    </p>

    <h3>Parameters</h3>

    IN: <tt>const GraphFirst&amp; graph1</tt> 
    <blockquote>
      The first graph of the pair to be searched.  The
      type <tt>GraphFirst</tt> must be a model of
      <a href="./VertexListGraph.html">Vertex List Graph</a>
      and <a href="./IncidenceGraph.html">Incidence Graph</a>.  All
      parameters with a "<tt>1</tt>"
      (i.e. <tt>vindex_map1</tt>, <tt>correspondence_map_1_to_2</tt>)
      use this graph's vertices as keys.
    </blockquote>

    IN: <tt>const GraphSecond&amp; graph2</tt> 
    <blockquote>
      The second graph of the pair to be searched.  The
      type <tt>Graphsecond</tt> must be a model of
      <a href="./VertexListGraph.html">Vertex List Graph</a>
      and <a href="./IncidenceGraph.html">Incidence Graph</a>.  All
      parameters with a "<tt>2</tt>"
      (i.e. <tt>vindex_map2</tt>, <tt>correspondence_map_2_to_1</tt>)
      use this graph's vertices as keys.
    </blockquote>

    IN: <tt>bool only_connected_subgraphs</tt>
    <blockquote>
      If <tt>true</tt>, subgraphs are expanded only when matching vertices
      have at least one edge connecting them to the existing subgraph.
    </blockquote>

    OUT: <tt>SubGraphCallback user_callback</tt> 
    <blockquote>
      A function object that will be invoked when a subgraph has been discovered.  The operator() must have the following form:
      <pre>
template &lt;typename CorrespondenceMapFirstToSecond,
          typename CorrespondenceMapSecondToFirst&gt;
bool operator()(CorrespondenceMapFirstToSecond correspondence_map_1_to_2,
                CorrespondenceMapSecondToFirst correspondence_map_2_to_1,
                typename graph_traits&lt;GraphFirst&gt;::vertices_size_type subgraph_size);
      </pre>
      Both the <tt>CorrespondenceMapFirstToSecond</tt>
      and <tt>CorresondenceMapSecondToFirst</tt> types are models
      of <a href="../../property_map/doc/ReadablePropertyMap.html">Readable
      Property Map</a> and map equivalent vertices across the two
      graphs given to <tt>mcgregor_common_subgraphs</tt>.  For
      example, if <tt>vertex1</tt> is
      from <tt>graph1</tt>, <tt>vertex2</tt> is from <tt>graph2</tt>,
      and the vertices can be considered equivalent in the subgraph,
      then <tt>get(correspondence_map_1_to_2, vertex1)</tt> will
      be <tt>vertex2</tt> and <tt>get(correspondence_map_2_to_1,
      vertex2)</tt> will be <tt>vertex1</tt>.  If any vertex,
      say <tt>vertex1</tt> in <tt>graph1</tt>, doesn't match a vertex
      in the other graph (<tt>graph2</tt> in this example),
      then <tt>get(correspondence_map_1_to_2, vertex1)</tt> will
      be <tt>graph_traits&lt;GraphSecond&gt;::null_vertex()</tt>.
      Likewise for any un-matched vertices from <tt>graph2</tt>,
      <tt>get(correspondence_map_2_to_1, vertex2)</tt> will
      be <tt>graph_traits&lt;GraphFirst&gt;::null_vertex()</tt>.
      <br /><br /> The <tt>subgraph_size</tt> parameter is the number
      of vertices in the subgraph, or the number of matched vertex
      pairs contained in the correspondence maps.  This can be used to
      quickly filter out subgraphs whose sizes do not fall within the
      desired range.<br /><br />Returning <tt>false</tt> from the
      callback will abort the search immediately. Otherwise, the
      entire search space will be explored [<a href="#1">1</a>].
    </blockquote>

