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
40namespace 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 (boost::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 (boost::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
125

source code of boost/boost/graph/sequential_vertex_coloring.hpp