1 /* This file is part of libDAI - http://www.libdai.org/
2 *
3 * libDAI is licensed under the terms of the GNU General Public License version
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 BipartiteGraph class, which represents a bipartite graph
16 #ifndef __defined_libdai_bipgraph_h
17 #define __defined_libdai_bipgraph_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, bipartite graph.
31 /** A bipartite graph has two types of nodes: type 1 and type 2. Edges can occur only between
32 * nodes of different type. Nodes are indexed by an unsigned integer. If there are nrNodes1()
33 * nodes of type 1 and nrNodes2() nodes of type 2, the nodes of type 1 are numbered
34 * 0,1,2,...,nrNodes1()-1 and the nodes of type 2 are numbered 0,1,2,...,nrNodes2()-1. An edge
35 * between node \a n1 of type 1 and node \a n2 of type 2 is represented by a BipartiteGraph::Edge(\a n1,\a n2).
36 *
37 * A BipartiteGraph is implemented as a sparse adjacency list, i.e., it stores for each node a list of
38 * its neighboring nodes. More precisely: it stores for each node of type 1 a vector of Neighbor structures
39 * (accessible by the nb1() method) describing the neighboring nodes of type 2; similarly, for each node
40 * of type 2 it stores a vector of Neighbor structures (accessibly by the nb2() method) describing the
41 * neighboring nodes of type 1.
42 * Thus, each node has an associated variable of type BipartiteGraph::Neighbors, which is a vector of
43 * Neighbor structures, describing its neighboring nodes of the other type.
44 * \idea Cache second-order neighborhoods in BipartiteGraph.
45 * \todo Check whether BGL isConnected improves performance.
46 */
47 class BipartiteGraph {
48 public:
49 /// Describes the neighbor relationship of two nodes in a BipartiteGraph.
50 /** Sometimes we want to do an action, such as sending a
51 * message, for all edges in a graph. However, most graphs
52 * will be sparse, so we need some way of storing a set of
53 * the neighbors of a node, which is both fast and
54 * memory-efficient. We also need to be able to go between
55 * viewing node \a a as a neighbor of node \a b, and node \a b
56 * as a neighbor of node \a a. The Neighbor struct solves
57 * both of these problems. Each node has a list of neighbors,
58 * stored as a std::vector<\link Neighbor \endlink>, and
59 * extra information is included in the Neighbor struct which
60 * allows us to access a node as a neighbor of its neighbor
61 * (the \c dual member).
62 *
63 * By convention, variable identifiers naming indices into a
64 * vector of neighbors are prefixed with an underscore ("_").
65 * The neighbor list which they point into is then understood
66 * from context. For example:
67 *
68 * \code
69 * void BP::calcNewMessage( size_t i, size_t _I )
70 * \endcode
71 *
72 * Here, \a i is the "absolute" index of node i, but \a _I is
73 * understood as a "relative" index, giving node \a I 's entry in
74 * <tt>nb1(i)</tt>. The corresponding Neighbor structure can be
75 * accessed as <tt>nb1(i,_I)</tt> or <tt>nb1(i)[_I]</tt>. The
76 * absolute index of \a _I, which would be called \a I, can be
77 * recovered from the \c node member: <tt>nb1(i,_I).node</tt>.
78 * The \c iter member gives the relative index \a _I, and the
79 * \c dual member gives the "dual" relative index, i.e., the
80 * index of \a i in \a I 's neighbor list.
81 *
82 * \code
83 * Neighbor n = nb1(i,_I);
84 * n.node == I &&
85 * n.iter == _I &&
86 * nb2(n.node,n.dual).node == i
87 * \endcode
88 *
89 * In a FactorGraph, the nodes of type 1 represent variables, and
90 * the nodes of type 2 represent factors. For convenience, nb1() is
91 * called FactorGraph::nbV(), and nb2() is called FactorGraph::nbF().
92 *
93 * There is no easy way to transform a pair of absolute node
94 * indices \a i and \a I into a Neighbor structure relative
95 * to one of the nodes. Such a feature has never yet been
96 * found to be necessary. Iteration over edges can always be
97 * accomplished using the Neighbor lists, and by writing
98 * functions that accept relative indices:
99 * \code
100 * for( size_t i = 0; i < nrVars(); ++i )
101 * foreach( const Neighbor &I, nbV(i) )
102 * calcNewMessage( i, I.iter );
103 * \endcode
104 */
105 struct Neighbor {
106 /// Corresponds to the index of this Neighbor entry in the vector of neighbors
107 size_t iter;
108 /// Contains the number of the neighboring node
109 size_t node;
110 /// Contains the "dual" iter
111 size_t dual;
113 /// Default constructor
114 Neighbor() {}
115 /// Constructor that sets the Neighbor members according to the parameters
116 Neighbor( size_t iter, size_t node, size_t dual ) : iter(iter), node(node), dual(dual) {}
118 /// Cast to \c size_t returns \c node member
119 operator size_t () const { return node; }
120 };
122 /// Describes the neighbors of some node.
