boost/graph/sequential_vertex_coloring.hpp
//=======================================================================
// Copyright 1997, 1998, 1999, 2000 University of Notre Dame.
// Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek
//
// This file is part of the Boost Graph Library
//
// You should have received a copy of the License Agreement for the
// Boost Graph Library along with the software; see the file LICENSE.
// If not, contact Office of Research, University of Notre Dame, Notre
// Dame, IN 46556.
//
// Permission to modify the code and to distribute modified code is
// granted, provided the text of this NOTICE is retained, a notice that
// the code was modified is included with the above COPYRIGHT NOTICE and
// with the COPYRIGHT NOTICE in the LICENSE file, and that the LICENSE
// file is distributed with the modified code.
//
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// By way of example, but not limitation, Licensor MAKES NO
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// OR OTHER RIGHTS.
//=======================================================================
#ifndef BOOST_GRAPH_SEQUENTIAL_VERTEX_COLORING_HPP
#define BOOST_GRAPH_SEQUENTIAL_VERTEX_COLORING_HPP
#include <vector>
#include <boost/graph/graph_traits.hpp>
/* 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 graph_traits<VertexListGraph>::size_type
sequential_vertex_coloring(const VertexListGraph& G, OrderPA order,
ColorMap color)
{
using graph_traits;
using boost::tie;
typedef graph_traits<VertexListGraph> GraphTraits;
typedef typename GraphTraits::vertex_descriptor Vertex;
typedef typename GraphTraits::size_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, numeric_limits_max(max_color));
//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 which 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;
}
}
#endif