Chris@16: /**
Chris@16:  *
Chris@16:  * Copyright (c) 2010 Matthias Walter (xammy@xammy.homelinux.net)
Chris@16:  *
Chris@16:  * Authors: Matthias Walter
Chris@16:  *
Chris@16:  * Distributed under the Boost Software License, Version 1.0. (See
Chris@16:  * accompanying file LICENSE_1_0.txt or copy at
Chris@16:  * http://www.boost.org/LICENSE_1_0.txt)
Chris@16:  *
Chris@16:  */
Chris@16: 
Chris@16: #ifndef BOOST_GRAPH_BIPARTITE_HPP
Chris@16: #define BOOST_GRAPH_BIPARTITE_HPP
Chris@16: 
Chris@16: #include <utility>
Chris@16: #include <vector>
Chris@16: #include <exception>
Chris@16: #include <boost/graph/properties.hpp>
Chris@16: #include <boost/graph/adjacency_list.hpp>
Chris@16: #include <boost/graph/depth_first_search.hpp>
Chris@16: #include <boost/graph/one_bit_color_map.hpp>
Chris@16: #include <boost/bind.hpp>
Chris@16: 
Chris@16: namespace boost {
Chris@16: 
Chris@16:   namespace detail {
Chris@16: 
Chris@16:     /**
Chris@16:      * The bipartite_visitor_error is thrown if an edge cannot be colored.
Chris@16:      * The witnesses are the edges incident vertices.
Chris@16:      */
Chris@16: 
Chris@16:     template <typename Vertex>
Chris@16:     struct bipartite_visitor_error: std::exception
Chris@16:     {
Chris@16:       std::pair <Vertex, Vertex> witnesses;
Chris@16: 
Chris@16:       bipartite_visitor_error (Vertex a, Vertex b) :
Chris@16:         witnesses (a, b)
Chris@16:       {
Chris@16: 
Chris@16:       }
Chris@16: 
Chris@16:       const char* what () const throw ()
Chris@16:       {
Chris@16:         return "Graph is not bipartite.";
Chris@16:       }
Chris@16:     };
Chris@16: 
Chris@16:     /**
Chris@16:      * Functor which colors edges to be non-monochromatic.
Chris@16:      */
Chris@16: 
Chris@16:     template <typename PartitionMap>
Chris@16:     struct bipartition_colorize
Chris@16:     {
Chris@16:       typedef on_tree_edge event_filter;
Chris@16: 
Chris@16:       bipartition_colorize (PartitionMap partition_map) :
Chris@16:         partition_map_ (partition_map)
Chris@16:       {
Chris@16: 
Chris@16:       }
Chris@16: 
Chris@16:       template <typename Edge, typename Graph>
Chris@16:       void operator() (Edge e, const Graph& g)
Chris@16:       {
Chris@16:         typedef typename graph_traits <Graph>::vertex_descriptor vertex_descriptor_t;
Chris@16:         typedef color_traits <typename property_traits <PartitionMap>::value_type> color_traits;
Chris@16: 
Chris@16:         vertex_descriptor_t source_vertex = source (e, g);
Chris@16:         vertex_descriptor_t target_vertex = target (e, g);
Chris@16:         if (get (partition_map_, source_vertex) == color_traits::white ())
Chris@16:           put (partition_map_, target_vertex, color_traits::black ());
Chris@16:         else
Chris@16:           put (partition_map_, target_vertex, color_traits::white ());
Chris@16:       }
Chris@16: 
Chris@16:     private:
Chris@16:       PartitionMap partition_map_;
Chris@16:     };
Chris@16: 
Chris@16:     /**
Chris@16:      * Creates a bipartition_colorize functor which colors edges
Chris@16:      * to be non-monochromatic.
Chris@16:      *
Chris@16:      * @param partition_map Color map for the bipartition
Chris@16:      * @return The functor.
Chris@16:      */
Chris@16: 
Chris@16:     template <typename PartitionMap>
Chris@16:     inline bipartition_colorize <PartitionMap> colorize_bipartition (PartitionMap partition_map)
Chris@16:     {
Chris@16:       return bipartition_colorize <PartitionMap> (partition_map);
Chris@16:     }
Chris@16: 
Chris@16:     /**
Chris@16:      * Functor which tests an edge to be monochromatic.
