include/dai/weightedgraph.h

   1 /*  Copyright (C) 2006-2008  Joris Mooij  [joris dot mooij at tuebingen dot mpg dot de]
   2     Radboud University Nijmegen, The Netherlands /
   3     Max Planck Institute for Biological Cybernetics, Germany
   4
   5     This file is part of libDAI.
   6
   7     libDAI is free software; you can redistribute it and/or modify
   8     it under the terms of the GNU General Public License as published by
   9     the Free Software Foundation; either version 2 of the License, or
  10     (at your option) any later version.
  11
  12     libDAI is distributed in the hope that it will be useful,
  13     but WITHOUT ANY WARRANTY; without even the implied warranty of
  14     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15     GNU General Public License for more details.
  16
  17     You should have received a copy of the GNU General Public License
  18     along with libDAI; if not, write to the Free Software
  19     Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
  20 */
  21
  22
  23 /// \file
  24 /// \brief Defines some utility functions for weighted graphs
  25 /// \todo Improve documentation
  26
  27
  28 #ifndef __defined_libdai_weightedgraph_h
  29 #define __defined_libdai_weightedgraph_h
  30
  31
  32 #include <vector>
  33 #include <map>
  34 #include <iostream>
  35 #include <set>
  36 #include <cassert>
  37 #include <limits>
  38
  39 #include <boost/graph/adjacency_list.hpp>
  40 #include <boost/graph/prim_minimum_spanning_tree.hpp>
  41
  42
  43 namespace dai {
  44
  45
  46 /// Represents a directed edge pointing from n1 to n2
  47 class DEdge {
  48     public:
  49         size_t n1;  ///< First node index
  50         size_t n2;  ///< Second node index
  51
  52         /// Default constructor
  53         DEdge() {}
  54
  55         /// Constructor
  56         DEdge( size_t m1, size_t m2 ) : n1(m1), n2(m2) {}
  57
  58         /// Tests for equality
  59         bool operator==( const DEdge &x ) const { return ((n1 == x.n1) && (n2 == x.n2)); }
  60
  61         /// Tests for inequality
  62         bool operator!=( const DEdge &x ) const { return !(*this == x); }
  63
  64         /// Smaller-than operator (performs lexicographical comparison)
  65         bool operator<( const DEdge &x ) const {
  66             return( (n1 < x.n1) || ((n1 == x.n1) && (n2 < x.n2)) );
  67         }
  68
  69         /// Writes a DEdge to an output stream
  70         friend std::ostream & operator << (std::ostream & os, const DEdge & e) {
  71             os << "(" << e.n1 << "," << e.n2 << ")";
  72             return os;
  73         }
  74 };
  75
  76
  77 /// Undirected edge between nodes n1 and n2
  78 class UEdge {
  79     public:
  80         size_t  n1;  ///< First node index
  81         size_t  n2;  ///< Second node index
  82
  83         /// Default constructor
  84         UEdge() {}
  85
  86         /// Constructor
  87         UEdge( size_t m1, size_t m2 ) : n1(m1), n2(m2) {}
  88
  89         /// Construct from DEdge
  90         UEdge( const DEdge & e ) : n1(e.n1), n2(e.n2) {}
  91
  92         /// Tests for inequality (disregarding the ordering of n1 and n2)
  93         bool operator==( const UEdge &x ) {
  94             return ((n1 == x.n1) && (n2 == x.n2)) || ((n1 == x.n2) && (n2 == x.n1));
  95         }
  96
  97         /// Smaller-than operator
  98         bool operator<( const UEdge &x ) const {
  99             size_t s = n1, l = n2;
 100             if( s > l )
 101                 std::swap( s, l );
 102             size_t xs = x.n1, xl = x.n2;
 103             if( xs > xl )
 104                 std::swap( xs, xl );
 105             return( (s < xs) || ((s == xs) && (l < xl)) );
 106         }
 107
 108         /// Writes a UEdge to an output stream
 109         friend std::ostream & operator << (std::ostream & os, const UEdge & e) {
 110             if( e.n1 < e.n2 )
 111                 os << "{" << e.n1 << "," << e.n2 << "}";
 112             else
 113                 os << "{" << e.n2 << "," << e.n1 << "}";
 114             return os;
 115         }
 116 };
 117
 118
 119 /// Vector of UEdge
 120 typedef std::vector<UEdge>  UEdgeVec;
 121
 122 /// Vector of DEdge
 123 typedef std::vector<DEdge>  DEdgeVec;
 124
 125 /// Represents an undirected weighted graph, with weights of type T
 126 template<class T> class WeightedGraph : public std::map<UEdge, T> {};
 127
 128 /// Represents an undirected graph
 129 typedef std::set<UEdge>     Graph;
 130
 131
 132 /// Uses Prim's algorithm to construct a minimal spanning tree from the (positively) weighted graph G.
