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) 2006-2010 Joris Mooij [joris dot mooij at libdai dot org]
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/smallset.h>
25 #include <dai/exceptions.h>
28 namespace dai {
31 /// Represents the neighborhood structure of nodes in an undirected, bipartite graph.
32 /** A bipartite graph has two types of nodes: type 1 and type 2. Edges can occur only between
33 * nodes of different type. Nodes are indexed by an unsigned integer. If there are nrNodes1()
34 * nodes of type 1 and nrNodes2() nodes of type 2, the nodes of type 1 are numbered
35 * 0,1,2,...,nrNodes1()-1 and the nodes of type 2 are numbered 0,1,2,...,nrNodes2()-1. An edge
36 * between node \a n1 of type 1 and node \a n2 of type 2 is represented by a BipartiteGraph::Edge(\a n1,\a n2).
37 *
38 * A BipartiteGraph is implemented as a sparse adjacency list, i.e., it stores for each node a list of
39 * its neighboring nodes. More precisely: it stores for each node of type 1 a vector of Neighbor structures
40 * (accessible by the nb1() method) describing the neighboring nodes of type 2; similarly, for each node
41 * of type 2 it stores a vector of Neighbor structures (accessibly by the nb2() method) describing the
42 * neighboring nodes of type 1.
43 * Thus, each node has an associated variable of type BipartiteGraph::Neighbors, which is a vector of
44 * Neighbor structures, describing its neighboring nodes of the other type.
45 * \idea Cache second-order neighborhoods in BipartiteGraph.
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,
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, with neighbors specified by a range of nodes of type 2.
233 /** \tparam NodeInputIterator Iterator that iterates over instances of \c size_t.
234 * \param begin Points to the first index of the nodes of type 2 that should become neighbors of the added node.
235 * \param end Points just beyond the last index of the nodes of type 2 that should become neighbors of the added node.
236 * \param sizeHint For improved efficiency, the size of the range may be specified by \a sizeHint.
237 * \returns Index of the added node.
238 */
239 template <typename NodeInputIterator>
240 size_t addNode1( NodeInputIterator begin, NodeInputIterator end, size_t sizeHint = 0 ) {
241 Neighbors nbs1new;
242 nbs1new.reserve( sizeHint );
243 size_t iter = 0;
244 for( NodeInputIterator it = begin; it != end; ++it ) {
245 DAI_ASSERT( *it < nrNodes2() );
246 Neighbor nb1new( iter, *it, nb2(*it).size() );
247 Neighbor nb2new( nb2(*it).size(), nrNodes1(), iter++ );
248 nbs1new.push_back( nb1new );
249 nb2( *it ).push_back( nb2new );
250 }
251 _nb1.push_back( nbs1new );
252 return _nb1.size() - 1;
253 }
255 /// Adds a node of type 2, with neighbors specified by a range of nodes of type 1.
256 /** \tparam NodeInputIterator Iterator that iterates over instances of \c size_t.
257 * \param begin Points to the first index of the nodes of type 1 that should become neighbors of the added node.
258 * \param end Points just beyond the last index of the nodes of type 1 that should become neighbors of the added node.
259 * \param sizeHint For improved efficiency, the size of the range may be specified by \a sizeHint.
260 * \returns Index of the added node.
261 */
262 template <typename NodeInputIterator>
263 size_t addNode2( NodeInputIterator begin, NodeInputIterator end, size_t sizeHint = 0 ) {
264 Neighbors nbs2new;
265 nbs2new.reserve( sizeHint );
266 size_t iter = 0;
267 for( NodeInputIterator it = begin; it != end; ++it ) {
268 DAI_ASSERT( *it < nrNodes1() );
269 Neighbor nb2new( iter, *it, nb1(*it).size() );
270 Neighbor nb1new( nb1(*it).size(), nrNodes2(), iter++ );
271 nbs2new.push_back( nb2new );
272 nb1( *it ).push_back( nb1new );
273 }
274 _nb2.push_back( nbs2new );
275 return _nb2.size() - 1;
276 }
278 /// Adds an edge between node \a n1 of type 1 and node \a n2 of type 2.
279 /** If \a check == \c true, only adds the edge if it does not exist already.
280 */
281 void addEdge( size_t n1, size_t n2, bool check = true );
282 //@}
284 /// \name Erasing nodes and edges
285 //@{
286 /// Removes node \a n1 of type 1 and all incident edges; indices of other nodes are changed accordingly.
287 void eraseNode1( size_t n1 );
289 /// Removes node \a n2 of type 2 and all incident edges; indices of other nodes are changed accordingly.
290 void eraseNode2( size_t n2 );
292 /// Removes edge between node \a n1 of type 1 and node \a n2 of type 2.
293 void eraseEdge( size_t n1, size_t n2 );
294 //@}
296 /// \name Queries
297 //@{
298 /// Returns number of nodes of type 1
299 size_t nrNodes1() const { return _nb1.size(); }
300 /// Returns number of nodes of type 2
301 size_t nrNodes2() const { return _nb2.size(); }
303 /// Calculates the number of edges, time complexity: O(nrNodes1())
304 size_t nrEdges() const {
305 size_t sum = 0;
306 for( size_t i1 = 0; i1 < nrNodes1(); i1++ )
307 sum += nb1(i1).size();
308 return sum;
309 }
311 /// Returns true if the graph contains an edge between node \a n1 of type 1 and node \a n2 of type 2.
