// (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 <vector> | |
#include <algorithm> //std::find | |
#include <boost/concept/requires.hpp> | |
#include <boost/concept_check.hpp> | |
#include <boost/graph/graph_traits.hpp> | |
#include <boost/graph/topological_sort.hpp> | |
// 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<Vertex>::reverse_iterator | |
} // { | |
} //for( typename vector<Vertex>::iterator | |
} //void transitive_reduction | |
} // namespace boost | |
#endif | |