boost/graph/bipartite.hpp

/**
 *
 * Copyright (c) 2010 Matthias Walter (xammy@xammy.homelinux.net)
 *
 * Authors: Matthias Walter
 *
 * 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_BIPARTITE_HPP
#define BOOST_GRAPH_BIPARTITE_HPP

#include <utility>
#include <vector>
#include <exception>
#include <boost/graph/properties.hpp>
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/depth_first_search.hpp>
#include <boost/graph/one_bit_color_map.hpp>
#include <boost/bind.hpp>

namespace boost
{

namespace detail
{

    /**
     * The bipartite_visitor_error is thrown if an edge cannot be colored.
     * The witnesses are the edges incident vertices.
     */

    template < typename Vertex >
    struct BOOST_SYMBOL_VISIBLE bipartite_visitor_error : std::exception
    {
        std::pair< Vertex, Vertex > witnesses;

        bipartite_visitor_error(Vertex a, Vertex b) : witnesses(a, b) {}

        const char* what() const throw() { return "Graph is not bipartite."; }
    };

    /**
     * Functor which colors edges to be non-monochromatic.
     */

    template < typename PartitionMap > struct bipartition_colorize
    {
        typedef on_tree_edge event_filter;

        bipartition_colorize(PartitionMap partition_map)
        : partition_map_(partition_map)
        {
        }

        template < typename Edge, typename Graph >
        void operator()(Edge e, const Graph& g)
        {
            typedef typename graph_traits< Graph >::vertex_descriptor
                vertex_descriptor_t;
            typedef color_traits<
                typename property_traits< PartitionMap >::value_type >
                color_traits;

            vertex_descriptor_t source_vertex = source(e, g);
            vertex_descriptor_t target_vertex = target(e, g);
            if (get(partition_map_, source_vertex) == color_traits::white())
                put(partition_map_, target_vertex, color_traits::black());
            else
                put(partition_map_, target_vertex, color_traits::white());
        }

    private:
        PartitionMap partition_map_;
    };

    /**
     * Creates a bipartition_colorize functor which colors edges
     * to be non-monochromatic.
     *
     * @param partition_map Color map for the bipartition
     * @return The functor.
     */

    template < typename PartitionMap >
    inline bipartition_colorize< PartitionMap > colorize_bipartition(
        PartitionMap partition_map)
    {
        return bipartition_colorize< PartitionMap >(partition_map);
    }

    /**
     * Functor which tests an edge to be monochromatic.
     */

    template < typename PartitionMap > struct bipartition_check
    {
        typedef on_back_edge event_filter;

        bipartition_check(PartitionMap partition_map)
        : partition_map_(partition_map)
        {
        }

        template < typename Edge, typename Graph >
        void operator()(Edge e, const Graph& g)
        {
            typedef typename graph_traits< Graph >::vertex_descriptor
                vertex_descriptor_t;

            vertex_descriptor_t source_vertex = source(e, g);
            vertex_descriptor_t target_vertex = target(e, g);
            if (get(partition_map_, source_vertex)
                == get(partition_map_, target_vertex))
                throw bipartite_visitor_error< vertex_descriptor_t >(
                    source_vertex, target_vertex);
        }

    private:
        PartitionMap partition_map_;
    };

    /**
     * Creates a bipartition_check functor which raises an error if a
     * monochromatic edge is found.
     *
     * @param partition_map The map for a bipartition.
     * @return The functor.
     */

    template < typename PartitionMap >
    inline bipartition_check< PartitionMap > check_bipartition(
        PartitionMap partition_map)
    {
        return bipartition_check< PartitionMap >(partition_map);
    }

    /**
     * Find the beginning of a common suffix of two sequences
     *
     * @param sequence1 Pair of bidirectional iterators defining the first
     * sequence.
     * @param sequence2 Pair of bidirectional iterators defining the second
     * sequence.
     * @return Pair of iterators pointing to the beginning of the common suffix.
     */

    template < typename BiDirectionalIterator1,
        typename BiDirectionalIterator2 >
    inline std::pair< BiDirectionalIterator1, BiDirectionalIterator2 >
    reverse_mismatch(
        std::pair< BiDirectionalIterator1, BiDirectionalIterator1 > sequence1,
        std::pair< BiDirectionalIterator2, BiDirectionalIterator2 > sequence2)
    {
        if (sequence1.first == sequence1.second
            || sequence2.first == sequence2.second)
            return std::make_pair(sequence1.first, sequence2.first);