    <h3>Named Parameters</h3>

    IN: <tt>vertex_index1(VertexIndexMapFirst vindex_map1)</tt>   
    <blockquote>
      This maps each vertex to an integer in the range <tt>[0,
        num_vertices(graph1)]</tt>.  This is necessary for efficient storage
      of the subgraphs.  The type VertexIndexMapFirst must be a model of
      <a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map</a>.
      <br />
      <b>Default:</b> <tt>get(vertex_index, graph1)</tt>
    </blockquote>

    IN: <tt>vertex_index2(VertexIndexMapsecond vindex_map2)</tt>   
    <blockquote>
      This maps each vertex to an integer in the range <tt>[0,
        num_vertices(graph2)]</tt>.  This is necessary for efficient storage
      of the subgraphs.  The type VertexIndexMapFirst must be a model of
      <a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map</a>.
      <br />
      <b>Default:</b> <tt>get(vertex_index, graph2)</tt>
    </blockquote>

    IN: <tt>edges_equivalent(EdgeEquivalencePredicate edges_equivalent)</tt> 
    <blockquote>
      This function is used to determine if edges
      between <tt>graph1</tt> and <tt>graph2</tt> are equivalent.
      The <tt>EdgeEquivalencePredicate</tt> type must be a model
      of <a href="http://www.sgi.com/tech/stl/BinaryPredicate.html">Binary
      Predicate</a> and have argument types
      of <tt>graph_traits&lt;GraphFirst&gt;::edge_descriptor</tt>
      and <tt>graph_traits&lt;GraphSecond&gt;::edge_descriptor</tt>.
      A return value of <tt>true</tt> indicates that the edges are
      equivalent.  <br />
      <b>Default:</b> <tt><a href="#always_equivalent">always_equivalent</a></tt>
    </blockquote>

    IN: <tt>vertices_equivalent(VertexEquivalencePredicate vertices_equivalent)</tt> 
    <blockquote>
      This function is used to determine if vertices
      between <tt>graph1</tt> and <tt>graph2</tt> are equivalent.
      The <tt>VertexEquivalencePredicate</tt> type must be a model
      of <a href="http://www.sgi.com/tech/stl/BinaryPredicate.html">Binary
      Predicate</a> and have argument types
      of <tt>graph_traits&lt;GraphFirst&gt;::vertex_descriptor</tt>
      and <tt>graph_traits&lt;GraphSecond&gt;::vertex_descriptor</tt>.
      A return value of <tt>true</tt> indicates that the vertices are
      equivalent.<br />
      <b>Default:</b> <tt><a href="#always_equivalent">always_equivalent</a></tt>
    </blockquote>

    <h3>Related Functions</h3>
    <p>
      Each <tt>mcgregor_common_subgraphs_*</tt> function below takes
      the same parameters as <tt>mcgregor_common_subgraphs</tt>.
    </p>
    <tt>mcgregor_common_subgraphs_unique(...);</tt>
    <blockquote>
      Keeps an internal cache of all discovered subgraphs and
      only invokes the <tt>user_callback</tt> for unique
      subgraphs.  Returning <tt>false</tt>
      from <tt>user_callback</tt> will terminate the search as
      expected.
    </blockquote>

    <tt>mcgregor_common_subgraphs_maximum(...);</tt>
    <blockquote>
      Explores the <em>entire</em> search space and invokes
      the <tt>user_callback</tt> afterward with each of the largest
      discovered subgraphs.  Returning <tt>false</tt> from
      the <tt>user_callback</tt> will <b>not</b> terminate the search
      because it is invoked after the search has been completed.
    </blockquote>

    <tt>mcgregor_common_subgraphs_maximum_unique(...);</tt>
    <blockquote>
      Explores the <em>entire</em> search space and invokes
      the <tt>user_callback</tt> afterward with each of the largest,
      unique discovered subgraphs.  Returning <tt>false</tt> from
      the <tt>user_callback</tt> will <b>not</b> terminate the search
      because it is invoked after the search has been completed.
    </blockquote>

