## File: transitive_reduction.h

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 `123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129` ``````// (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::vertex_descriptor >)) ((Integer< typename property_traits< VertexIndexMap >::value_type >)) ((LvaluePropertyMapConcept< G_to_TR_VertexMap, typename graph_traits::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::vertex_descriptor Vertex; typedef typename graph_traits::vertex_iterator VertexIterator; typedef typename std::vector::size_type size_type; std::vector topo_order; topological_sort(g, std::back_inserter(topo_order)); std::vector topo_number_storage(num_vertices(g)); iterator_property_map topo_number( &topo_number_storage, g_index_map ); { typename std::vector::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( num_vertices(g), false)); { typename std::vector::reverse_iterator it = topo_order.rbegin(); for( ; it != topo_order.rend(); ++it ) { g_to_tr_map[*it] = add_vertex(tr); } } typename std::vector::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 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( 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::reverse_iterator rit = topo_order.rbegin(); typename std::vector::reverse_iterator 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 ``````