From 534e7f6acdeaba755345163615409aaaa5d04cfa Mon Sep 17 00:00:00 2001
From: Andrew Sutton <andrew.n.sutton@gmail.com>
Date: Thu, 23 Apr 2009 14:19:19 +0000
Subject: [PATCH] Added preliminary version of transitive_reduction. This has
 no test or documentation, and needs to be thoroughly reviewed.

[SVN r52562]
---
 include/boost/graph/transitive_reduction.hpp | 130 +++++++++++++++++++
 1 file changed, 130 insertions(+)
 create mode 100644 include/boost/graph/transitive_reduction.hpp

diff --git a/include/boost/graph/transitive_reduction.hpp b/include/boost/graph/transitive_reduction.hpp
new file mode 100644
index 00000000..5cfa9627
--- /dev/null
+++ b/include/boost/graph/transitive_reduction.hpp
@@ -0,0 +1,130 @@
+// (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( 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
+