1 // (C) Copyright 2009 Eric Bose-Wolf 2 // 3 // Use, modification and distribution are subject to the 4 // Boost Software License, Version 1.0 (See accompanying file 5 // LICENSE_1_0.txt or http://www.boost.org/LICENSE_1_0.txt) 6 7 #ifndef BOOST_GRAPH_TRANSITIVE_REDUCTION_HPP 8 #define BOOST_GRAPH_TRANSITIVE_REDUCTION_HPP 9 10 #include <vector> 11 #include <algorithm> //std::find 12 #include <boost/concept/requires.hpp> 13 #include <boost/concept_check.hpp> 14 15 #include <boost/graph/graph_traits.hpp> 16 #include <boost/graph/topological_sort.hpp> 17 18 // also I didn't got all of the concepts thin. Am I suppose to check 19 // for all concepts, which are needed for functions I call? (As if I 20 // wouldn't do that, the users would see the functions called by 21 // complaining about missings concepts, which would be clearly an error 22 // message revealing internal implementation and should therefore be avoided?) 23 24 // the pseudocode which I followed implementing this algorithmn was taken 25 // from the german book Algorithmische Graphentheorie by Volker Turau 26 // it is proposed to be of O(n + nm_red ) where n is the number 27 // of vertices and m_red is the number of edges in the transitive 28 // reduction, but I think my implementation spoiled this up at some point 29 // indicated below. 30 31 namespace boost { 32 33 template < 34 typename Graph, typename GraphTR, typename G_to_TR_VertexMap, 35 typename VertexIndexMap 36 > 37 BOOST_CONCEPT_REQUIRES( 38 ((VertexListGraphConcept< Graph >)) 39 ((IncidenceGraphConcept< Graph >)) 40 ((MutableGraphConcept< GraphTR >)) 41 ((ReadablePropertyMapConcept< VertexIndexMap, 42 typename graph_traits<Graph>::vertex_descriptor >)) 43 ((Integer< typename 44 property_traits< VertexIndexMap >::value_type >)) 45 ((LvaluePropertyMapConcept< G_to_TR_VertexMap, 46 typename graph_traits<Graph>::vertex_descriptor >)), 47 (void)) transitive_reduction(const Graph & g,GraphTR & tr,G_to_TR_VertexMap g_to_tr_map,VertexIndexMap g_index_map)48 transitive_reduction(const Graph& g, GraphTR& tr, 49 G_to_TR_VertexMap g_to_tr_map, 50 VertexIndexMap g_index_map ) 51 { 52 typedef typename graph_traits<Graph>::vertex_descriptor Vertex; 53 typedef typename graph_traits<Graph>::vertex_iterator VertexIterator; 54 typedef typename std::vector<Vertex>::size_type size_type; 55 56 std::vector<Vertex> topo_order; 57 topological_sort(g, std::back_inserter(topo_order)); 58 59 std::vector<size_type> topo_number_storage(num_vertices(g)); 60 61 iterator_property_map<size_type*, VertexIndexMap, 62 size_type, size_type&> topo_number( &topo_number_storage[0], g_index_map ); 63 64 { 65 typename std::vector<Vertex>::reverse_iterator it = topo_order.rbegin(); 66 size_type n = 0; 67 for(; it != topo_order.rend(); ++it,++n ) { 68 topo_number[ *it ] = n; 69 } 70 } 71 72 std::vector< std::vector< bool > > edge_in_closure(num_vertices(g), 73 std::vector<bool>( num_vertices(g), false)); 74 { 75 typename std::vector<Vertex>::reverse_iterator it = topo_order.rbegin(); 76 for( ; it != topo_order.rend(); ++it ) { 77 g_to_tr_map[*it] = add_vertex(tr); 78 } 79 } 80 81 typename std::vector<Vertex>::iterator 82 it = topo_order.begin(), 83 end = topo_order.end(); 84 for( ; it != end; ++it ) { 85 size_type i = topo_number[ *it ]; 86 edge_in_closure[i][i] = true; 87 std::vector<Vertex> neighbors; 88 89 //I have to collect the successors of *it and traverse them in 90 //ascending topological order. I didn't know a better way, how to 91 //do that. So what I'm doint is, collection the successors of *it here 92 { 93 typename Graph::out_edge_iterator oi,oi_end; 94 for( tie(oi, oi_end) = out_edges( *it, g ); oi != oi_end; ++oi ) { 95 neighbors.push_back( target( *oi, g ) ); 96 } 97 } 98 99 { 100 //and run through all vertices in topological order 101 typename std::vector<Vertex>::reverse_iterator rit = topo_order.rbegin(); 102 typename std::vector<Vertex>::reverse_iterator rend = topo_order.rend(); 103 for(; rit != rend; ++rit ) { 104 //looking if they are successors of *it 105 if( std::find( neighbors.begin(), neighbors.end(), *rit) != neighbors.end() ) { 106 size_type j = topo_number[ *rit ]; 107 if( not edge_in_closure[i][j] ) { 108 for(size_type k = j; k < num_vertices(g); ++k) { 109 if( not edge_in_closure[i][k] ) { 110 //here we need edge_in_closure to be in topological order, 111 edge_in_closure[i][k] = edge_in_closure[j][k]; 112 } 113 } 114 //therefore we only access edge_in_closure only through 115 //topo_number property_map 116 add_edge(g_to_tr_map[*it], g_to_tr_map[*rit], tr); 117 } //if ( not edge_in_ 118 } //if (find ( 119 } //for( typename vector<Vertex>::reverse_iterator 120 } // { 121 122 } //for( typename vector<Vertex>::iterator 123 124 } //void transitive_reduction 125 126 } // namespace boost 127 128 #endif 129 130