        BiDirectionalIterator1 iter1 = sequence1.second;
        BiDirectionalIterator2 iter2 = sequence2.second;

        while (true)
        {
            --iter1;
            --iter2;
            if (*iter1 != *iter2)
            {
                ++iter1;
                ++iter2;
                break;
            }
            if (iter1 == sequence1.first)
                break;
            if (iter2 == sequence2.first)
                break;
        }

        return std::make_pair(iter1, iter2);
    }

}

/**
 * Checks a given graph for bipartiteness and fills the given color map with
 * white and black according to the bipartition. If the graph is not
 * bipartite, the contents of the color map are undefined. Runs in linear
 * time in the size of the graph, if access to the property maps is in
 * constant time.
 *
 * @param graph The given graph.
 * @param index_map An index map associating vertices with an index.
 * @param partition_map A color map to fill with the bipartition.
 * @return true if and only if the given graph is bipartite.
 */

template < typename Graph, typename IndexMap, typename PartitionMap >
bool is_bipartite(
    const Graph& graph, const IndexMap index_map, PartitionMap partition_map)
{
    /// General types and variables
    typedef
        typename property_traits< PartitionMap >::value_type partition_color_t;
    typedef
        typename graph_traits< Graph >::vertex_descriptor vertex_descriptor_t;

    /// Declare dfs visitor
    //    detail::empty_recorder recorder;
    //    typedef detail::bipartite_visitor <PartitionMap,
    //    detail::empty_recorder> dfs_visitor_t; dfs_visitor_t dfs_visitor
    //    (partition_map, recorder);

    /// Call dfs
    try
    {
        depth_first_search(graph,
            vertex_index_map(index_map).visitor(make_dfs_visitor(
                std::make_pair(detail::colorize_bipartition(partition_map),
                    std::make_pair(detail::check_bipartition(partition_map),
                        put_property(partition_map,
                            color_traits< partition_color_t >::white(),
                            on_start_vertex()))))));
    }
    catch (const detail::bipartite_visitor_error< vertex_descriptor_t >&)
    {
        return false;
    }

    return true;
}

/**
 * Checks a given graph for bipartiteness.
 *
 * @param graph The given graph.
 * @param index_map An index map associating vertices with an index.
 * @return true if and only if the given graph is bipartite.
 */

template < typename Graph, typename IndexMap >
bool is_bipartite(const Graph& graph, const IndexMap index_map)
{
    typedef one_bit_color_map< IndexMap > partition_map_t;
    partition_map_t partition_map(num_vertices(graph), index_map);

    return is_bipartite(graph, index_map, partition_map);
}

/**
 * Checks a given graph for bipartiteness. The graph must
 * have an internal vertex_index property. Runs in linear time in the
 * size of the graph, if access to the property maps is in constant time.
 *
 * @param graph The given graph.
 * @return true if and only if the given graph is bipartite.
 */

template < typename Graph > bool is_bipartite(const Graph& graph)
{
    return is_bipartite(graph, get(vertex_index, graph));
}

/**
 * Checks a given graph for bipartiteness and fills a given color map with
 * white and black according to the bipartition. If the graph is not
 * bipartite, a sequence of vertices, producing an odd-cycle, is written to
 * the output iterator. The final iterator value is returned. Runs in linear
 * time in the size of the graph, if access to the property maps is in
 * constant time.
 *
 * @param graph The given graph.
 * @param index_map An index map associating vertices with an index.
 * @param partition_map A color map to fill with the bipartition.
 * @param result An iterator to write the odd-cycle vertices to.
 * @return The final iterator value after writing.
 */

template < typename Graph, typename IndexMap, typename PartitionMap,
    typename OutputIterator >
OutputIterator find_odd_cycle(const Graph& graph, const IndexMap index_map,
    PartitionMap partition_map, OutputIterator result)
{
    /// General types and variables
    typedef
        typename property_traits< PartitionMap >::value_type partition_color_t;
    typedef
        typename graph_traits< Graph >::vertex_descriptor vertex_descriptor_t;
    typedef typename graph_traits< Graph >::vertex_iterator vertex_iterator_t;
    vertex_iterator_t vertex_iter, vertex_end;

