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


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.

So, please don't shoot me.


#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>
                       ((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 >)),
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[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);
  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
            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


Best regards,


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