//=======================================================================
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// Copyright 1997, 1998, 1999, 2000 University of Notre Dame.
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// Copyright 2004 The Trustees of Indiana University
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// Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek
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//
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// Distributed under the Boost Software License, Version 1.0. (See
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// accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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//=======================================================================
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#ifndef BOOST_GRAPH_SEQUENTIAL_VERTEX_COLORING_HPP
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#define BOOST_GRAPH_SEQUENTIAL_VERTEX_COLORING_HPP
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#include <vector>
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#include <boost/graph/graph_traits.hpp>
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#include <boost/tuple/tuple.hpp>
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#include <boost/property_map/property_map.hpp>
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#include <boost/limits.hpp>
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#ifdef BOOST_NO_TEMPLATED_ITERATOR_CONSTRUCTORS
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#include <iterator>
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#endif
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/* This algorithm is to find coloring of a graph
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Algorithm:
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Let G = (V,E) be a graph with vertices (somehow) ordered v_1, v_2, ...,
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v_n. For k = 1, 2, ..., n the sequential algorithm assigns v_k to the
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smallest possible color.
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Reference:
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Thomas F. Coleman and Jorge J. More, Estimation of sparse Jacobian
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matrices and graph coloring problems. J. Numer. Anal. V20, P187-209, 1983
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v_k is stored as o[k] here.
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The color of the vertex v will be stored in color[v].
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i.e., vertex v belongs to coloring color[v] */
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namespace boost
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{
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template < class VertexListGraph, class OrderPA, class ColorMap >
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typename property_traits< ColorMap >::value_type sequential_vertex_coloring(
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const VertexListGraph& G, OrderPA order, ColorMap color)
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{
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typedef graph_traits< VertexListGraph > GraphTraits;
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typedef typename GraphTraits::vertex_descriptor Vertex;
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typedef typename property_traits< ColorMap >::value_type size_type;
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size_type max_color = 0;
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const size_type V = num_vertices(G);
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// We need to keep track of which colors are used by
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// adjacent vertices. We do this by marking the colors
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// that are used. The mark array contains the mark
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// for each color. The length of mark is the
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// number of vertices since the maximum possible number of colors
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// is the number of vertices.
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std::vector< size_type > mark(V,
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std::numeric_limits< size_type >::max
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BOOST_PREVENT_MACRO_SUBSTITUTION());
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// Initialize colors
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typename GraphTraits::vertex_iterator v, vend;
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for (boost::tie(v, vend) = vertices(G); v != vend; ++v)
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put(color, *v, V - 1);
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// Determine the color for every vertex one by one
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for (size_type i = 0; i < V; i++)
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{
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Vertex current = get(order, i);
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typename GraphTraits::adjacency_iterator v, vend;
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// Mark the colors of vertices adjacent to current.
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// i can be the value for marking since i increases successively
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for (boost::tie(v, vend) = adjacent_vertices(current, G); v != vend;
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++v)
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mark[get(color, *v)] = i;
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// Next step is to assign the smallest un-marked color
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// to the current vertex.
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size_type j = 0;
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// Scan through all useable colors, find the smallest possible
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// color that is not used by neighbors. Note that if mark[j]
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// is equal to i, color j is used by one of the current vertex's
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// neighbors.
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while (j < max_color && mark[j] == i)
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++j;
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if (j == max_color) // All colors are used up. Add one more color
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++max_color;
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// At this point, j is the smallest possible color
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put(color, current, j); // Save the color of vertex current
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}
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return max_color;
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}
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template < class VertexListGraph, class ColorMap >
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typename property_traits< ColorMap >::value_type sequential_vertex_coloring(
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const VertexListGraph& G, ColorMap color)
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{
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typedef typename graph_traits< VertexListGraph >::vertex_descriptor
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vertex_descriptor;
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typedef typename graph_traits< VertexListGraph >::vertex_iterator
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vertex_iterator;
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std::pair< vertex_iterator, vertex_iterator > v = vertices(G);
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#ifndef BOOST_NO_TEMPLATED_ITERATOR_CONSTRUCTORS
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std::vector< vertex_descriptor > order(v.first, v.second);
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#else
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std::vector< vertex_descriptor > order;
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order.reserve(std::distance(v.first, v.second));
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while (v.first != v.second)
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order.push_back(*v.first++);
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#endif
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return sequential_vertex_coloring(G,
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make_iterator_property_map(order.begin(), identity_property_map(),
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graph_traits< VertexListGraph >::null_vertex()),
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color);
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}
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}
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#endif
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