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// (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 #include //std::find #include #include #include #include // 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::reverse_iterator } // { } // for( typename vector::iterator } // void transitive_reduction } // namespace boost #endif