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- //=======================================================================
- // 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
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