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
  26
  27 #ifndef __defined_libdai_weightedgraph_h
  28 #define __defined_libdai_weightedgraph_h
  29
  30
  31 #include <vector>
  32 #include <map>
  33 #include <iostream>
  34 #include <set>
  35 #include <cassert>
  36 #include <limits>
  37
  38 #include <boost/graph/adjacency_list.hpp>
  39 #include <boost/graph/prim_minimum_spanning_tree.hpp>
  40
  41
  42 namespace dai {
  43
  44
  45 /// Represents a directed edge pointing from n1 to n2
  46 class DEdge {
  47     public:
  48         size_t n1;  ///< First node index
  49         size_t n2;  ///< Second node index
  50
  51         /// Default constructor
  52         DEdge() {}
  53
  54         /// Constructor
  55         DEdge( size_t m1, size_t m2 ) : n1(m1), n2(m2) {}
  56
  57         /// Tests for equality
  58         bool operator==( const DEdge &x ) const { return ((n1 == x.n1) && (n2 == x.n2)); }
  59
  60         /// Tests for inequality
  61         bool operator!=( const DEdge &x ) const { return !(*this == x); }
  62
  63         /// Smaller-than operator (performs lexicographical comparison)
  64         bool operator<( const DEdge &x ) const {
  65             return( (n1 < x.n1) || ((n1 == x.n1) && (n2 < x.n2)) );
  66         }
  67
  68         /// Writes a DEdge to an output stream
  69         friend std::ostream & operator << (std::ostream & os, const DEdge & e) {
  70             os << "(" << e.n1 << "," << e.n2 << ")";
  71             return os;
  72         }
  73 };
  74
  75
  76 /// Undirected edge between nodes n1 and n2
  77 class UEdge {
  78     public:
  79         size_t  n1;  ///< First node index
  80         size_t  n2;  ///< Second node index
  81
  82         /// Default constructor
  83         UEdge() {}
  84
  85         /// Constructor
  86         UEdge( size_t m1, size_t m2 ) : n1(m1), n2(m2) {}
  87
  88         /// Construct from DEdge
  89         UEdge( const DEdge & e ) : n1(e.n1), n2(e.n2) {}
  90
  91         /// Tests for inequality (disregarding the ordering of n1 and n2)
  92         bool operator==( const UEdge &x ) {
  93             return ((n1 == x.n1) && (n2 == x.n2)) || ((n1 == x.n2) && (n2 == x.n1));
  94         }
  95
  96         /// Smaller-than operator
  97         bool operator<( const UEdge &x ) const {
  98             size_t s = n1, l = n2;
  99             if( s > l )
 100                 std::swap( s, l );
 101             size_t xs = x.n1, xl = x.n2;
 102             if( xs > xl )
 103                 std::swap( xs, xl );
 104             return( (s < xs) || ((s == xs) && (l < xl)) );
 105         }
 106
 107         /// Writes a UEdge to an output stream
 108         friend std::ostream & operator << (std::ostream & os, const UEdge & e) {
 109             if( e.n1 < e.n2 )
 110                 os << "{" << e.n1 << "," << e.n2 << "}";
 111             else
 112                 os << "{" << e.n2 << "," << e.n1 << "}";
 113             return os;
 114         }
 115 };
 116
 117
 118 /// Vector of UEdge
 119 typedef std::vector<UEdge>  UEdgeVec;
 120
 121 /// Vector of DEdge
 122 typedef std::vector<DEdge>  DEdgeVec;
 123
 124 /// Represents an undirected weighted graph, with weights of type T
 125 template<class T> class WeightedGraph : public std::map<UEdge, T> {};
 126
 127 /// Represents an undirected graph
 128 typedef std::set<UEdge>     Graph;
 129
 130
 131 /// Uses Prim's algorithm to construct a minimal spanning tree from the (positively) weighted graph G.
 132 /** Uses implementation in Boost Graph Library.
