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boost/graph/cuthill_mckee_ordering.hpp

//=======================================================================
// Copyright 1997, 1998, 1999, 2000 University of Notre Dame.
// Copyright 2004, 2005 Trustees of Indiana University
// Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek,
//          Doug Gregor, D. Kevin McGrath
//
// Distributed under 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)
//=======================================================================
#ifndef BOOST_GRAPH_CUTHILL_MCKEE_HPP
#define BOOST_GRAPH_CUTHILL_MCKEE_HPP

#include <boost/config.hpp>
#include <boost/graph/detail/sparse_ordering.hpp>
#include <boost/graph/graph_utility.hpp>
#include <algorithm>


/*
  (Reverse) Cuthill-McKee Algorithm for matrix reordering
*/

namespace boost {

  namespace detail {



    template < typename OutputIterator, typename Buffer, typename DegreeMap > 
    class bfs_rcm_visitor:public default_bfs_visitor
    {
    public:
      bfs_rcm_visitor(OutputIterator *iter, Buffer *b, DegreeMap deg): 
        permutation(iter), Qptr(b), degree(deg) { }
      template <class Vertex, class Graph>
      void examine_vertex(Vertex u, Graph&) {
        *(*permutation)++ = u;
        index_begin = Qptr->size();
      }
      template <class Vertex, class Graph>
      void finish_vertex(Vertex, Graph&) {
        using std::sort;

        typedef typename property_traits<DegreeMap>::value_type ds_type;

        typedef indirect_cmp<DegreeMap, std::less<ds_type> > Compare;
        Compare comp(degree);
                
        sort(Qptr->begin()+index_begin, Qptr->end(), comp);
      }
    protected:
      OutputIterator *permutation;
      int index_begin;
      Buffer *Qptr;
      DegreeMap degree;
    };

  } // namespace detail  


  // Reverse Cuthill-McKee algorithm with a given starting Vertex.
  //
  // If user provides a reverse iterator, this will be a reverse-cuthill-mckee
  // algorithm, otherwise it will be a standard CM algorithm

  template <class Graph, class OutputIterator,
            class ColorMap, class DegreeMap>
  OutputIterator
  cuthill_mckee_ordering(const Graph& g,
                         std::deque< typename
                         graph_traits<Graph>::vertex_descriptor > vertex_queue,
                         OutputIterator permutation, 
                         ColorMap color, DegreeMap degree)
  {

    //create queue, visitor...don't forget namespaces!
    typedef typename property_traits<DegreeMap>::value_type ds_type;
    typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
    typedef typename boost::sparse::sparse_ordering_queue<Vertex> queue;
    typedef typename detail::bfs_rcm_visitor<OutputIterator, queue, DegreeMap> Visitor;
    typedef typename property_traits<ColorMap>::value_type ColorValue;
    typedef color_traits<ColorValue> Color;


    queue Q;

    //create a bfs_rcm_visitor as defined above
    Visitor     vis(&permutation, &Q, degree);

    typename graph_traits<Graph>::vertex_iterator ui, ui_end;    

    // Copy degree to pseudo_degree
    // initialize the color map
    for (boost::tie(ui, ui_end) = vertices(g); ui != ui_end; ++ui){
      put(color, *ui, Color::white());
    }


    while( !vertex_queue.empty() ) {
      Vertex s = vertex_queue.front();
      vertex_queue.pop_front();
      
      //call BFS with visitor
      breadth_first_visit(g, s, Q, vis, color);
    }
    return permutation;
  }
    

  // This is the case where only a single starting vertex is supplied.
  template <class Graph, class OutputIterator,
            class ColorMap, class DegreeMap>
  OutputIterator
  cuthill_mckee_ordering(const Graph& g,
                         typename graph_traits<Graph>::vertex_descriptor s,
                         OutputIterator permutation, 
                         ColorMap color, DegreeMap degree)
  {

    std::deque< typename graph_traits<Graph>::vertex_descriptor > vertex_queue;
    vertex_queue.push_front( s );

    return cuthill_mckee_ordering(g, vertex_queue, permutation, color, degree);
  
  }
  

  // This is the version of CM which selects its own starting vertex
  template < class Graph, class OutputIterator, 
             class ColorMap, class DegreeMap>
  OutputIterator 
  cuthill_mckee_ordering(const Graph& G, OutputIterator permutation, 
                         ColorMap color, DegreeMap degree)
  {
    if (boost::graph::has_no_vertices(G))
      return permutation;

    typedef typename boost::graph_traits<Graph>::vertex_descriptor Vertex;
    typedef typename boost::graph_traits<Graph>::vertex_iterator   VerIter;
    typedef typename property_traits<ColorMap>::value_type ColorValue;
    typedef color_traits<ColorValue> Color;

    std::deque<Vertex>      vertex_queue;

    // Mark everything white
    BGL_FORALL_VERTICES_T(v, G, Graph) put(color, v, Color::white());

    // Find one vertex from each connected component 
    BGL_FORALL_VERTICES_T(v, G, Graph) {
      if (get(color, v) == Color::white()) {
        depth_first_visit(G, v, dfs_visitor<>(), color);
        vertex_queue.push_back(v);
      }
    }

    // Find starting nodes for all vertices
    // TBD: How to do this with a directed graph?
    for (typename std::deque<Vertex>::iterator i = vertex_queue.begin();
         i != vertex_queue.end(); ++i)
      *i = find_starting_node(G, *i, color, degree);
    
    return cuthill_mckee_ordering(G, vertex_queue, permutation,
                                  color, degree);
  }

  template<typename Graph, typename OutputIterator, typename VertexIndexMap>
  OutputIterator 
  cuthill_mckee_ordering(const Graph& G, OutputIterator permutation, 
                         VertexIndexMap index_map)
  {
    if (boost::graph::has_no_vertices(G))
      return permutation;
    
    typedef out_degree_property_map<Graph> DegreeMap;
    std::vector<default_color_type> colors(num_vertices(G));
    return cuthill_mckee_ordering(G, permutation, 
                                  make_iterator_property_map(&colors[0], 
                                                             index_map,
                                                             colors[0]),
                                  make_out_degree_map(G));
  }

  template<typename Graph, typename OutputIterator>
  inline OutputIterator 
  cuthill_mckee_ordering(const Graph& G, OutputIterator permutation)
  { return cuthill_mckee_ordering(G, permutation, get(vertex_index, G)); }
} // namespace boost


#endif // BOOST_GRAPH_CUTHILL_MCKEE_HPP