123 typedef std::vector<Neighbor> Neighbors;
125 /// Represents an edge: an Edge(\a n1,\a n2) corresponds to the edge between node \a n1 of type 1 and node \a n2 of type 2.
126 typedef std::pair<size_t,size_t> Edge;
128 private:
129 /// Contains for each node of type 1 a vector of its neighbors
130 std::vector<Neighbors> _nb1;
132 /// Contains for each node of type 2 a vector of its neighbors
133 std::vector<Neighbors> _nb2;
135 /// Used internally by isTree()
136 struct levelType {
137 /// Indices of nodes of type 1
138 std::vector<size_t> ind1;
139 /// Indices of nodes of type 2
140 std::vector<size_t> ind2;
141 };
143 public:
144 /// \name Constructors and destructors
145 //@{
146 /// Default constructor (creates an empty bipartite graph)
147 BipartiteGraph() : _nb1(), _nb2() {}
149 /// Constructs BipartiteGraph from a range of edges.
150 /** \tparam EdgeInputIterator Iterator that iterates over instances of BipartiteGraph::Edge.
151 * \param nrNodes1 The number of nodes of type 1.
152 * \param nrNodes2 The number of nodes of type 2.
153 * \param begin Points to the first edge.
154 * \param end Points just beyond the last edge.
155 */
156 template<typename EdgeInputIterator>
157 BipartiteGraph( size_t nrNodes1, size_t nrNodes2, EdgeInputIterator begin, EdgeInputIterator end ) : _nb1(), _nb2() {
158 construct( nrNodes1, nrNodes2, begin, end );
159 }
160 //@}
162 /// \name Accessors and mutators
163 //@{
164 /// Returns constant reference to the \a _i2 'th neighbor of node \a i1 of type 1
165 const Neighbor & nb1( size_t i1, size_t _i2 ) const {
166 DAI_DEBASSERT( i1 < _nb1.size() );
167 DAI_DEBASSERT( _i2 < _nb1[i1].size() );
168 return _nb1[i1][_i2];
169 }
170 /// Returns reference to the \a _i2 'th neighbor of node \a i1 of type 1
171 Neighbor & nb1( size_t i1, size_t _i2 ) {
172 DAI_DEBASSERT( i1 < _nb1.size() );
173 DAI_DEBASSERT( _i2 < _nb1[i1].size() );
174 return _nb1[i1][_i2];
175 }
177 /// Returns constant reference to the \a _i1 'th neighbor of node \a i2 of type 2
178 const Neighbor & nb2( size_t i2, size_t _i1 ) const {
179 DAI_DEBASSERT( i2 < _nb2.size() );
180 DAI_DEBASSERT( _i1 < _nb2[i2].size() );
181 return _nb2[i2][_i1];
182 }
183 /// Returns reference to the \a _i1 'th neighbor of node \a i2 of type 2
184 Neighbor & nb2( size_t i2, size_t _i1 ) {
185 DAI_DEBASSERT( i2 < _nb2.size() );
186 DAI_DEBASSERT( _i1 < _nb2[i2].size() );
187 return _nb2[i2][_i1];
188 }
190 /// Returns constant reference to all neighbors of node \a i1 of type 1
191 const Neighbors & nb1( size_t i1 ) const {
192 DAI_DEBASSERT( i1 < _nb1.size() );
193 return _nb1[i1];
194 }
195 /// Returns reference to all neighbors of node \a i1 of type 1
196 Neighbors & nb1( size_t i1 ) {
197 DAI_DEBASSERT( i1 < _nb1.size() );
198 return _nb1[i1];
199 }
201 /// Returns constant reference to all neighbors of node \a i2 of type 2
202 const Neighbors & nb2( size_t i2 ) const {
203 DAI_DEBASSERT( i2 < _nb2.size() );
204 return _nb2[i2];
205 }
206 /// Returns reference to all neighbors of node \a i2 of type 2
207 Neighbors & nb2( size_t i2 ) {
208 DAI_DEBASSERT( i2 < _nb2.size() );
209 return _nb2[i2];
210 }
211 //@}
213 /// \name Adding nodes and edges
214 //@{
215 /// (Re)constructs BipartiteGraph from a range of edges.
216 /** \tparam EdgeInputIterator Iterator that iterates over instances of BipartiteGraph::Edge.
217 * \param nrNodes1 The number of nodes of type 1.
218 * \param nrNodes2 The number of nodes of type 2.
219 * \param begin Points to the first edge.
220 * \param end Points just beyond the last edge.