312 /** \note The time complexity is linear in the number of neighbors of \a n1 or \a n2
313 */
314 bool hasEdge( size_t n1, size_t n2 ) {
315 if( nb1(n1).size() < nb2(n2).size() ) {
316 for( size_t _n2 = 0; _n2 < nb1(n1).size(); _n2++ )
317 if( nb1( n1, _n2 ) == n2 )
318 return true;
319 } else {
320 for( size_t _n1 = 0; _n1 < nb2(n2).size(); _n1++ )
321 if( nb2( n2, _n1 ) == n1 )
322 return true;
323 }
324 return false;
325 }
327 /// Returns the index of a given node \a n2 of type 2 amongst the neighbors of node \a n1 of type 1
328 /** \note The time complexity is linear in the number of neighbors of \a n1
329 * \throw OBJECT_NOT_FOUND if \a n2 is not a neighbor of \a n1
330 */
331 size_t findNb1( size_t n1, size_t n2 ) {
332 for( size_t _n2 = 0; _n2 < nb1(n1).size(); _n2++ )
333 if( nb1( n1, _n2 ) == n2 )
334 return _n2;
335 DAI_THROW(OBJECT_NOT_FOUND);
336 return nb1(n1).size();
337 }
339 /// Returns the index of a given node \a n1 of type 1 amongst the neighbors of node \a n2 of type 2
340 /** \note The time complexity is linear in the number of neighbors of \a n2
341 * \throw OBJECT_NOT_FOUND if \a n1 is not a neighbor of \a n2
342 */
343 size_t findNb2( size_t n1, size_t n2 ) {
344 for( size_t _n1 = 0; _n1 < nb2(n2).size(); _n1++ )
345 if( nb2( n2, _n1 ) == n1 )
346 return _n1;
347 DAI_THROW(OBJECT_NOT_FOUND);
348 return nb2(n2).size();
349 }
351 /// Calculates second-order neighbors (i.e., neighbors of neighbors) of node \a n1 of type 1.
352 /** If \a include == \c true, includes \a n1 itself, otherwise excludes \a n1.
353 */
354 SmallSet<size_t> delta1( size_t n1, bool include = false ) const;
356 /// Calculates second-order neighbors (i.e., neighbors of neighbors) of node \a n2 of type 2.
357 /** If \a include == \c true, includes \a n2 itself, otherwise excludes \a n2.
358 */
359 SmallSet<size_t> delta2( size_t n2, bool include = false ) const;
361 /// Returns true if the graph is connected
362 bool isConnected() const;
364 /// Returns true if the graph is a tree, i.e., if it is singly connected and connected.
365 bool isTree() const;
367 /// Asserts internal consistency
368 void checkConsistency() const;
369 //@}
371 /// \name Input and output
372 //@{
373 /// Writes this BipartiteGraph to an output stream in GraphViz .dot syntax
374 void printDot( std::ostream& os ) const;
375 //@}
376 };
379 template<typename EdgeInputIterator>
380 void BipartiteGraph::construct( size_t nrNodes1, size_t nrNodes2, EdgeInputIterator begin, EdgeInputIterator end ) {
381 _nb1.clear();
382 _nb1.resize( nrNodes1 );
383 _nb2.clear();
384 _nb2.resize( nrNodes2 );
386 for( EdgeInputIterator e = begin; e != end; e++ ) {
387 #ifdef DAI_DEBUG
388 addEdge( e->first, e->second, true );
389 #else
390 addEdge( e->first, e->second, false );
391 #endif
392 }
393 }
396 } // end of namespace dai
399 /** \example example_bipgraph.cpp
400 * This example deals with the following bipartite graph:
401 * \dot
402 * graph example {
403 * ordering=out;
404 * subgraph cluster_type1 {
405 * node[shape=circle,width=0.4,fixedsize=true,style=filled];
406 * 12 [label="2"];
407 * 11 [label="1"];
408 * 10 [label="0"];
409 * }
410 * subgraph cluster_type2 {
411 * node[shape=polygon,regular=true,sides=4,width=0.4,fixedsize=true,style=filled];
412 * 21 [label="1"];
413 * 20 [label="0"];
414 * }
415 * 10 -- 20;
416 * 11 -- 20;
417 * 12 -- 20;
418 * 11 -- 21;
419 * 12 -- 21;
420 * }
421 * \enddot
422 * It has three nodes of type 1 (drawn as circles) and two nodes of type 2 (drawn as rectangles).
423 * 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).
424 * The example code shows how to construct a BipartiteGraph object representing this bipartite graph and
425 * how to iterate over nodes and their neighbors.
426 *
427 * \section Output
428 * \verbinclude examples/example_bipgraph.out
429 *
430 * \section Source
431 */
434 #endif