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
5 This file is part of libDAI.
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.
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.
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 */
23 /// \file
24 /// \brief Defines BipartiteGraph class
27 #ifndef __defined_libdai_bipgraph_h
28 #define __defined_libdai_bipgraph_h
31 #include <ostream>
32 #include <vector>
33 #include <cassert>
34 #include <algorithm>
35 #include <dai/util.h>
38 namespace dai {
41 /// Represents the neighborhood structure of nodes in a bipartite graph.
42 /** A bipartite graph has two types of nodes: type 1 and type 2. Edges can occur only between
43 * nodes of different type. Nodes are indexed by an unsigned integer. If there are nr1()
44 * nodes of type 1 and nr2() nodes of type 2, the nodes of type 1 are numbered
45 * 0,1,2,...,nr1()-1 and the nodes of type 2 are numbered 0,1,2,...,nr2()-1. An edge
46 * between node \a n1 of type 1 and node \a n2 of type 2 is represented by a BipartiteGraph::Edge(\a n1,\a n2).
47 *
48 * A BipartiteGraph is implemented as a sparse adjacency list, i.e., it stores for each node a list of
49 * its neighboring nodes. In particular, it stores for each node of type 1 a vector of Neighbor structures
50 * (accessible by the nb1() method) describing the neighboring nodes of type 2; similarly, for each node
51 * of type 2 it stores a vector of Neighbor structures (accessibly by the nb2() method) describing the
52 * neighboring nodes of type 1.
53 * Thus, each node has an associated variable of type BipartiteGraph::Neighbors, which is a vector of
54 * Neighbor structures, describing its neighboring nodes of the other type.
55 * \idea Cache second-order neighborhoods in BipartiteGraph.
56 */
57 class BipartiteGraph {
58 public:
59 /// Describes the neighbor relationship of two nodes in a BipartiteGraph.
60 /** Sometimes we want to do an action, such as sending a
61 * message, for all edges in a graph. However, most graphs
62 * will be sparse, so we need some way of storing a set of
63 * the neighbors of a node, which is both fast and
64 * memory-efficient. We also need to be able to go between
65 * viewing node \a A as a neighbor of node \a B, and node \a
66 * B as a neighbor of node \a A. The Neighbor struct solves
67 * both of these problems. Each node has a list of neighbors,
68 * stored as a vector<Neighbor>, and extra information is
69 * included in the Neighbor struct which allows us to access
70 * a node as a neighbor of its neighbor (the \a dual member).
71 *
72 * By convention, variable identifiers naming indices into a
73 * vector of neighbors are prefixed with an underscore ("_").
74 * The neighbor list which they point into is then understood
75 * from context. For example:
76 *
77 * \code
78 * void BP::calcNewMessage( size_t i, size_t _I )
79 * \endcode
80 *
81 * Here, \a i is the "absolute" index of node i, but \a _I is
82 * understood as a "relative" index, giving node I's entry in
83 * nb1(i). The corresponding Neighbor structure can be
84 * accessed as nb1(i,_I) or nb1(i)[_I]. The absolute index of
85 * \a _I, which would be called \a I, can be recovered from
86 * the \a node member: nb1(i,_I).node. The \a iter member
87 * gives the relative index \a _I, and the \a dual member
88 * gives the "dual" relative index, i.e. the index of \a i in
89 * \a I's neighbor list.
90 *
91 * \code
92 * Neighbor n = nb1(i,_I);
93 * n.node == I &&
94 * n.iter == _I &&
95 * nb2(n.node,n.dual).node == i
96 * \endcode
97 *
98 * In a FactorGraph, nb1 is called nbV, and nb2 is called
99 * nbF.
100 *
101 * There is no easy way to transform a pair of absolute node
102 * indices \a i and \a I into a Neighbor structure relative
103 * to one of the nodes. Such a feature has never yet been
104 * found to be necessary. Iteration over edges can always be
105 * accomplished using the Neighbor lists, and by writing
106 * functions that accept relative indices:
107 * \code
108 * for( size_t i = 0; i < nrVars(); ++i )
109 * foreach( const Neighbor &I, nbV(i) )
110 * calcNewMessage( i, I.iter );
111 * \endcode
112 */
113 struct Neighbor {
114 /// Corresponds to the index of this Neighbor entry in the vector of neighbors
115 size_t iter;
116 /// Contains the number of the neighboring node
117 size_t node;
118 /// Contains the "dual" iter
119 size_t dual;
121 /// Default constructor
122 Neighbor() {}
123 /// Constructor that sets the Neighbor members according to the parameters
124 Neighbor( size_t iter, size_t node, size_t dual ) : iter(iter), node(node), dual(dual) {}
126 /// Cast to size_t returns node member
127 operator size_t () const { return node; }
128 };
130 /// Describes the neighbors of some node.
