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