GreedyColoring.h

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#ifndef LIMBO_ALGORITHMS_COLORING_GREEDYCOLORING
#define LIMBO_ALGORITHMS_COLORING_GREEDYCOLORING

#include <iostream>
#include <vector>
#include <set>
#include <map>
#include <boost/graph/graph_concepts.hpp>
using std::cout;
using std::endl;
using std::vector;
using std::set;
using std::map;

namespace limbo 
{ 
namespace algorithms 
{ 
namespace coloring 
{

template <typename GraphType>
class DsatColoring
{
    public:
        typedef GraphType graph_type;
        typedef typename boost::graph_traits<graph_type>::vertex_descriptor graph_vertex_type;

        class saturation_degree_type
        {
            public:
                saturation_degree_type(DsatColoring const& dc) : m_dc(dc) {}

                int saturation_degree(graph_vertex_type const& v) const 
                {
                    set<int> sColor; // used colors 
                    typename boost::graph_traits<graph_type>::out_edge_iterator ite, ite_end;
                    for (boost::tie(ite, ite_end) = boost::out_edges(v, m_dc.m_graph); 
                            ite != ite_end; ++ite)
                    {
                        BOOST_AUTO(found, m_dc.m_mColor.find(boost::target(*ite, m_dc.m_graph)));
                        assert(found != m_dc.m_mColor.end());
                        int color = found->second;
                        if (color >= 0)
                            sColor.insert(color);
                    }

                    return sColor.size();
                }
                bool operator()(graph_vertex_type const& v1, graph_vertex_type const& v2) const
                {
                    return this->saturation_degree(v1) < this->saturation_degree(v2)
                        || boost::out_degree(v1, m_dc.m_graph) < boost::out_degree(v2, m_dc.m_graph);
                }
            protected:
                DsatColoring const& m_dc; 
        };

        DsatColoring(graph_type const& g) : m_graph(g)
        {
            BGL_FORALL_VERTICES_T(v, g, graph_type)
            {
                m_mColor[v] = -1;
            }
        }

        map<graph_vertex_type, int> const& color_map() const {return m_mColor;}
        int color(graph_vertex_type v) const 
        {
            BOOST_AUTO(found, m_mColor.find(v));
            if (found == m_mColor.end()) return -1;
            else return found->second;
        }

        int operator()()
        {
            return this->run();
        }
    protected:
        int run()
        {
            vector<graph_vertex_type> vNode;
            vNode.reserve(boost::num_vertices(m_graph));
            BGL_FORALL_VERTICES_T(v, m_graph, graph_type)
            {
                vNode.push_back(v);
            }

            int color_cnt = 0; // total number of colors used 
            // color assignment starts from 0 to color_cnt-1
            while (!vNode.empty())
            {
                // choose a node
                typename vector<graph_vertex_type>::iterator itv = std::max_element(vNode.begin(), vNode.end(), saturation_degree_type(*this));

                // assign color to current node 
                set<int> sUsedColor; // used colors 
                typename boost::graph_traits<graph_type>::out_edge_iterator ite, ite_end;
                for (boost::tie(ite, ite_end) = boost::out_edges(*itv, m_graph);
                        ite != ite_end; ++ite)
                {
                    int color = m_mColor[boost::target(*ite, m_graph)];
                    sUsedColor.insert(color);
                }
                for (int i = 0; i < color_cnt+1; ++i)
                {
                    if (!sUsedColor.count(i))
                    {
                        m_mColor[*itv] = i;
                        break;
                    }
                }
                assert(m_mColor[*itv] >= 0);
                color_cnt = std::max(color_cnt, 1+m_mColor[*itv]);

                // erase itv 
                *itv = vNode.back();
                vNode.pop_back();
            }

            return color_cnt;
        }

        graph_type const& m_graph; 
        map<graph_vertex_type, int> m_mColor; 

};

} // namespace coloring
} // namespace algorithms
} // namespace limbo
    
#endif