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boost/graph/sequential_vertex_coloring.hpp

```//=======================================================================
// 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
//
// accompanying file LICENSE_1_0.txt or copy at
//=======================================================================
#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);

//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
```