boost/graph/sequential_vertex_coloring.hpp

   1 //=======================================================================
   2 // Copyright 1997, 1998, 1999, 2000 University of Notre Dame.
   3 // Copyright 2004 The Trustees of Indiana University
   4 // Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek
   5 //
   6 // Distributed under the Boost Software License, Version 1.0. (See
   7 // accompanying file LICENSE_1_0.txt or copy at
   8 // http://www.boost.org/LICENSE_1_0.txt)
   9 //=======================================================================
  10 #ifndef BOOST_GRAPH_SEQUENTIAL_VERTEX_COLORING_HPP
  11 #define BOOST_GRAPH_SEQUENTIAL_VERTEX_COLORING_HPP
  12
  13 #include <vector>
  14 #include <boost/graph/graph_traits.hpp>
  15 #include <boost/tuple/tuple.hpp>
  16 #include <boost/property_map/property_map.hpp>
  17 #include <boost/limits.hpp>
  18
  19 #ifdef BOOST_NO_TEMPLATED_ITERATOR_CONSTRUCTORS
  20 #  include <iterator>
  21 #endif
  22
  23 /* This algorithm is to find coloring of a graph
  24
  25    Algorithm:
  26    Let G = (V,E) be a graph with vertices (somehow) ordered v_1, v_2, ...,
  27    v_n. For k = 1, 2, ..., n the sequential algorithm assigns v_k to the
  28    smallest possible color.
  29
  30    Reference:
  31
  32    Thomas F. Coleman and Jorge J. More, Estimation of sparse Jacobian
  33    matrices and graph coloring problems. J. Numer. Anal. V20, P187-209, 1983
  34
  35    v_k is stored as o[k] here.
  36
  37    The color of the vertex v will be stored in color[v].
  38    i.e., vertex v belongs to coloring color[v] */
  39
  40 namespace boost {
  41   template <class VertexListGraph, class OrderPA, class ColorMap>
  42   typename property_traits<ColorMap>::value_type
  43   sequential_vertex_coloring(const VertexListGraph& G, OrderPA order,
  44                              ColorMap color)
  45   {
  46     typedef graph_traits<VertexListGraph> GraphTraits;
  47     typedef typename GraphTraits::vertex_descriptor Vertex;
  48     typedef typename property_traits<ColorMap>::value_type size_type;
  49
  50     size_type max_color = 0;
  51     const size_type V = num_vertices(G);
  52
  53     // We need to keep track of which colors are used by
  54     // adjacent vertices. We do this by marking the colors
  55     // that are used. The mark array contains the mark
  56     // for each color. The length of mark is the
  57     // number of vertices since the maximum possible number of colors
  58     // is the number of vertices.
  59     std::vector<size_type> mark(V,
  60                                 std::numeric_limits<size_type>::max BOOST_PREVENT_MACRO_SUBSTITUTION());
  61
  62     //Initialize colors
  63     typename GraphTraits::vertex_iterator v, vend;
  64     for (tie(v, vend) = vertices(G); v != vend; ++v)
  65       put(color, *v, V-1);
  66
  67     //Determine the color for every vertex one by one
  68     for ( size_type i = 0; i < V; i++) {
  69       Vertex current = get(order,i);
  70       typename GraphTraits::adjacency_iterator v, vend;
  71
  72       //Mark the colors of vertices adjacent to current.
  73       //i can be the value for marking since i increases successively
  74       for (tie(v,vend) = adjacent_vertices(current, G); v != vend; ++v)
  75         mark[get(color,*v)] = i;
  76
  77       //Next step is to assign the smallest un-marked color
  78       //to the current vertex.
  79       size_type j = 0;
  80
  81       //Scan through all useable colors, find the smallest possible
  82       //color that is not used by neighbors.  Note that if mark[j]
  83       //is equal to i, color j is used by one of the current vertex's
  84       //neighbors.
  85       while ( j < max_color && mark[j] == i )
  86         ++j;
  87
  88       if ( j == max_color )  //All colors are used up. Add one more color
  89         ++max_color;
  90
  91       //At this point, j is the smallest possible color
  92       put(color, current, j);  //Save the color of vertex current
  93     }
  94
  95     return max_color;
  96   }
  97
  98   template<class VertexListGraph, class ColorMap>
  99   typename property_traits<ColorMap>::value_type
 100   sequential_vertex_coloring(const VertexListGraph& G, ColorMap color)
 101   {
 102     typedef typename graph_traits<VertexListGraph>::vertex_descriptor
 103       vertex_descriptor;
 104     typedef typename graph_traits<VertexListGraph>::vertex_iterator
 105       vertex_iterator;
 106
 107     std::pair<vertex_iterator, vertex_iterator> v = vertices(G);
 108 #ifndef BOOST_NO_TEMPLATED_ITERATOR_CONSTRUCTORS
 109     std::vector<vertex_descriptor> order(v.first, v.second);
 110 #else
 111     std::vector<vertex_descriptor> order;
 112     order.reserve(std::distance(v.first, v.second));
 113     while (v.first != v.second) order.push_back(*v.first++);
 114 #endif
 115     return sequential_vertex_coloring
 116              (G,
 117               make_iterator_property_map
 118               (order.begin(), identity_property_map(),
 119                graph_traits<VertexListGraph>::null_vertex()),
 120               color);
 121   }
 122 }
 123
 124 #endif