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  *  \todo Improve general support for graphs and trees.
  27  */
  28
  29
  30 #ifndef __defined_libdai_weightedgraph_h
  31 #define __defined_libdai_weightedgraph_h
  32
  33
  34 #include <vector>
  35 #include <map>
  36 #include <iostream>
  37 #include <set>
  38 #include <cassert>
  39 #include <limits>
  40
  41 #include <boost/graph/adjacency_list.hpp>
  42 #include <boost/graph/prim_minimum_spanning_tree.hpp>
  43
  44
  45 namespace dai {
  46
  47
  48 /// Represents a directed edge pointing from n1 to n2
  49 class DEdge {
  50     public:
  51         size_t n1;  ///< First node index
  52         size_t n2;  ///< Second node index
  53
  54         /// Default constructor
  55         DEdge() {}
  56
  57         /// Constructor
  58         DEdge( size_t m1, size_t m2 ) : n1(m1), n2(m2) {}
  59
  60         /// Tests for equality
  61         bool operator==( const DEdge &x ) const { return ((n1 == x.n1) && (n2 == x.n2)); }
  62
  63         /// Tests for inequality
  64         bool operator!=( const DEdge &x ) const { return !(*this == x); }
  65
  66         /// Smaller-than operator (performs lexicographical comparison)
  67         bool operator<( const DEdge &x ) const {
  68             return( (n1 < x.n1) || ((n1 == x.n1) && (n2 < x.n2)) );
  69         }
  70
  71         /// Writes a DEdge to an output stream
  72         friend std::ostream & operator << (std::ostream & os, const DEdge & e) {
  73             os << "(" << e.n1 << "," << e.n2 << ")";
  74             return os;
  75         }
  76 };
  77
  78
  79 /// Undirected edge between nodes n1 and n2
  80 class UEdge {
  81     public:
  82         size_t  n1;  ///< First node index
  83         size_t  n2;  ///< Second node index
  84
  85         /// Default constructor
  86         UEdge() {}
  87
  88         /// Constructor
  89         UEdge( size_t m1, size_t m2 ) : n1(m1), n2(m2) {}
  90
  91         /// Construct from DEdge
  92         UEdge( const DEdge & e ) : n1(e.n1), n2(e.n2) {}
  93
  94         /// Tests for inequality (disregarding the ordering of n1 and n2)
  95         bool operator==( const UEdge &x ) {
  96             return ((n1 == x.n1) && (n2 == x.n2)) || ((n1 == x.n2) && (n2 == x.n1));
  97         }
  98
  99         /// Smaller-than operator
 100         bool operator<( const UEdge &x ) const {
 101             size_t s = n1, l = n2;
 102             if( s > l )
 103                 std::swap( s, l );
 104             size_t xs = x.n1, xl = x.n2;
 105             if( xs > xl )
 106                 std::swap( xs, xl );
 107             return( (s < xs) || ((s == xs) && (l < xl)) );
 108         }
 109
 110         /// Writes a UEdge to an output stream
 111         friend std::ostream & operator << (std::ostream & os, const UEdge & e) {
 112             if( e.n1 < e.n2 )
 113                 os << "{" << e.n1 << "," << e.n2 << "}";
 114             else
 115                 os << "{" << e.n2 << "," << e.n1 << "}";
 116             return os;
 117         }
 118 };
 119
 120
 121 /// Vector of UEdge
 122 typedef std::vector<UEdge>  UEdgeVec;
 123
 124 /// Vector of DEdge
 125 typedef std::vector<DEdge>  DEdgeVec;
 126
 127 /// Represents an undirected weighted graph, with weights of type T
 128 template<class T> class WeightedGraph : public std::map<UEdge, T> {};
 129
 130 /// Represents an undirected graph
 131 typedef std::set<UEdge>     Graph;
 132
 133
 134 /// Uses Prim's algorithm to construct a minimal spanning tree from the (positively) weighted graph G.
 135 /** Uses implementation in Boost Graph Library.
