1 /* This file is part of libDAI - http://www.libdai.org/
2 *
4 * 2, or (at your option) any later version. libDAI is distributed without any
5 * warranty. See the file COPYING for more details.
6 *
7 * Copyright (C) 2006-2009 Joris Mooij [joris dot mooij at libdai dot org]
8 * Copyright (C) 2006-2007 Radboud University Nijmegen, The Netherlands
9 */
12 /// \file
13 /// \brief Defines the GraphAL class, which represents an undirected graph as an adjacency list
16 #ifndef __defined_libdai_graph_h
17 #define __defined_libdai_graph_h
20 #include <ostream>
21 #include <vector>
22 #include <algorithm>
23 #include <dai/util.h>
24 #include <dai/exceptions.h>
27 namespace dai {
30 /// Represents the neighborhood structure of nodes in an undirected graph.
31 /** A graph has nodes connected by edges. Nodes are indexed by an unsigned integer.
32 * If there are nrNodes() nodes, they are numbered 0,1,2,...,nrNodes()-1. An edge
33 * between node \a n1 and node \a n2 is represented by a GraphAL::Edge(\a n1,\a n2).
34 *
35 * GraphAL is implemented as a sparse adjacency list, i.e., it stores for each node a list of
36 * its neighboring nodes. The list of neighboring nodes is implemented as a vector of Neighbor
37 * structures (accessible by the nb() method). Thus, each node has an associated variable of
38 * type GraphAL::Neighbors, which is a vector of Neighbor structures, describing its
39 * neighboring nodes.
40 */
41 class GraphAL {
42 public:
43 /// Describes the neighbor relationship of two nodes in a GraphAL.
44 /** Sometimes we want to do an action, such as sending a
45 * message, for all edges in a graph. However, most graphs
46 * will be sparse, so we need some way of storing a set of
47 * the neighbors of a node, which is both fast and
48 * memory-efficient. We also need to be able to go between
49 * viewing node \a a as a neighbor of node \a b, and node \a b
50 * as a neighbor of node \a a. The Neighbor struct solves
51 * both of these problems. Each node has a list of neighbors,
52 * stored as a std::vector<\link Neighbor \endlink>, and
53 * extra information is included in the Neighbor struct which
54 * allows us to access a node as a neighbor of its neighbor
55 * (the \c dual member).
56 *
57 * By convention, variable identifiers naming indices into a
58 * vector of neighbors are prefixed with an underscore ("_").
59 * The neighbor list which they point into is then understood
60 * from context. For example:
61 *
62 * \code
63 * Real MR::T( size_t i, size_t _j );
64 * \endcode
65 *
66 * Here, \a i is the "absolute" index of node i, but \a _j is
67 * understood as a "relative" index, giving node \a j 's entry in
68 * <tt>nb(i)</tt>. The corresponding Neighbor structure can be
69 * accessed as <tt>nb(i,_j)</tt> or <tt>nb(i)[_j]</tt>. The
70 * absolute index of \a _j, which would be called \a j, can be
71 * recovered from the \c node member: <tt>nb(i,_j).node</tt>.
72 * The \c iter member gives the relative index \a _j, and the
73 * \c dual member gives the "dual" relative index, i.e., the
74 * index of \a i in \a j 's neighbor list.