 133 /** Uses implementation in Boost Graph Library.
 134  */
 135 template<typename T> DEdgeVec MinSpanningTreePrims( const WeightedGraph<T> &G ) {
 136     DEdgeVec result;
 137     if( G.size() > 0 ) {
 138         using namespace boost;
 139         using namespace std;
 140         typedef adjacency_list< vecS, vecS, undirectedS, property<vertex_distance_t, int>, property<edge_weight_t, double> > boostGraph;
 141         typedef pair<size_t, size_t> E;
 142
 143         set<size_t> nodes;
 144         vector<E> edges;
 145         vector<double> weights;
 146         edges.reserve( G.size() );
 147         weights.reserve( G.size() );
 148         for( typename WeightedGraph<T>::const_iterator e = G.begin(); e != G.end(); e++ ) {
 149             weights.push_back( e->second );
 150             edges.push_back( E( e->first.n1, e->first.n2 ) );
 151             nodes.insert( e->first.n1 );
 152             nodes.insert( e->first.n2 );
 153         }
 154
 155         boostGraph g( edges.begin(), edges.end(), weights.begin(), nodes.size() );
 156         vector< graph_traits< boostGraph >::vertex_descriptor > p( num_vertices(g) );
 157         prim_minimum_spanning_tree( g, &(p[0]) );
 158
 159         // Store tree edges in result
 160         result.reserve( nodes.size() - 1 );
 161         size_t root = 0;
 162         for( size_t i = 0; i != p.size(); i++ )
 163             if( p[i] != i )
 164                 result.push_back( DEdge( p[i], i ) );
 165             else
 166                 root = i;
 167
 168         // We have to store the minimum spanning tree in the right
 169         // order, such that for all (i1, j1), (i2, j2) in result,
 170         // if j1 == i2 then (i1, j1) comes before (i2, j2) in result.
 171         // We do this by reordering the contents of result, effectively
 172         // growing the tree starting at the root. At each step,
 173         // result[0..N-1] are the edges already added to the tree,
 174         // whereas the other elements of result still have to be added.
 175         // The elements of nodes are the vertices that still have to
 176         // be added to the tree.
 177
 178         // Start with the root
 179         nodes.erase( root );
 180         size_t N = 0;
 181
 182         // Iteratively add edges and nodes to the growing tree
 183         while( N != result.size() ) {
 184             for( size_t e = N; e != result.size(); e++ ) {
 185                 bool e1_in_tree = !nodes.count( result[e].n1 );
 186                 if( e1_in_tree ) {
 187                     nodes.erase( result[e].n2 );
 188                     swap( result[N], result[e] );
 189                     N++;
 190                     break;
 191                 }
 192             }
 193         }
 194     }
 195
 196     return result;
 197 }
 198
 199
 200 /// Use Prim's algorithm to construct a minimal spanning tree from the (positively) weighted graph G.
 201 /** Uses implementation in Boost Graph Library.
 202  */
 203 template<typename T> DEdgeVec MaxSpanningTreePrims( const WeightedGraph<T> & Graph ) {
 204     T maxweight = Graph.begin()->second;
 205     for( typename WeightedGraph<T>::const_iterator it = Graph.begin(); it != Graph.end(); it++ )
 206         if( it->second > maxweight )
 207             maxweight = it->second;
 208     // make a copy of the graph
 209     WeightedGraph<T> gr( Graph );
 210     // invoke MinSpanningTreePrims with negative weights
 211     // (which have to be shifted to satisfy positivity criterion)
 212     for( typename WeightedGraph<T>::iterator it = gr.begin(); it != gr.end(); it++ )
 213         it->second = maxweight - it->second;
 214     return MinSpanningTreePrims( gr );
 215 }
 216
 217
 218 /// Constructs a rooted tree from a tree and a root
 219 DEdgeVec GrowRootedTree( const Graph & T, size_t Root );
 220
 221
 222 /// Constructs a random undirected graph of N nodes, where each node has connectivity d
 223 UEdgeVec RandomDRegularGraph( size_t N, size_t d );
 224
 225
 226 } // end of namespace dai
 227
 228
 229 #endif