    <h3>Utility Functions/Structs</h3>
    <tt id="make_property_map_equivalent">
property_map_equivalent&lt;PropertyMapFirst, PropertyMapSecond&gt;<br />
&nbsp;&nbsp;make_property_map_equivalent(const PropertyMapFirst property_map1, const PropertyMapSecond property_map2);
    </tt>
    <blockquote>
      Returns a binary predicate function object
      (<tt>property_map_equivalent&lt;PropertyMapFirst,
      PropertyMapSecond&gt;</tt>) that compares vertices or edges
      between graphs using property maps.  If, for
      example, <tt>vertex1</tt> and <tt>vertex2</tt> are the two
      parameters given when the function object is invoked,
      the <tt>operator()</tt> is effectively:
      <tt>return (get(m_property_map1, vertex1) == get(m_property_map2, vertex2));</tt>
    </blockquote>
    
    <tt id="always_equivalent">struct always_equivalent</tt>
    <blockquote>
      A binary function object that returns true for any pair of items.
    </blockquote>

    <tt>
void fill_membership_map&lt;GraphSecond&gt;<br />
(const GraphFirst& graph1, const CorrespondenceMapFirstToSecond correspondence_map_1_to_2, MembershipMapFirst membership_map1);
    </tt>
    <blockquote>
      Takes a subgraph (represented as a correspondence map) and fills
      the vertex membership map (vertex -> bool) (<tt>true</tt> means
      the vertex is present in the subgraph).
      <tt>MembershipMapFirst</tt> must
      model <a href="../../property_map/doc/WritablePropertyMap.html">Writable
      Property Map</a>.
    </blockquote>

    <tt>
typename membership_filtered_graph_traits&lt;Graph, MembershipMap&gt;::graph_type<br />
&nbsp;&nbsp;make_membership_filtered_graph(const Graph&amp; graph, MembershipMap&amp; membership_map);
    </tt>
    <blockquote>
      Creates a <a href="filtered_graph.html">Filtered Graph</a> from
      a subgraph, represented here as a vertex membership map (vertex
      -> bool where a value of <tt>true</tt> means that the vertex is
      present in the subgraph).  All edges between the included
      vertices are preserved.  See the example section for details.
    </blockquote>

    <h3>Complexity</h3>
    <p>
      The time complexity for searching the entire space is <em>O(V1 *
      V2)</em> where V1 is number of vertices in the first graph and
      V2 is the number of vertices in the second graph.
    </p>

    <h3>Examples</h3>
    <p>
      Before calling any of the <tt>mcregor_common_subgraphs</tt>
      algorithms, you must create a function object to act as a callback:
    </p>
    <pre>
template &lt;typename GraphFirst,
          typename GraphSecond&gt;
struct print_callback {

  print_callback(const GraphFirst&amp; graph1,
                 const GraphSecond&amp; graph2) :
    m_graph1(graph1), m_graph2(graph2) { }

template &lt;typename CorrespondenceMapFirstToSecond,
          typename CorrespondenceMapSecondToFirst&gt;
  bool operator()(CorrespondenceMapFirstToSecond correspondence_map_1_to_2,
                  CorrespondenceMapSecondToFirst correspondence_map_2_to_1,
                  typename graph_traits&lt;GraphFirst&gt;::vertices_size_type subgraph_size) {

    <em class="comment">// Print out correspondences between vertices</em>
    BGL_FORALL_VERTICES_T(vertex1, m_graph1, GraphFirst) {

      <em class="comment">// Skip unmapped vertices</em>
      if (get(correspondence_map_1_to_2, vertex1) != graph_traits&lt;GraphSecond&gt;::null_vertex()) {
        std::cout << vertex1 << " <-> " << get(correspondence_map_1_to_2, vertex1) << std::endl;
      }

    }

    std::cout << "---" << std::endl;

    return (true);
  }

  private:
    const GraphFirst&amp; m_graph1;
    const GraphSecond&amp; m_graph2;

