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