 # Boost :

Subject: [boost] [Graph] transitive reduction
From: Eric Böse-Wolf (boese-wolf_at_[hidden])
Date: 2009-03-18 06:00:30

Hi!

May I propose the following implementation for a transitive reduction
to be added to the boost graph library?

I'm a novice and the quality of the code I produced surely does not meet
boosts standards, but maybe with some help, I'm able to improve it.

#ifndef MY_OWN_TRANSITIVE_REDUCTION_HPP_INCLUDED
#define MY_OWN_TRANSITIVE_REDUCTION_HPP_INCLUDED

#include <vector>
#include <algorithm> //std::find
#include <boost/concept/requires.hpp>
#include <boost/concept_check.hpp>
#include <boost/graph/topological_sort.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/property_map.hpp>

//I actually didn't care which of those heades include some of the
//others and whicht could be left out, for this reason, I simply added a
//header when I used a function, described to be in this header by the
//boost graph documentation

//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

using namespace boost;

template <typename Graph, typename GraphTR,
typename G_to_TR_VertexMap, typename VertexIndexMap>
BOOST_CONCEPT_REQUIRES(
((VertexListGraphConcept< Graph >))
((IncidenceGraphConcept< Graph >))
((MutableGraphConcept< GraphTR >))
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,
const 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, 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 ) {
}
}

for( typename std::vector<Vertex>::iterator it = topo_order.begin();
it != topo_order.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( 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
for( typename std::vector<Vertex>::reverse_iterator rit = topo_order.rbegin();
rit != topo_order.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