 136  */
 137 template<typename T> DEdgeVec MinSpanningTreePrims( const WeightedGraph<T> &G ) {
 138     DEdgeVec result;
 139     if( G.size() > 0 ) {
 140         using namespace boost;
 141         using namespace std;
 142         typedef adjacency_list< vecS, vecS, undirectedS, property<vertex_distance_t, int>, property<edge_weight_t, double> > boostGraph;
 143         typedef pair<size_t, size_t> E;
 144
 145         set<size_t> nodes;
 146         vector<E> edges;
 147         vector<double> weights;
 148         edges.reserve( G.size() );
 149         weights.reserve( G.size() );
 150         for( typename WeightedGraph<T>::const_iterator e = G.begin(); e != G.end(); e++ ) {
 151             weights.push_back( e->second );
 152             edges.push_back( E( e->first.n1, e->first.n2 ) );
 153             nodes.insert( e->first.n1 );
 154             nodes.insert( e->first.n2 );
 155         }
 156
 157         boostGraph g( edges.begin(), edges.end(), weights.begin(), nodes.size() );
 158         vector< graph_traits< boostGraph >::vertex_descriptor > p( num_vertices(g) );
 159         prim_minimum_spanning_tree( g, &(p[0]) );
 160
 161         // Store tree edges in result
 162         result.reserve( nodes.size() - 1 );
 163         size_t root = 0;
 164         for( size_t i = 0; i != p.size(); i++ )
 165             if( p[i] != i )
 166                 result.push_back( DEdge( p[i], i ) );
 167             else
 168                 root = i;
 169
 170         // We have to store the minimum spanning tree in the right
 171         // order, such that for all (i1, j1), (i2, j2) in result,
 172         // if j1 == i2 then (i1, j1) comes before (i2, j2) in result.
 173         // We do this by reordering the contents of result, effectively
 174         // growing the tree starting at the root. At each step,
 175         // result[0..N-1] are the edges already added to the tree,
 176         // whereas the other elements of result still have to be added.
 177         // The elements of nodes are the vertices that still have to
 178         // be added to the tree.
 179
 180         // Start with the root
 181         nodes.erase( root );
 182         size_t N = 0;
 183
 184         // Iteratively add edges and nodes to the growing tree
 185         while( N != result.size() ) {
 186             for( size_t e = N; e != result.size(); e++ ) {
 187                 bool e1_in_tree = !nodes.count( result[e].n1 );
 188                 if( e1_in_tree ) {
 189                     nodes.erase( result[e].n2 );
 190                     swap( result[N], result[e] );
 191                     N++;
 192                     break;
 193                 }
 194             }
 195         }
 196     }
 197
 198     return result;
 199 }
 200
 201
 202 /// Use Prim's algorithm to construct a minimal spanning tree from the (positively) weighted graph G.
 203 /** Uses implementation in Boost Graph Library.
 204  */
 205 template<typename T> DEdgeVec MaxSpanningTreePrims( const WeightedGraph<T> & Graph ) {
 206     T maxweight = Graph.begin()->second;
 207     for( typename WeightedGraph<T>::const_iterator it = Graph.begin(); it != Graph.end(); it++ )
 208         if( it->second > maxweight )
 209             maxweight = it->second;
 210     // make a copy of the graph
 211     WeightedGraph<T> gr( Graph );
 212     // invoke MinSpanningTreePrims with negative weights
 213     // (which have to be shifted to satisfy positivity criterion)
 214     for( typename WeightedGraph<T>::iterator it = gr.begin(); it != gr.end(); it++ )
 215         it->second = maxweight - it->second;
 216     return MinSpanningTreePrims( gr );
 217 }
 218
 219
 220 /// Constructs a rooted tree from a tree and a root
 221 DEdgeVec GrowRootedTree( const Graph & T, size_t Root );
 222
 223
 224 /// Constructs a random undirected graph of N nodes, where each node has connectivity d
 225 UEdgeVec RandomDRegularGraph( size_t N, size_t d );
 226
 227
 228 } // end of namespace dai
 229
 230
 231 #endif