};

<em class="comment">// Assuming the graph types GraphFirst and GraphSecond have already been defined</em>
GraphFirst graph1;
GraphSecond graph2;

print_callback&lt;GraphFirst, GraphSecond&gt; my_callback(graph1, graph2);
    </pre>

    <h4>Example 1</h4>
    <p>
      If all the vertices and edges in your graph are identical, you
      can start enumerating subgraphs immediately:
    </p>
    <pre>
<em class="comment">// Print out all connected common subgraphs between graph1 and graph2.
// All vertices and edges are assumed to be equivalent and both graph1 and graph2
// have implicit vertex index properties.</em>
mcgregor_common_subgraphs(graph1, graph2, true, my_callback);
    </pre>

    <h4>Example 2</h4>
    <p>
      If the vertices and edges of your graphs can be differentiated
      with property maps, you can use
      the <tt>make_property_map_equivalent</tt> function to create a
      binary predicate for vertex or edge equivalence:
    </p>

    <pre>
<em class="comment">// Assume both graphs were defined with implicit vertex name,
// edge name, and vertex index properties</em>
property_map&lt;GraphFirst, vertex_name_t&gt; vname_map1 = get(vertex_name, graph1);
property_map&lt;GraphSecond, vertex_name_t&gt; vname_map1 = get(vertex_name, graph2);

property_map&lt;GraphFirst, edge_name_t&gt; ename_map1 = get(edge_name, graph1);
property_map&lt;GraphSecond, edge_name_t&gt; ename_map1 = get(edge_name, graph2);

<em class="comment">// Print out all connected common subgraphs between graph1 and graph2.</em>
mcgregor_common_subgraphs(graph1, graph2, true, my_callback,
  edges_equivalent(make_property_map_equivalent(ename_map1, ename_map2)).
  vertices_equivalent(make_property_map_equivalent(vname_map1, vname_map2)));
    </pre>

    <h4>Example 3</h4>
    <p>
      There are some helper functions that can be used to obtain a
      filtered graph from the correspondence maps given in your
      callback:
    </p>
    <pre>
<em class="comment">// Assuming we're inside the operator() of the callback with a member variable m_graph1 representing the first graph passed to mcgregor_common_subgraphs.
// ...</em>

<em class="comment">// Step 1: Transform a correspondence map into a membership map. Any vertex -> bool property map will work</em>
typedef shared_array_property_map<bool, VertexIndexMap> MembershipMap;      
MembershipMap membership_map1(num_vertices(m_graph1), get(vertex_index, m_graph1));

<em class="comment">// Fill the membership map for m_graph1. GraphSecond is the type of the second graph given to mcgregor_common_subgraphs.</em>
fill_membership_map&lt;GraphSecond&gt;(m_graph1, correspondence_map_1_to_2, membership_map1);

<em class="comment">// Step 2: Use the membership map from Step 1 to obtain a filtered graph</em>
typedef typename membership_filtered_graph_traits&lt;GraphFirst, MembershipMap&gt;::graph_type
  MembershipFilteredGraph;

MembershipFilteredGraph subgraph1 = make_membership_filtered_graph(m_graph1, membership_map1);

<em class="comment">// The filtered graph can be used like a regular BGL graph...</em>
BGL_FORALL_VERTICES_T(vertex1, subgraph1, MembershipFilteredGraph) {
  std::cout << vertex1 << " is present in the subgraph of graph1" << std::endl;
}
    </pre>

    <h3>Notes</h3>
    <p>
      <a name="1">[1]</a>
      For <tt>mcgregor_common_subgraphs_maximum</tt>
      and <tt>mcgregor_common_subgraphs_maximum_unique</tt> the entire
      search space is always explored, so the return value of the
      callback has no effect.
    </p>

    <hr />
    Copyright &copy; 2009 Trustees of Indiana University

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