    /// Declare predecessor map
    typedef std::vector< vertex_descriptor_t > predecessors_t;
    typedef iterator_property_map< typename predecessors_t::iterator, IndexMap,
        vertex_descriptor_t, vertex_descriptor_t& >
        predecessor_map_t;

    predecessors_t predecessors(
        num_vertices(graph), graph_traits< Graph >::null_vertex());
    predecessor_map_t predecessor_map(predecessors.begin(), index_map);

    /// Initialize predecessor map
    for (boost::tie(vertex_iter, vertex_end) = vertices(graph);
         vertex_iter != vertex_end; ++vertex_iter)
    {
        put(predecessor_map, *vertex_iter, *vertex_iter);
    }

    /// Call dfs
    try
    {
        depth_first_search(graph,
            vertex_index_map(index_map).visitor(make_dfs_visitor(
                std::make_pair(detail::colorize_bipartition(partition_map),
                    std::make_pair(detail::check_bipartition(partition_map),
                        std::make_pair(
                            put_property(partition_map,
                                color_traits< partition_color_t >::white(),
                                on_start_vertex()),
                            record_predecessors(
                                predecessor_map, on_tree_edge())))))));
    }
    catch (const detail::bipartite_visitor_error< vertex_descriptor_t >& error)
    {
        typedef std::vector< vertex_descriptor_t > path_t;

        path_t path1, path2;
        vertex_descriptor_t next, current;

        /// First path
        next = error.witnesses.first;
        do
        {
            current = next;
            path1.push_back(current);
            next = predecessor_map[current];
        } while (current != next);

        /// Second path
        next = error.witnesses.second;
        do
        {
            current = next;
            path2.push_back(current);
            next = predecessor_map[current];
        } while (current != next);

        /// Find beginning of common suffix
        std::pair< typename path_t::iterator, typename path_t::iterator >
            mismatch = detail::reverse_mismatch(
                std::make_pair(path1.begin(), path1.end()),
                std::make_pair(path2.begin(), path2.end()));

        /// Copy the odd-length cycle
        result = std::copy(path1.begin(), mismatch.first + 1, result);
        return std::reverse_copy(path2.begin(), mismatch.second, result);
    }

    return result;
}

/**
 * Checks a given graph for bipartiteness. If the graph is not bipartite, a
 * sequence of vertices, producing an odd-cycle, is written to the output
 * iterator. The final iterator value is returned. Runs in linear time in the
 * size of the graph, if access to the property maps is in constant time.
 *
 * @param graph The given graph.
 * @param index_map An index map associating vertices with an index.
 * @param result An iterator to write the odd-cycle vertices to.
 * @return The final iterator value after writing.
 */

template < typename Graph, typename IndexMap, typename OutputIterator >
OutputIterator find_odd_cycle(
    const Graph& graph, const IndexMap index_map, OutputIterator result)
{
    typedef one_bit_color_map< IndexMap > partition_map_t;
    partition_map_t partition_map(num_vertices(graph), index_map);

    return find_odd_cycle(graph, index_map, partition_map, result);
}

/**
 * Checks a given graph for bipartiteness. If the graph is not bipartite, a
 * sequence of vertices, producing an odd-cycle, is written to the output
 * iterator. The final iterator value is returned. The graph must have an
 * internal vertex_index property. Runs in linear time in the size of the
 * graph, if access to the property maps is in constant time.
 *
 * @param graph The given graph.
 * @param result An iterator to write the odd-cycle vertices to.
 * @return The final iterator value after writing.
 */

template < typename Graph, typename OutputIterator >
OutputIterator find_odd_cycle(const Graph& graph, OutputIterator result)
{
    return find_odd_cycle(graph, get(vertex_index, graph), result);
}
}

#endif /// BOOST_GRAPH_BIPARTITE_HPP