Chris@16:      */
Chris@16: 
Chris@16:     template <typename PartitionMap>
Chris@16:     struct bipartition_check
Chris@16:     {
Chris@16:       typedef on_back_edge event_filter;
Chris@16: 
Chris@16:       bipartition_check (PartitionMap partition_map) :
Chris@16:         partition_map_ (partition_map)
Chris@16:       {
Chris@16: 
Chris@16:       }
Chris@16: 
Chris@16:       template <typename Edge, typename Graph>
Chris@16:       void operator() (Edge e, const Graph& g)
Chris@16:       {
Chris@16:         typedef typename graph_traits <Graph>::vertex_descriptor vertex_descriptor_t;
Chris@16: 
Chris@16:         vertex_descriptor_t source_vertex = source (e, g);
Chris@16:         vertex_descriptor_t target_vertex = target (e, g);
Chris@16:         if (get (partition_map_, source_vertex) == get (partition_map_, target_vertex))
Chris@16:           throw bipartite_visitor_error <vertex_descriptor_t> (source_vertex, target_vertex);
Chris@16:       }
Chris@16: 
Chris@16:     private:
Chris@16:       PartitionMap partition_map_;
Chris@16:     };
Chris@16: 
Chris@16:     /**
Chris@16:      * Creates a bipartition_check functor which raises an error if a
Chris@16:      * monochromatic edge is found.
Chris@16:      *
Chris@16:      * @param partition_map The map for a bipartition.
Chris@16:      * @return The functor.
Chris@16:      */
Chris@16: 
Chris@16:     template <typename PartitionMap>
Chris@16:     inline bipartition_check <PartitionMap> check_bipartition (PartitionMap partition_map)
Chris@16:     {
Chris@16:       return bipartition_check <PartitionMap> (partition_map);
Chris@16:     }
Chris@16: 
Chris@16:     /**
Chris@16:      * Find the beginning of a common suffix of two sequences
Chris@16:      * 
Chris@16:      * @param sequence1 Pair of bidirectional iterators defining the first sequence.
Chris@16:      * @param sequence2 Pair of bidirectional iterators defining the second sequence.
Chris@16:      * @return Pair of iterators pointing to the beginning of the common suffix.
Chris@16:      */
Chris@16: 
Chris@16:     template <typename BiDirectionalIterator1, typename BiDirectionalIterator2>
Chris@16:     inline std::pair <BiDirectionalIterator1, BiDirectionalIterator2> reverse_mismatch (std::pair <
Chris@16:         BiDirectionalIterator1, BiDirectionalIterator1> sequence1, std::pair <BiDirectionalIterator2,
Chris@16:         BiDirectionalIterator2> sequence2)
Chris@16:     {
Chris@16:       if (sequence1.first == sequence1.second || sequence2.first == sequence2.second)
Chris@16:         return std::make_pair (sequence1.first, sequence2.first);
Chris@16: 
Chris@16:       BiDirectionalIterator1 iter1 = sequence1.second;
Chris@16:       BiDirectionalIterator2 iter2 = sequence2.second;
Chris@16: 
Chris@16:       while (true)
Chris@16:       {
Chris@16:         --iter1;
Chris@16:         --iter2;
Chris@16:         if (*iter1 != *iter2)
Chris@16:         {
Chris@16:           ++iter1;
Chris@16:           ++iter2;
Chris@16:           break;
Chris@16:         }
Chris@16:         if (iter1 == sequence1.first)
Chris@16:           break;
Chris@16:         if (iter2 == sequence2.first)
Chris@16:           break;
Chris@16:       }
Chris@16: 
Chris@16:       return std::make_pair (iter1, iter2);
Chris@16:     }
Chris@16: 
Chris@16:   }
Chris@16: 
Chris@16:   /**
Chris@16:    * Checks a given graph for bipartiteness and fills the given color map with
Chris@16:    * white and black according to the bipartition. If the graph is not
Chris@16:    * bipartite, the contents of the color map are undefined. Runs in linear
Chris@16:    * time in the size of the graph, if access to the property maps is in
Chris@16:    * constant time.
Chris@16:    *
Chris@16:    * @param graph The given graph.
Chris@16:    * @param index_map An index map associating vertices with an index.
Chris@16:    * @param partition_map A color map to fill with the bipartition.
Chris@16:    * @return true if and only if the given graph is bipartite.