 133  */
 134 template<typename T> DEdgeVec MinSpanningTreePrims( const WeightedGraph<T> &G ) {
 135     DEdgeVec result;
 136     if( G.size() > 0 ) {
 137         using namespace boost;
 138         using namespace std;
 139         typedef adjacency_list< vecS, vecS, undirectedS, property<vertex_distance_t, int>, property<edge_weight_t, double> > boostGraph;
 140         typedef pair<size_t, size_t> E;
 141
 142         set<size_t> nodes;
 143         vector<E> edges;
 144         vector<double> weights;
 145         edges.reserve( G.size() );
 146         weights.reserve( G.size() );
 147         for( typename WeightedGraph<T>::const_iterator e = G.begin(); e != G.end(); e++ ) {
 148             weights.push_back( e->second );
 149             edges.push_back( E( e->first.n1, e->first.n2 ) );
 150             nodes.insert( e->first.n1 );
 151             nodes.insert( e->first.n2 );
 152         }
 153
 154         boostGraph g( edges.begin(), edges.end(), weights.begin(), nodes.size() );
 155         vector< graph_traits< boostGraph >::vertex_descriptor > p( num_vertices(g) );
 156         prim_minimum_spanning_tree( g, &(p[0]) );
 157
 158         // Store tree edges in result
 159         result.reserve( nodes.size() - 1 );
 160         size_t root = 0;
 161         for( size_t i = 0; i != p.size(); i++ )
 162             if( p[i] != i )
 163                 result.push_back( DEdge( p[i], i ) );
 164             else
 165                 root = i;
 166
 167         // We have to store the minimum spanning tree in the right
 168         // order, such that for all (i1, j1), (i2, j2) in result,
 169         // if j1 == i2 then (i1, j1) comes before (i2, j2) in result.
 170         // We do this by reordering the contents of result, effectively
 171         // growing the tree starting at the root. At each step,
 172         // result[0..N-1] are the edges already added to the tree,
 173         // whereas the other elements of result still have to be added.
 174         // The elements of nodes are the vertices that still have to
 175         // be added to the tree.
 176
 177         // Start with the root
 178         nodes.erase( root );
 179         size_t N = 0;
 180
 181         // Iteratively add edges and nodes to the growing tree
 182         while( N != result.size() ) {
 183             for( size_t e = N; e != result.size(); e++ ) {
 184                 bool e1_in_tree = !nodes.count( result[e].n1 );
 185                 if( e1_in_tree ) {
 186                     nodes.erase( result[e].n2 );
 187                     swap( result[N], result[e] );
 188                     N++;
 189                     break;
 190                 }
 191             }
 192         }
 193     }
 194
 195     return result;
 196 }
 197
 198
 199 /// Use Prim's algorithm to construct a minimal spanning tree from the (positively) weighted graph G.
 200 /** Uses implementation in Boost Graph Library.
 201  */
 202 template<typename T> DEdgeVec MaxSpanningTreePrims( const WeightedGraph<T> & Graph ) {
 203     T maxweight = Graph.begin()->second;
 204     for( typename WeightedGraph<T>::const_iterator it = Graph.begin(); it != Graph.end(); it++ )
 205         if( it->second > maxweight )
 206             maxweight = it->second;
 207     // make a copy of the graph
 208     WeightedGraph<T> gr( Graph );
 209     // invoke MinSpanningTreePrims with negative weights
 210     // (which have to be shifted to satisfy positivity criterion)
 211     for( typename WeightedGraph<T>::iterator it = gr.begin(); it != gr.end(); it++ )
 212         it->second = maxweight - it->second;
 213     return MinSpanningTreePrims( gr );
 214 }
 215
 216
 217 /// Constructs a rooted tree from a tree and a root
 218 DEdgeVec GrowRootedTree( const Graph & T, size_t Root );
 219
 220
 221 /// Constructs a random undirected graph of N nodes, where each node has connectivity d
 222 UEdgeVec RandomDRegularGraph( size_t N, size_t d );
 223
 224
 225 } // end of namespace dai
 226
 227
 228 #endif