221 */
222 template<typename EdgeInputIterator>
223 void construct( size_t nrNodes1, size_t nrNodes2, EdgeInputIterator begin, EdgeInputIterator end );
225 /// Adds a node of type 1 without neighbors and returns the index of the added node.
226 size_t addNode1() { _nb1.push_back( Neighbors() ); return _nb1.size() - 1; }
228 /// Adds a node of type 2 without neighbors and returns the index of the added node.
229 size_t addNode2() { _nb2.push_back( Neighbors() ); return _nb2.size() - 1; }
232 /// Adds a node of type 1 without neighbors and returns the index of the added node.
233 /** \deprecated Please use dai::BipartiteGraph::addNode1() instead.
234 */
235 size_t add1() { return addNode1(); }
237 /// Adds a node of type 2 without neighbors and returns the index of the added node.
238 /** \deprecated Please use dai::BipartiteGraph::addNode2() instead.
239 */
240 size_t add2() { return addNode2(); }
242 /// Adds a node of type 1, with neighbors specified by a range of nodes of type 2.
243 /** \tparam NodeInputIterator Iterator that iterates over instances of \c size_t.
244 * \param begin Points to the first index of the nodes of type 2 that should become neighbors of the added node.
245 * \param end Points just beyond the last index of the nodes of type 2 that should become neighbors of the added node.
246 * \param sizeHint For improved efficiency, the size of the range may be specified by \a sizeHint.
247 * \returns Index of the added node.
248 */
249 template <typename NodeInputIterator>
250 size_t addNode1( NodeInputIterator begin, NodeInputIterator end, size_t sizeHint = 0 ) {
251 Neighbors nbs1new;
252 nbs1new.reserve( sizeHint );
253 size_t iter = 0;
254 for( NodeInputIterator it = begin; it != end; ++it ) {
255 DAI_ASSERT( *it < nrNodes2() );
256 Neighbor nb1new( iter, *it, nb2(*it).size() );
257 Neighbor nb2new( nb2(*it).size(), nrNodes1(), iter++ );
258 nbs1new.push_back( nb1new );
259 nb2( *it ).push_back( nb2new );
260 }
261 _nb1.push_back( nbs1new );
262 return _nb1.size() - 1;
263 }
265 /// Adds a node of type 2, with neighbors specified by a range of nodes of type 1.
266 /** \tparam NodeInputIterator Iterator that iterates over instances of \c size_t.
267 * \param begin Points to the first index of the nodes of type 1 that should become neighbors of the added node.
268 * \param end Points just beyond the last index of the nodes of type 1 that should become neighbors of the added node.
269 * \param sizeHint For improved efficiency, the size of the range may be specified by \a sizeHint.
270 * \returns Index of the added node.
271 */
272 template <typename NodeInputIterator>
273 size_t addNode2( NodeInputIterator begin, NodeInputIterator end, size_t sizeHint = 0 ) {
274 Neighbors nbs2new;
275 nbs2new.reserve( sizeHint );
276 size_t iter = 0;
277 for( NodeInputIterator it = begin; it != end; ++it ) {
278 DAI_ASSERT( *it < nrNodes1() );
279 Neighbor nb2new( iter, *it, nb1(*it).size() );
280 Neighbor nb1new( nb1(*it).size(), nrNodes2(), iter++ );
281 nbs2new.push_back( nb2new );
282 nb1( *it ).push_back( nb1new );
283 }
284 _nb2.push_back( nbs2new );
285 return _nb2.size() - 1;
286 }
288 /// Adds a node of type 1, with neighbors specified by a range of nodes of type 2.
289 /** \deprecated Please use dai::BipartiteGraph::addNode1( NodeInputIterator, NodeInputIterator, size_t) instead.
290 */
291 template <typename NodeInputIterator>
292 size_t add1( NodeInputIterator begin, NodeInputIterator end, size_t sizeHint = 0 ) {
293 return addNode1( begin, end, sizeHint );
294 }
296 /// Adds a node of type 2, with neighbors specified by a range of nodes of type 1.
297 /** \deprecated Please use dai::BipartiteGraph::addNode2( NodeInputIterator, NodeInputIterator, size_t) instead.
298 */
299 template <typename NodeInputIterator>
300 size_t add2( NodeInputIterator begin, NodeInputIterator end, size_t sizeHint = 0 ) {
301 return addNode2( begin, end, sizeHint );
302 }
304 /// Adds an edge between node \a n1 of type 1 and node \a n2 of type 2.
305 /** If \a check == \c true, only adds the edge if it does not exist already.
306 */
307 void addEdge( size_t n1, size_t n2, bool check = true );
308 //@}
310 /// \name Erasing nodes and edges
311 //@{
312 /// Removes node \a n1 of type 1 and all incident edges; indices of other nodes are changed accordingly.