Chris@16:    */
Chris@16: 
Chris@16:   template <typename Graph, typename IndexMap, typename PartitionMap>
Chris@16:   bool is_bipartite (const Graph& graph, const IndexMap index_map, PartitionMap partition_map)
Chris@16:   {
Chris@16:     /// General types and variables
Chris@16:     typedef typename property_traits <PartitionMap>::value_type partition_color_t;
Chris@16:     typedef typename graph_traits <Graph>::vertex_descriptor vertex_descriptor_t;
Chris@16: 
Chris@16:     /// Declare dfs visitor
Chris@16:     //    detail::empty_recorder recorder;
Chris@16:     //    typedef detail::bipartite_visitor <PartitionMap, detail::empty_recorder> dfs_visitor_t;
Chris@16:     //    dfs_visitor_t dfs_visitor (partition_map, recorder);
Chris@16: 
Chris@16: 
Chris@16:     /// Call dfs
Chris@16:     try
Chris@16:     {
Chris@16:       depth_first_search (graph, vertex_index_map (index_map).visitor (make_dfs_visitor (std::make_pair (
Chris@16:           detail::colorize_bipartition (partition_map), std::make_pair (detail::check_bipartition (partition_map),
Chris@16:               put_property (partition_map, color_traits <partition_color_t>::white (), on_start_vertex ()))))));
Chris@16:     }
Chris@16:     catch (detail::bipartite_visitor_error <vertex_descriptor_t> error)
Chris@16:     {
Chris@16:       return false;
Chris@16:     }
Chris@16: 
Chris@16:     return true;
Chris@16:   }
Chris@16: 
Chris@16:   /**
Chris@16:    * Checks a given graph for bipartiteness.
Chris@16:    *
Chris@16:    * @param graph The given graph.
Chris@16:    * @param index_map An index map associating vertices with an index.
Chris@16:    * @return true if and only if the given graph is bipartite.
Chris@16:    */
Chris@16: 
Chris@16:   template <typename Graph, typename IndexMap>
Chris@16:   bool is_bipartite (const Graph& graph, const IndexMap index_map)
Chris@16:   {
Chris@16:     typedef one_bit_color_map <IndexMap> partition_map_t;
Chris@16:     partition_map_t partition_map (num_vertices (graph), index_map);
Chris@16: 
Chris@16:     return is_bipartite (graph, index_map, partition_map);
Chris@16:   }
Chris@16: 
Chris@16:   /**
Chris@16:    * Checks a given graph for bipartiteness. The graph must
Chris@16:    * have an internal vertex_index property. Runs in linear time in the
Chris@16:    * size of the graph, if access to the property maps is in constant time.
Chris@16:    *
Chris@16:    * @param graph The given graph.
Chris@16:    * @return true if and only if the given graph is bipartite.
Chris@16:    */
Chris@16: 
Chris@16:   template <typename Graph>
Chris@16:   bool is_bipartite (const Graph& graph)
Chris@16:   {
Chris@16:     return is_bipartite (graph, get (vertex_index, graph));
Chris@16:   }
Chris@16: 
Chris@16:   /**
Chris@16:    * Checks a given graph for bipartiteness and fills a given color map with
Chris@16:    * white and black according to the bipartition. If the graph is not
Chris@16:    * bipartite, a sequence of vertices, producing an odd-cycle, is written to
Chris@16:    * the output iterator. The final iterator value is returned. Runs in linear
Chris@16:    * time in the size of the graph, if access to the property maps is in
Chris@16:    * constant time.
Chris@16:    *
Chris@16:    * @param graph The given graph.
Chris@16:    * @param index_map An index map associating vertices with an index.
Chris@16:    * @param partition_map A color map to fill with the bipartition.
Chris@16:    * @param result An iterator to write the odd-cycle vertices to.
Chris@16:    * @return The final iterator value after writing.
Chris@16:    */
Chris@16: 
Chris@16:   template <typename Graph, typename IndexMap, typename PartitionMap, typename OutputIterator>
Chris@16:   OutputIterator find_odd_cycle (const Graph& graph, const IndexMap index_map, PartitionMap partition_map,
Chris@16:       OutputIterator result)
Chris@16:   {
Chris@16:     /// General types and variables
Chris@16:     typedef typename property_traits <PartitionMap>::value_type partition_color_t;
Chris@16:     typedef typename graph_traits <Graph>::vertex_descriptor vertex_descriptor_t;
Chris@16:     typedef typename graph_traits <Graph>::vertex_iterator vertex_iterator_t;
Chris@16:     vertex_iterator_t vertex_iter, vertex_end;
Chris@16: 
Chris@16:     /// Declare predecessor map
Chris@16:     typedef std::vector <vertex_descriptor_t> predecessors_t;
Chris@16:     typedef iterator_property_map <typename predecessors_t::iterator, IndexMap, vertex_descriptor_t,
Chris@16:         vertex_descriptor_t&> predecessor_map_t;
Chris@16: 
