## File: sequential_vertex_coloring.hpp

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boost1.62 1.62.0+dfsg-4
 `123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124` ``````//======================================================================= // 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 #include #include #include #include #ifdef BOOST_NO_TEMPLATED_ITERATOR_CONSTRUCTORS # include #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 typename property_traits::value_type sequential_vertex_coloring(const VertexListGraph& G, OrderPA order, ColorMap color) { typedef graph_traits GraphTraits; typedef typename GraphTraits::vertex_descriptor Vertex; typedef typename property_traits::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 mark(V, std::numeric_limits::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 typename property_traits::value_type sequential_vertex_coloring(const VertexListGraph& G, ColorMap color) { typedef typename graph_traits::vertex_descriptor vertex_descriptor; typedef typename graph_traits::vertex_iterator vertex_iterator; std::pair v = vertices(G); #ifndef BOOST_NO_TEMPLATED_ITERATOR_CONSTRUCTORS std::vector order(v.first, v.second); #else std::vector 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::null_vertex()), color); } } #endif ``````