75 *
76 * \code
77 * Neighbor n = nb(i,_j);
78 * n.node == j &&
79 * n.iter == _j &&
80 * nb(n.node,n.dual).node == i
81 * \endcode
82 *
83 * There is no easy way to transform a pair of absolute node
84 * indices \a i and \a j into a Neighbor structure relative
85 * to one of the nodes. Such a feature has never yet been
86 * found to be necessary. Iteration over edges can always be
87 * accomplished using the Neighbor lists, and by writing
88 * functions that accept relative indices:
89 * \code
90 * for( size_t i = 0; i < nrNodes(); ++i )
91 * foreach( const Neighbor &j, nb(i) )
92 * T( i, j.iter );
93 * \endcode
94 */
95 struct Neighbor {
96 /// Corresponds to the index of this Neighbor entry in the vector of neighbors
97 size_t iter;
98 /// Contains the number of the neighboring node
99 size_t node;
100 /// Contains the "dual" iter
101 size_t dual;
103 /// Default constructor
104 Neighbor() {}
105 /// Constructor that sets the Neighbor members according to the parameters
106 Neighbor( size_t iter, size_t node, size_t dual ) : iter(iter), node(node), dual(dual) {}
108 /// Cast to \c size_t returns \c node member
109 operator size_t () const { return node; }
110 };
112 /// Describes the neighbors of some node.
113 typedef std::vector<Neighbor> Neighbors;
115 /// Represents an edge: an Edge(\a n1,\a n2) corresponds to the edge between node \a n1 and node \a n2.
116 typedef std::pair<size_t,size_t> Edge;
118 private:
119 /// Contains for each node a vector of its neighbors
120 std::vector<Neighbors> _nb;
122 /// Used internally by isTree()
123 typedef std::vector<size_t> levelType;
125 public:
126 /// \name Constructors and destructors
127 //@{
128 /// Default constructor (creates an empty graph).
129 GraphAL() : _nb() {}
131 /// Constructs GraphAL with \a nr nodes and no edges.
132 GraphAL( size_t nr ) : _nb( nr ) {}
134 /// Constructs GraphAL from a range of edges.
135 /** \tparam EdgeInputIterator Iterator that iterates over instances of GraphAL::Edge.
136 * \param nr The number of nodes.
137 * \param begin Points to the first edge.
138 * \param end Points just beyond the last edge.
139 */
140 template<typename EdgeInputIterator>
141 GraphAL( size_t nr, EdgeInputIterator begin, EdgeInputIterator end ) : _nb() {
142 construct( nr, begin, end );
143 }
144 //@}
146 /// \name Accessors and mutators
147 //@{
148 /// Returns constant reference to the \a _n2 'th neighbor of node \a n1
149 const Neighbor & nb( size_t n1, size_t _n2 ) const {
150 DAI_DEBASSERT( n1 < _nb.size() );
151 DAI_DEBASSERT( _n2 < _nb[n1].size() );
152 return _nb[n1][_n2];
153 }
154 /// Returns reference to the \a _n2 'th neighbor of node \a n1
155 Neighbor & nb( size_t n1, size_t _n2 ) {
156 DAI_DEBASSERT( n1 < _nb.size() );
157 DAI_DEBASSERT( _n2 < _nb[n1].size() );
158 return _nb[n1][_n2];
159 }
161 /// Returns constant reference to all neighbors of node \a n
162 const Neighbors & nb( size_t n ) const {
163 DAI_DEBASSERT( n < _nb.size() );
164 return _nb[n];
165 }
166 /// Returns reference to all neighbors of node \a n
167 Neighbors & nb( size_t n ) {
168 DAI_DEBASSERT( n < _nb.size() );
169 return _nb[n];
170 }
171 //@}
173 /// \name Adding nodes and edges
174 //@{
175 /// (Re)constructs GraphAL from a range of edges.
176 /** \tparam EdgeInputIterator Iterator that iterates over instances of GraphAL::Edge.
177 * \param nr The number of nodes.
178 * \param begin Points to the first edge.
179 * \param end Points just beyond the last edge.
180 */
181 template<typename EdgeInputIterator>
182 void construct( size_t nr, EdgeInputIterator begin, EdgeInputIterator end );
184 /// Adds a node without neighbors and returns the index of the added node.
185 size_t addNode() { _nb.push_back( Neighbors() ); return _nb.size() - 1; }
187 /// Adds a node, with neighbors specified by a range of nodes.
188 /** \tparam NodeInputIterator Iterator that iterates over instances of \c size_t.
