//======================================================================= | |
// Copyright 1997, 1998, 1999, 2000 University of Notre Dame. | |
// Copyright 2004 The Trustees of Indiana University | |
// Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek | |
// | |
// 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_SEQUENTIAL_VERTEX_COLORING_HPP | |
#define BOOST_GRAPH_SEQUENTIAL_VERTEX_COLORING_HPP | |
#include <vector> | |
#include <boost/graph/graph_traits.hpp> | |
#include <boost/tuple/tuple.hpp> | |
#include <boost/property_map/property_map.hpp> | |
#include <boost/limits.hpp> | |
#ifdef BOOST_NO_TEMPLATED_ITERATOR_CONSTRUCTORS | |
# include <iterator> | |
#endif | |
/* This algorithm is to find coloring of a graph | |
Algorithm: | |
Let G = (V,E) be a graph with vertices (somehow) ordered v_1, v_2, ..., | |
v_n. For k = 1, 2, ..., n the sequential algorithm assigns v_k to the | |
smallest possible color. | |
Reference: | |
Thomas F. Coleman and Jorge J. More, Estimation of sparse Jacobian | |
matrices and graph coloring problems. J. Numer. Anal. V20, P187-209, 1983 | |
v_k is stored as o[k] here. | |
The color of the vertex v will be stored in color[v]. | |
i.e., vertex v belongs to coloring color[v] */ | |
namespace boost { | |
template <class VertexListGraph, class OrderPA, class ColorMap> | |
typename property_traits<ColorMap>::value_type | |
sequential_vertex_coloring(const VertexListGraph& G, OrderPA order, | |
ColorMap color) | |
{ | |
typedef graph_traits<VertexListGraph> GraphTraits; | |
typedef typename GraphTraits::vertex_descriptor Vertex; | |
typedef typename property_traits<ColorMap>::value_type size_type; | |
size_type max_color = 0; | |
const size_type V = num_vertices(G); | |
// We need to keep track of which colors are used by | |
// adjacent vertices. We do this by marking the colors | |
// that are used. The mark array contains the mark | |
// for each color. The length of mark is the | |
// number of vertices since the maximum possible number of colors | |
// is the number of vertices. | |
std::vector<size_type> mark(V, | |
std::numeric_limits<size_type>::max BOOST_PREVENT_MACRO_SUBSTITUTION()); | |
//Initialize colors | |
typename GraphTraits::vertex_iterator v, vend; | |
for (boost::tie(v, vend) = vertices(G); v != vend; ++v) | |
put(color, *v, V-1); | |
//Determine the color for every vertex one by one | |
for ( size_type i = 0; i < V; i++) { | |
Vertex current = get(order,i); | |
typename GraphTraits::adjacency_iterator v, vend; | |
//Mark the colors of vertices adjacent to current. | |
//i can be the value for marking since i increases successively | |
for (boost::tie(v,vend) = adjacent_vertices(current, G); v != vend; ++v) | |
mark[get(color,*v)] = i; | |
//Next step is to assign the smallest un-marked color | |
//to the current vertex. | |
size_type j = 0; | |
//Scan through all useable colors, find the smallest possible | |
//color that is not used by neighbors. Note that if mark[j] | |
//is equal to i, color j is used by one of the current vertex's | |
//neighbors. | |
while ( j < max_color && mark[j] == i ) | |
++j; | |
if ( j == max_color ) //All colors are used up. Add one more color | |
++max_color; | |
//At this point, j is the smallest possible color | |
put(color, current, j); //Save the color of vertex current | |
} | |
return max_color; | |
} | |
template<class VertexListGraph, class ColorMap> | |
typename property_traits<ColorMap>::value_type | |
sequential_vertex_coloring(const VertexListGraph& G, ColorMap color) | |
{ | |
typedef typename graph_traits<VertexListGraph>::vertex_descriptor | |
vertex_descriptor; | |
typedef typename graph_traits<VertexListGraph>::vertex_iterator | |
vertex_iterator; | |
std::pair<vertex_iterator, vertex_iterator> v = vertices(G); | |
#ifndef BOOST_NO_TEMPLATED_ITERATOR_CONSTRUCTORS | |
std::vector<vertex_descriptor> order(v.first, v.second); | |
#else | |
std::vector<vertex_descriptor> order; | |
order.reserve(std::distance(v.first, v.second)); | |
while (v.first != v.second) order.push_back(*v.first++); | |
#endif | |
return sequential_vertex_coloring | |
(G, | |
make_iterator_property_map | |
(order.begin(), identity_property_map(), | |
graph_traits<VertexListGraph>::null_vertex()), | |
color); | |
} | |
} | |
#endif |