boost/graph/transitive_reduction.hpp

   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))
  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
 102                 rit = topo_order.rbegin();
 103                 rend = topo_order.rend();
 104             for(; rit != rend; ++rit ) {
 105                 //looking if they are successors of *it
 106                 if( std::find( neighbors.begin(), neighbors.end(), *rit) != neighbors.end() ) {
 107                     size_type j = topo_number[ *rit ];
 108                     if( not edge_in_closure[i][j] ) {
 109                     for(size_type k = j; k < num_vertices(g); ++k) {
 110                         if( not edge_in_closure[i][k] ) {
 111                         //here we need edge_in_closure to be in topological order,
 112                         edge_in_closure[i][k] = edge_in_closure[j][k];
 113                         }
 114                     }
 115                     //therefore we only access edge_in_closure only through
 116                     //topo_number property_map
 117                     add_edge(g_to_tr_map[*it], g_to_tr_map[*rit], tr);
 118                     } //if ( not edge_in_
 119                 } //if (find (
 120             } //for( typename vector<Vertex>::reverse_iterator
 121         } // {
 122
 123     } //for( typename vector<Vertex>::iterator
 124
 125 } //void transitive_reduction
 126
 127 } // namespace boost
 128
 129 #endif
 130