131 typedef std::vector<Neighbor> Neighbors;
133 /// 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.
134 typedef std::pair<size_t,size_t> Edge;
136 private:
137 /// Contains for each node of type 1 a vector of its neighbors
138 std::vector<Neighbors> _nb1;
140 /// Contains for each node of type 2 a vector of its neighbors
141 std::vector<Neighbors> _nb2;
143 /// Used internally by isTree()
144 struct levelType {
145 std::vector<size_t> ind1; // indices of nodes of type 1
146 std::vector<size_t> ind2; // indices of nodes of type 2
147 };
149 // OBSOLETE
150 /// @name Backwards compatibility layer (to be removed soon)
151 //@{
152 /// Enable backwards compatibility layer?
153 bool _edge_indexed;
154 /// Call indexEdges() first to initialize these members
155 std::vector<Edge> _edges;
156 /// Call indexEdges() first to initialize these members
157 hash_map<Edge,size_t> _vv2e;
158 //}@
160 public:
161 /// Default constructor (creates an empty bipartite graph)
162 BipartiteGraph() : _nb1(), _nb2(), _edge_indexed(false) {}
164 /// Constructs BipartiteGraph from a range of edges.
165 /** \tparam EdgeInputIterator Iterator that iterates over instances of BipartiteGraph::Edge.
166 * \param nr1 The number of nodes of type 1.
167 * \param nr2 The number of nodes of type 2.
168 * \param begin Points to the first edge.
169 * \param end Points just beyond the last edge.
170 */
171 template<typename EdgeInputIterator>
172 BipartiteGraph( size_t nr1, size_t nr2, EdgeInputIterator begin, EdgeInputIterator end ) : _nb1( nr1 ), _nb2( nr2 ), _edge_indexed(false) {
173 construct( nr1, nr2, begin, end );
174 }
176 /// (Re)constructs BipartiteGraph from a range of edges.
177 /** \tparam EdgeInputIterator Iterator that iterates over instances of BipartiteGraph::Edge.
178 * \param nr1 The number of nodes of type 1.
179 * \param nr2 The number of nodes of type 2.
180 * \param begin Points to the first edge.
181 * \param end Points just beyond the last edge.
182 */
183 template<typename EdgeInputIterator>
184 void construct( size_t nr1, size_t nr2, EdgeInputIterator begin, EdgeInputIterator end );
186 /// Returns constant reference to the _i2'th neighbor of node i1 of type 1
187 const Neighbor & nb1( size_t i1, size_t _i2 ) const {
188 DAI_DEBASSERT( i1 < _nb1.size() );
189 DAI_DEBASSERT( _i2 < _nb1[i1].size() );
190 return _nb1[i1][_i2];
191 }
192 /// Returns reference to the _i2'th neighbor of node i1 of type 1
193 Neighbor & nb1( size_t i1, size_t _i2 ) {
194 DAI_DEBASSERT( i1 < _nb1.size() );
195 DAI_DEBASSERT( _i2 < _nb1[i1].size() );
196 return _nb1[i1][_i2];
197 }
199 /// Returns constant reference to the _i1'th neighbor of node i2 of type 2
200 const Neighbor & nb2( size_t i2, size_t _i1 ) const {
201 DAI_DEBASSERT( i2 < _nb2.size() );
202 DAI_DEBASSERT( _i1 < _nb2[i2].size() );
203 return _nb2[i2][_i1];
204 }
205 /// Returns reference to the _i1'th neighbor of node i2 of type 2
206 Neighbor & nb2( size_t i2, size_t _i1 ) {
207 DAI_DEBASSERT( i2 < _nb2.size() );
208 DAI_DEBASSERT( _i1 < _nb2[i2].size() );
209 return _nb2[i2][_i1];
210 }
212 /// Returns constant reference to all neighbors of node i1 of type 1
213 const Neighbors & nb1( size_t i1 ) const {
214 DAI_DEBASSERT( i1 < _nb1.size() );
215 return _nb1[i1];
216 }
217 /// Returns reference to all neighbors of node of i1 type 1
218 Neighbors & nb1( size_t i1 ) {
219 DAI_DEBASSERT( i1 < _nb1.size() );
220 return _nb1[i1];
221 }
223 /// Returns constant reference to all neighbors of node i2 of type 2
224 const Neighbors & nb2( size_t i2 ) const {
225 DAI_DEBASSERT( i2 < _nb2.size() );
226 return _nb2[i2];
227 }
228 /// Returns reference to all neighbors of node i2 of type 2
229 Neighbors & nb2( size_t i2 ) {
230 DAI_DEBASSERT( i2 < _nb2.size() );
231 return _nb2[i2];
232 }
234 /// Returns number of nodes of type 1
235 size_t nr1() const { return _nb1.size(); }
236 /// Returns number of nodes of type 2
237 size_t nr2() const { return _nb2.size(); }
239 /// Calculates the number of edges, time complexity: O(nr1())
240 size_t nrEdges() const {
241 size_t sum = 0;
242 for( size_t i1 = 0; i1 < nr1(); i1++ )
243 sum += nb1(i1).size();
244 return sum;
245 }
247 /// Adds a node of type 1 without neighbors.