189 * \param begin Points to the first index of the nodes that should become neighbors of the added node.
190 * \param end Points just beyond the last index of the nodes that should become neighbors of the added node.
191 * \param sizeHint For improved efficiency, the size of the range may be specified by \a sizeHint.
192 * \returns Index of the added node.
193 */
194 template <typename NodeInputIterator>
195 size_t addNode( NodeInputIterator begin, NodeInputIterator end, size_t sizeHint = 0 ) {
196 Neighbors nbsnew;
197 nbsnew.reserve( sizeHint );
198 size_t iter = 0;
199 for( NodeInputIterator it = begin; it != end; ++it ) {
200 DAI_ASSERT( *it < nrNodes() );
201 Neighbor nb1new( iter, *it, nb(*it).size() );
202 Neighbor nb2new( nb(*it).size(), nrNodes(), iter++ );
203 nbsnew.push_back( nb1new );
204 nb( *it ).push_back( nb2new );
205 }
206 _nb.push_back( nbsnew );
207 return _nb.size() - 1;
208 }
210 /// Adds an edge between node \a n1 and node \a n2.
211 /** If \a check == \c true, only adds the edge if it does not exist already.
212 */
213 void addEdge( size_t n1, size_t n2, bool check = true );
214 //@}
216 /// \name Erasing nodes and edges
217 //@{
218 /// Removes node \a n and all incident edges; indices of other nodes are changed accordingly.
219 void eraseNode( size_t n );
221 /// Removes edge between node \a n1 and node \a n2.
222 void eraseEdge( size_t n1, size_t n2 );
223 //@}
225 /// \name Queries
226 //@{
227 /// Returns number of nodes
228 size_t nrNodes() const { return _nb.size(); }
230 /// Calculates the number of edges, time complexity: O(nrNodes())
231 size_t nrEdges() const {
232 size_t sum = 0;
233 for( size_t i = 0; i < nrNodes(); i++ )
234 sum += nb(i).size();
235 return sum;
236 }
238 /// Returns true if the graph is connected
239 bool isConnected() const;
241 /// Returns true if the graph is a tree, i.e., if it is singly connected and connected.
242 bool isTree() const;
244 /// Checks internal consistency
245 void checkConsistency() const;
246 //@}
248 /// \name Input and output
249 //@{
250 /// Writes this GraphAL to an output stream in GraphALViz .dot syntax
251 void printDot( std::ostream& os ) const;
252 //@}
253 };
256 template<typename EdgeInputIterator>
257 void GraphAL::construct( size_t nr, EdgeInputIterator begin, EdgeInputIterator end ) {
258 _nb.clear();
259 _nb.resize( nr );
261 for( EdgeInputIterator e = begin; e != end; e++ ) {
262 #ifdef DAI_DEBUG
263 addEdge( e->first, e->second, true );
264 #else
265 addEdge( e->first, e->second, false );
266 #endif
267 }
268 }
271 /// Creates a fully-connected graph with \a N nodes
272 GraphAL createGraphFull( size_t N );
273 /// Creates a two-dimensional rectangular grid of \a n1 by \a n2 nodes, which can be \a periodic
274 GraphAL createGraphGrid( size_t n1, size_t n2, bool periodic );
275 /// Creates a three-dimensional rectangular grid of \a n1 by \a n2 by \a n3 nodes, which can be \a periodic
276 GraphAL createGraphGrid3D( size_t n1, size_t n2, size_t n3, bool periodic );
277 /// Creates a graph consisting of a single loop of \a N nodes
278 GraphAL createGraphLoop( size_t N );
279 /// Creates a random tree-structured graph of \a N nodes
280 GraphAL createGraphTree( size_t N );
281 /// Creates a random regular graph of \a N nodes with uniform connectivity \a d
282 GraphAL createGraphRegular( size_t N, size_t d );
285 } // end of namespace dai
288 #endif