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