248 void add1() { _nb1.push_back( Neighbors() ); }
250 /// Adds a node of type 2 without neighbors.
251 void add2() { _nb2.push_back( Neighbors() ); }
253 /// Adds a node of type 1, with neighbors specified by a range of nodes of type 2.
254 /** \tparam NodeInputIterator Iterator that iterates over instances of size_t.
255 * \param begin Points to the first index of the nodes of type 2 that should become neighbors of the added node.
256 * \param end Points just beyond the last index of the nodes of type 2 that should become neighbors of the added node.
257 * \param sizeHint For improved efficiency, the size of the range may be specified by sizeHint.
258 */
259 template <typename NodeInputIterator>
260 void add1( NodeInputIterator begin, NodeInputIterator end, size_t sizeHint = 0 ) {
261 Neighbors nbs1new;
262 nbs1new.reserve( sizeHint );
263 size_t iter = 0;
264 for( NodeInputIterator it = begin; it != end; ++it ) {
265 assert( *it < nr2() );
266 Neighbor nb1new( iter, *it, nb2(*it).size() );
267 Neighbor nb2new( nb2(*it).size(), nr1(), iter++ );
268 nbs1new.push_back( nb1new );
269 nb2( *it ).push_back( nb2new );
270 }
271 _nb1.push_back( nbs1new );
272 }
274 /// Adds a node of type 2, with neighbors specified by a range of nodes of type 1.
275 /** \tparam NodeInputIterator Iterator that iterates over instances of size_t.
276 * \param begin Points to the first index of the nodes of type 1 that should become neighbors of the added node.
277 * \param end Points just beyond the last index of the nodes of type 1 that should become neighbors of the added node.
278 * \param sizeHint For improved efficiency, the size of the range may be specified by sizeHint.
279 */
280 template <typename NodeInputIterator>
281 void add2( NodeInputIterator begin, NodeInputIterator end, size_t sizeHint = 0 ) {
282 Neighbors nbs2new;
283 nbs2new.reserve( sizeHint );
284 size_t iter = 0;
285 for( NodeInputIterator it = begin; it != end; ++it ) {
286 assert( *it < nr1() );
287 Neighbor nb2new( iter, *it, nb1(*it).size() );
288 Neighbor nb1new( nb1(*it).size(), nr2(), iter++ );
289 nbs2new.push_back( nb2new );
290 nb1( *it ).push_back( nb1new );
291 }
292 _nb2.push_back( nbs2new );
293 }
295 /// Removes node n1 of type 1 and all incident edges.
296 void erase1( size_t n1 );
298 /// Removes node n2 of type 2 and all incident edges.
299 void erase2( size_t n2 );
301 /// Removes edge between node n1 of type 1 and node n2 of type 2.
302 void eraseEdge( size_t n1, size_t n2 ) {
303 assert( n1 < nr1() );
304 assert( n2 < nr2() );
305 for( Neighbors::iterator i1 = _nb1[n1].begin(); i1 != _nb1[n1].end(); i1++ )
306 if( i1->node == n2 ) {
307 _nb1[n1].erase( i1 );
308 break;
309 }
310 for( Neighbors::iterator i2 = _nb2[n2].begin(); i2 != _nb2[n2].end(); i2++ )
311 if( i2->node == n1 ) {
312 _nb2[n2].erase( i2 );
313 break;
314 }
315 }
317 /// Adds an edge between node n1 of type 1 and node n2 of type 2.
318 /** If check == true, only adds the edge if it does not exist already.