Chris@16:     predecessors_t predecessors (num_vertices (graph), graph_traits <Graph>::null_vertex ());
Chris@16:     predecessor_map_t predecessor_map (predecessors.begin (), index_map);
Chris@16: 
Chris@16:     /// Initialize predecessor map
Chris@16:     for (boost::tie (vertex_iter, vertex_end) = vertices (graph); vertex_iter != vertex_end; ++vertex_iter)
Chris@16:     {
Chris@16:       put (predecessor_map, *vertex_iter, *vertex_iter);
Chris@16:     }
Chris@16: 
Chris@16:     /// Call dfs
Chris@16:     try
Chris@16:     {
Chris@16:       depth_first_search (graph, vertex_index_map (index_map).visitor (make_dfs_visitor (std::make_pair (
Chris@16:           detail::colorize_bipartition (partition_map), std::make_pair (detail::check_bipartition (partition_map),
Chris@16:               std::make_pair (put_property (partition_map, color_traits <partition_color_t>::white (),
Chris@16:                   on_start_vertex ()), record_predecessors (predecessor_map, on_tree_edge ())))))));
Chris@16:     }
Chris@16:     catch (detail::bipartite_visitor_error <vertex_descriptor_t> error)
Chris@16:     {
Chris@16:       typedef std::vector <vertex_descriptor_t> path_t;
Chris@16: 
Chris@16:       path_t path1, path2;
Chris@16:       vertex_descriptor_t next, current;
Chris@16: 
Chris@16:       /// First path
Chris@16:       next = error.witnesses.first;
Chris@16:       do
Chris@16:       {
Chris@16:         current = next;
Chris@16:         path1.push_back (current);
Chris@16:         next = predecessor_map[current];
Chris@16:       }
Chris@16:       while (current != next);
Chris@16: 
Chris@16:       /// Second path
Chris@16:       next = error.witnesses.second;
Chris@16:       do
Chris@16:       {
Chris@16:         current = next;
Chris@16:         path2.push_back (current);
Chris@16:         next = predecessor_map[current];
Chris@16:       }
Chris@16:       while (current != next);
Chris@16: 
Chris@16:       /// Find beginning of common suffix
Chris@16:       std::pair <typename path_t::iterator, typename path_t::iterator> mismatch = detail::reverse_mismatch (
Chris@16:           std::make_pair (path1.begin (), path1.end ()), std::make_pair (path2.begin (), path2.end ()));
Chris@16: 
Chris@16:       /// Copy the odd-length cycle
Chris@16:       result = std::copy (path1.begin (), mismatch.first + 1, result);
Chris@16:       return std::reverse_copy (path2.begin (), mismatch.second, result);
Chris@16:     }
Chris@16: 
Chris@16:     return result;
Chris@16:   }
Chris@16: 
Chris@16:   /**
Chris@16:    * Checks a given graph for bipartiteness. If the graph is not bipartite, a
Chris@16:    * sequence of vertices, producing an odd-cycle, is written to the output
Chris@16:    * iterator. The final iterator value is returned. Runs in linear time in the
Chris@16:    * size of the graph, if access to the property maps is in constant time.
Chris@16:    *
Chris@16:    * @param graph The given graph.
Chris@16:    * @param index_map An index map associating vertices with an index.
Chris@16:    * @param result An iterator to write the odd-cycle vertices to.
Chris@16:    * @return The final iterator value after writing.
Chris@16:    */
Chris@16: 
Chris@16:   template <typename Graph, typename IndexMap, typename OutputIterator>
Chris@16:   OutputIterator find_odd_cycle (const Graph& graph, const IndexMap index_map, OutputIterator result)
Chris@16:   {
Chris@16:     typedef one_bit_color_map <IndexMap> partition_map_t;
Chris@16:     partition_map_t partition_map (num_vertices (graph), index_map);
Chris@16: 
Chris@16:     return find_odd_cycle (graph, index_map, partition_map, result);
Chris@16:   }
Chris@16: 
Chris@16:   /**
Chris@16:    * Checks a given graph for bipartiteness. If the graph is not bipartite, a
Chris@16:    * sequence of vertices, producing an odd-cycle, is written to the output
Chris@16:    * iterator. The final iterator value is returned. The graph must have an
Chris@16:    * internal vertex_index property. Runs in linear time in the size of the
Chris@16:    * graph, if access to the property maps is in constant time.
Chris@16:    *
Chris@16:    * @param graph The given graph.
Chris@16:    * @param result An iterator to write the odd-cycle vertices to.
Chris@16:    * @return The final iterator value after writing.
Chris@16:    */
Chris@16: 
Chris@16:   template <typename Graph, typename OutputIterator>
Chris@16:   OutputIterator find_odd_cycle (const Graph& graph, OutputIterator result)
Chris@16:   {
Chris@16:     return find_odd_cycle (graph, get (vertex_index, graph), result);
Chris@16:   }
Chris@16: }
Chris@16: 
Chris@16: #endif /// BOOST_GRAPH_BIPARTITE_HPP