| //======================================================================= |
| // 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 (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 (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 |