Chris@16: // (C) Copyright 2009 Eric Bose-Wolf
Chris@16: //
Chris@16: // Use, modification and distribution are subject to the
Chris@16: // Boost Software License, Version 1.0 (See accompanying file
Chris@16: // LICENSE_1_0.txt or http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_GRAPH_TRANSITIVE_REDUCTION_HPP
Chris@16: #define BOOST_GRAPH_TRANSITIVE_REDUCTION_HPP
Chris@16: 
Chris@16: #include <vector>
Chris@16: #include <algorithm> //std::find
Chris@16: #include <boost/concept/requires.hpp>
Chris@16: #include <boost/concept_check.hpp>
Chris@16: 
Chris@16: #include <boost/graph/graph_traits.hpp>
Chris@16: #include <boost/graph/topological_sort.hpp>
Chris@16: 
Chris@16: // also I didn't got all of the concepts thin. Am I suppose to check
Chris@16: // for all concepts, which are needed for functions I call? (As if I
Chris@16: // wouldn't do that, the users would see the functions called by
Chris@16: // complaining about missings concepts, which would be clearly an error
Chris@16: // message revealing internal implementation and should therefore be avoided?)
Chris@16: 
Chris@16: // the pseudocode which I followed implementing this algorithmn was taken
Chris@16: // from the german book Algorithmische Graphentheorie by Volker Turau
Chris@16: // it is proposed to be of O(n + nm_red ) where n is the number
Chris@16: // of vertices and m_red is the number of edges in the transitive
Chris@16: // reduction, but I think my implementation spoiled this up at some point
Chris@16: // indicated below.
Chris@16: 
Chris@16: namespace boost {
Chris@16: 
Chris@16: template <
Chris@16:     typename Graph, typename GraphTR, typename G_to_TR_VertexMap,
Chris@16:     typename VertexIndexMap
Chris@16: >
Chris@16: BOOST_CONCEPT_REQUIRES(
Chris@16:                       ((VertexListGraphConcept< Graph >))
Chris@16:                       ((IncidenceGraphConcept< Graph >))
Chris@16:                       ((MutableGraphConcept< GraphTR >))
Chris@16:                       ((ReadablePropertyMapConcept< VertexIndexMap,
Chris@16:                           typename graph_traits<Graph>::vertex_descriptor >))
Chris@16:                       ((Integer< typename
Chris@16:                           property_traits< VertexIndexMap >::value_type >))
Chris@16:                       ((LvaluePropertyMapConcept< G_to_TR_VertexMap,
Chris@16:                           typename graph_traits<Graph>::vertex_descriptor >)),
Chris@16:                        (void))
Chris@16: transitive_reduction(const Graph& g, GraphTR& tr,
Chris@16:                      G_to_TR_VertexMap g_to_tr_map,
Chris@16:                      VertexIndexMap g_index_map )
Chris@16: {
Chris@16:     typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
Chris@16:     typedef typename graph_traits<Graph>::vertex_iterator VertexIterator;
Chris@16:     typedef typename std::vector<Vertex>::size_type size_type;
Chris@16: 
Chris@16:     std::vector<Vertex> topo_order;
Chris@16:     topological_sort(g, std::back_inserter(topo_order));
Chris@16: 
Chris@16:     std::vector<size_type> topo_number_storage(num_vertices(g));
Chris@16: 
Chris@16:     iterator_property_map<size_type*, VertexIndexMap,
Chris@16:     size_type, size_type&> topo_number( &topo_number_storage[0], g_index_map );
Chris@16: 
Chris@16:     {
Chris@16:         typename std::vector<Vertex>::reverse_iterator it = topo_order.rbegin();
Chris@16:         size_type n = 0;
Chris@16:         for(; it != topo_order.rend(); ++it,++n ) {
Chris@16:             topo_number[ *it ] = n;
Chris@16:         }
Chris@16:     }
Chris@16: 
Chris@16:     std::vector< std::vector< bool > > edge_in_closure(num_vertices(g),
Chris@16:                                             std::vector<bool>( num_vertices(g), false));
Chris@16:     {
Chris@16:         typename std::vector<Vertex>::reverse_iterator it = topo_order.rbegin();
Chris@16:             for( ; it != topo_order.rend(); ++it ) {
Chris@16:             g_to_tr_map[*it] = add_vertex(tr);
Chris@16:         }
Chris@16:     }
Chris@16: 
Chris@16:     typename std::vector<Vertex>::iterator
Chris@16:         it = topo_order.begin(),
Chris@16:         end = topo_order.end();
Chris@16:     for( ; it != end; ++it ) {
Chris@16:         size_type i = topo_number[ *it ];
Chris@16:         edge_in_closure[i][i] = true;
Chris@16:         std::vector<Vertex> neighbors;
Chris@16: 
Chris@16:         //I have to collect the successors of *it and traverse them in
Chris@16:         //ascending topological order. I didn't know a better way, how to
Chris@16:         //do that. So what I'm doint is, collection the successors of *it here
Chris@16:         {
Chris@16:             typename Graph::out_edge_iterator oi,oi_end;
Chris@16:             for( boost::tie(oi, oi_end) = out_edges( *it, g ); oi != oi_end; ++oi ) {
Chris@16:                 neighbors.push_back( target( *oi, g ) );
Chris@16:             }
Chris@16:         }
Chris@16: 
Chris@16:         {
Chris@16:             //and run through all vertices in topological order
Chris@16:             typename std::vector<Vertex>::reverse_iterator
Chris@16:                 rit = topo_order.rbegin(),
Chris@16:                 rend = topo_order.rend();
Chris@16:             for(; rit != rend; ++rit ) {
Chris@16:                 //looking if they are successors of *it
Chris@16:                 if( std::find( neighbors.begin(), neighbors.end(), *rit) != neighbors.end() ) {
Chris@16:                     size_type j = topo_number[ *rit ];
Chris@16:                     if( not edge_in_closure[i][j] ) {
Chris@16:                     for(size_type k = j; k < num_vertices(g); ++k) {
Chris@16:                         if( not edge_in_closure[i][k] ) {
Chris@16:                         //here we need edge_in_closure to be in topological order,
Chris@16:                         edge_in_closure[i][k] = edge_in_closure[j][k];
Chris@16:                         }
Chris@16:                     }
Chris@16:                     //therefore we only access edge_in_closure only through
Chris@16:                     //topo_number property_map
Chris@16:                     add_edge(g_to_tr_map[*it], g_to_tr_map[*rit], tr);
Chris@16:                     } //if ( not edge_in_
Chris@16:                 } //if (find (
Chris@16:             } //for( typename vector<Vertex>::reverse_iterator
Chris@16:         } // {
Chris@16: 
Chris@16:     } //for( typename vector<Vertex>::iterator
Chris@16: 
Chris@16: } //void transitive_reduction
Chris@16: 
Chris@16: } // namespace boost
Chris@16: 
Chris@16: #endif
Chris@16: