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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 | |
f67539c2 | 20 | #include <iterator> |
7c673cae FG |
21 | #endif |
22 | ||
23 | /* This algorithm is to find coloring of a graph | |
24 | ||
f67539c2 | 25 | Algorithm: |
7c673cae FG |
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 | |
f67539c2 | 28 | smallest possible color. |
7c673cae FG |
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 | ||
f67539c2 | 35 | v_k is stored as o[k] here. |
7c673cae FG |
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 | ||
f67539c2 TL |
40 | namespace boost |
41 | { | |
42 | template < class VertexListGraph, class OrderPA, class ColorMap > | |
43 | typename property_traits< ColorMap >::value_type sequential_vertex_coloring( | |
44 | const VertexListGraph& G, OrderPA order, ColorMap color) | |
45 | { | |
46 | typedef graph_traits< VertexListGraph > GraphTraits; | |
7c673cae | 47 | typedef typename GraphTraits::vertex_descriptor Vertex; |
f67539c2 TL |
48 | typedef typename property_traits< ColorMap >::value_type size_type; |
49 | ||
7c673cae FG |
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. | |
f67539c2 TL |
59 | std::vector< size_type > mark(V, |
60 | std::numeric_limits< size_type >::max | |
61 | BOOST_PREVENT_MACRO_SUBSTITUTION()); | |
62 | ||
63 | // Initialize colors | |
7c673cae FG |
64 | typename GraphTraits::vertex_iterator v, vend; |
65 | for (boost::tie(v, vend) = vertices(G); v != vend; ++v) | |
f67539c2 TL |
66 | put(color, *v, V - 1); |
67 | ||
68 | // Determine the color for every vertex one by one | |
69 | for (size_type i = 0; i < V; i++) | |
70 | { | |
71 | Vertex current = get(order, i); | |
72 | typename GraphTraits::adjacency_iterator v, vend; | |
73 | ||
74 | // Mark the colors of vertices adjacent to current. | |
75 | // i can be the value for marking since i increases successively | |
76 | for (boost::tie(v, vend) = adjacent_vertices(current, G); v != vend; | |
77 | ++v) | |
78 | mark[get(color, *v)] = i; | |
79 | ||
80 | // Next step is to assign the smallest un-marked color | |
81 | // to the current vertex. | |
82 | size_type j = 0; | |
83 | ||
84 | // Scan through all useable colors, find the smallest possible | |
85 | // color that is not used by neighbors. Note that if mark[j] | |
86 | // is equal to i, color j is used by one of the current vertex's | |
87 | // neighbors. | |
88 | while (j < max_color && mark[j] == i) | |
89 | ++j; | |
90 | ||
91 | if (j == max_color) // All colors are used up. Add one more color | |
92 | ++max_color; | |
93 | ||
94 | // At this point, j is the smallest possible color | |
95 | put(color, current, j); // Save the color of vertex current | |
7c673cae | 96 | } |
f67539c2 | 97 | |
7c673cae | 98 | return max_color; |
f67539c2 TL |
99 | } |
100 | ||
101 | template < class VertexListGraph, class ColorMap > | |
102 | typename property_traits< ColorMap >::value_type sequential_vertex_coloring( | |
103 | const VertexListGraph& G, ColorMap color) | |
104 | { | |
105 | typedef typename graph_traits< VertexListGraph >::vertex_descriptor | |
106 | vertex_descriptor; | |
107 | typedef typename graph_traits< VertexListGraph >::vertex_iterator | |
108 | vertex_iterator; | |
109 | ||
110 | std::pair< vertex_iterator, vertex_iterator > v = vertices(G); | |
7c673cae | 111 | #ifndef BOOST_NO_TEMPLATED_ITERATOR_CONSTRUCTORS |
f67539c2 | 112 | std::vector< vertex_descriptor > order(v.first, v.second); |
7c673cae | 113 | #else |
f67539c2 | 114 | std::vector< vertex_descriptor > order; |
7c673cae | 115 | order.reserve(std::distance(v.first, v.second)); |
f67539c2 TL |
116 | while (v.first != v.second) |
117 | order.push_back(*v.first++); | |
7c673cae | 118 | #endif |
f67539c2 TL |
119 | return sequential_vertex_coloring(G, |
120 | make_iterator_property_map(order.begin(), identity_property_map(), | |
121 | graph_traits< VertexListGraph >::null_vertex()), | |
122 | color); | |
123 | } | |
7c673cae FG |
124 | } |
125 | ||
126 | #endif |