313 void eraseNode1( size_t n1 );
315 /// Removes node \a n2 of type 2 and all incident edges; indices of other nodes are changed accordingly.
316 void eraseNode2( size_t n2 );
318 /// Removes node \a n1 of type 1 and all incident edges; indices of other nodes are changed accordingly.
319 /** \deprecated Please use dai::BipartiteGraph::eraseNode1(size_t) instead.
320 */
321 void erase1( size_t n1 ) { eraseNode1( n1 ); }
323 /// Removes node \a n2 of type 2 and all incident edges; indices of other nodes are changed accordingly.
324 /** \deprecated Please use dai::BipartiteGraph::eraseNode2(size_t) instead.
325 */
326 void erase2( size_t n2 ) { eraseNode2( n2 ); }
328 /// Removes edge between node \a n1 of type 1 and node \a n2 of type 2.
329 void eraseEdge( size_t n1, size_t n2 );
330 //@}
332 /// \name Queries
333 //@{
334 /// Returns number of nodes of type 1
335 size_t nrNodes1() const { return _nb1.size(); }
336 /// Returns number of nodes of type 2
337 size_t nrNodes2() const { return _nb2.size(); }
339 /// Returns number of nodes of type 1
340 /** \deprecated Please use dai::BipartiteGraph::nrNodes1() instead.
341 */
342 size_t nr1() const { return nrNodes1(); }
344 /// Returns number of nodes of type 2
345 /** \deprecated Please use dai::BipartiteGraph::nrNodes2() instead.
346 */
347 size_t nr2() const { return nrNodes2(); }
349 /// Calculates the number of edges, time complexity: O(nrNodes1())
350 size_t nrEdges() const {
351 size_t sum = 0;
352 for( size_t i1 = 0; i1 < nrNodes1(); i1++ )
353 sum += nb1(i1).size();
354 return sum;
355 }
357 /// Calculates second-order neighbors (i.e., neighbors of neighbors) of node \a n1 of type 1.
358 /** If \a include == \c true, includes \a n1 itself, otherwise excludes \a n1.
359 */
360 std::vector<size_t> delta1( size_t n1, bool include = false ) const;
362 /// Calculates second-order neighbors (i.e., neighbors of neighbors) of node \a n2 of type 2.
363 /** If \a include == \c true, includes \a n2 itself, otherwise excludes \a n2.
364 */
365 std::vector<size_t> delta2( size_t n2, bool include = false ) const;
367 /// Returns true if the graph is connected
368 bool isConnected() const;
370 /// Returns true if the graph is a tree, i.e., if it is singly connected and connected.
371 bool isTree() const;
373 /// Checks internal consistency
374 void checkConsistency() const;
375 //@}
377 /// \name Input and output
378 //@{
379 /// Writes this BipartiteGraph to an output stream in GraphViz .dot syntax
380 void printDot( std::ostream& os ) const;
381 //@}
382 };
385 template<typename EdgeInputIterator>
386 void BipartiteGraph::construct( size_t nrNodes1, size_t nrNodes2, EdgeInputIterator begin, EdgeInputIterator end ) {
387 _nb1.clear();
388 _nb1.resize( nrNodes1 );
389 _nb2.clear();
390 _nb2.resize( nrNodes2 );
392 for( EdgeInputIterator e = begin; e != end; e++ ) {
393 #ifdef DAI_DEBUG
394 addEdge( e->first, e->second, true );
395 #else
396 addEdge( e->first, e->second, false );
397 #endif
398 }
399 }
402 } // end of namespace dai
405 /** \example example_bipgraph.cpp
406 * This example deals with the following bipartite graph:
407 * \dot
408 * graph example {
409 * ordering=out;
410 * subgraph cluster_type1 {
411 * node[shape=circle,width=0.4,fixedsize=true,style=filled];
412 * 12 [label="2"];
413 * 11 [label="1"];
414 * 10 [label="0"];
415 * }
416 * subgraph cluster_type2 {
417 * node[shape=polygon,regular=true,sides=4,width=0.4,fixedsize=true,style=filled];
418 * 21 [label="1"];
419 * 20 [label="0"];
420 * }
421 * 10 -- 20;
422 * 11 -- 20;
423 * 12 -- 20;
424 * 11 -- 21;
425 * 12 -- 21;
426 * }
427 * \enddot
428 * It has three nodes of type 1 (drawn as circles) and two nodes of type 2 (drawn as rectangles).
429 * Node 0 of type 1 has only one neighbor (node 0 of type 2), but node 0 of type 2 has three neighbors (nodes 0,1,2 of type 1).
430 * The example code shows how to construct a BipartiteGraph object representing this bipartite graph and
431 * how to iterate over nodes and their neighbors.
432 *
433 * \section Output
434 * \verbinclude examples/example_bipgraph.out
435 *
436 * \section Source
437 */
440 #endif