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