319 */
320 void addEdge( size_t n1, size_t n2, bool check = true ) {
321 assert( n1 < nr1() );
322 assert( n2 < nr2() );
323 bool exists = false;
324 if( check ) {
325 // Check whether the edge already exists
326 foreach( const Neighbor &nb2, nb1(n1) )
327 if( nb2 == n2 ) {
328 exists = true;
329 break;
330 }
331 }
332 if( !exists ) { // Add edge
333 Neighbor nb_1( _nb1[n1].size(), n2, _nb2[n2].size() );
334 Neighbor nb_2( nb_1.dual, n1, nb_1.iter );
335 _nb1[n1].push_back( nb_1 );
336 _nb2[n2].push_back( nb_2 );
337 }
338 }
340 /// Calculates second-order neighbors (i.e., neighbors of neighbors) of node n1 of type 1.
341 /** If include == true, includes n1 itself, otherwise excludes n1.
342 */
343 std::vector<size_t> delta1( size_t n1, bool include = false ) const;
345 /// Calculates second-order neighbors (i.e., neighbors of neighbors) of node n2 of type 2.
346 /** If include == true, includes n2 itself, otherwise excludes n2.
347 */
348 std::vector<size_t> delta2( size_t n2, bool include = false ) const;
350 /// Returns true if the graph is connected
351 /** \todo Should be optimized by invoking boost::graph library
352 */
353 bool isConnected() const;
355 /// Returns true if the graph is a tree, i.e., if it is singly connected and connected.
356 bool isTree() const;
358 /// Writes this BipartiteGraph to an output stream in GraphViz .dot syntax
359 void printDot( std::ostream& os ) const;
361 // OBSOLETE
362 /// @name Backwards compatibility layer (to be removed soon)
363 //@{
364 void indexEdges() {
365 std::cerr << "Warning: this BipartiteGraph edge interface is obsolete!" << std::endl;
366 _edges.clear();
367 _vv2e.clear();
368 size_t i=0;
369 foreach(const Neighbors &nb1s, _nb1) {
370 foreach(const Neighbor &n2, nb1s) {
371 Edge e(i, n2.node);
372 _edges.push_back(e);
373 }
374 i++;
375 }
376 sort(_edges.begin(), _edges.end()); // unnecessary?
378 i=0;
379 foreach(const Edge& e, _edges) {
380 _vv2e[e] = i++;
381 }
383 _edge_indexed = true;
384 }
386 const Edge& edge(size_t e) const {
387 assert(_edge_indexed);
388 return _edges[e];
389 }
391 const std::vector<Edge>& edges() const {
392 return _edges;
393 }
395 size_t VV2E(size_t n1, size_t n2) const {
396 assert(_edge_indexed);
397 Edge e(n1,n2);
398 hash_map<Edge,size_t>::const_iterator i = _vv2e.find(e);
399 assert(i != _vv2e.end());
400 return i->second;
401 }
403 size_t nr_edges() const {
404 assert(_edge_indexed);
405 return _edges.size();
406 }
407 //}@
409 private:
410 /// Checks internal consistency
411 void check() const;
412 };
415 template<typename EdgeInputIterator>
416 void BipartiteGraph::construct( size_t nr1, size_t nr2, EdgeInputIterator begin, EdgeInputIterator end ) {
417 _nb1.clear();
418 _nb1.resize( nr1 );
419 _nb2.clear();
420 _nb2.resize( nr2 );
422 for( EdgeInputIterator e = begin; e != end; e++ ) {
423 #ifdef DAI_DEBUG
424 addEdge( e->first, e->second, true );
425 #else
426 addEdge( e->first, e->second, false );
427 #endif
428 }
429 }
432 } // end of namespace dai
435 /** \example example_bipgraph.cpp
436 * This example deals with the following bipartite graph:
437 * \dot
438 * graph example {
439 * ordering=out;
440 * subgraph cluster_type1 {
441 * node[shape=circle,width=0.4,fixedsize=true,style=filled];
442 * 12 [label="2"];
443 * 11 [label="1"];
444 * 10 [label="0"];
445 * }
446 * subgraph cluster_type2 {
447 * node[shape=polygon,regular=true,sides=4,width=0.4,fixedsize=true,style=filled];
448 * 21 [label="1"];
449 * 20 [label="0"];
450 * }
451 * 10 -- 20;
452 * 11 -- 20;
453 * 12 -- 20;
454 * 11 -- 21;
455 * 12 -- 21;
456 * }
457 * \enddot
458 * It has three nodes of type 1 (drawn as circles) and two nodes of type 2 (drawn as rectangles).
459 * 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).
460 * The example code shows how to construct a BipartiteGraph object representing this bipartite graph and
461 * how to iterate over nodes and their neighbors.
462 *
463 * \section Output
464 * \verbinclude examples/example_bipgraph.out
465 *
466 * \section Source
467 */
470 #endif