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
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 a neighboring node of some other node in a BipartiteGraph.
60 /** A Neighbor structure has three members: \a iter, \a node and \a dual. The \a
61 * node member is the most important member: it contains the index of the neighboring node. The \a iter
62 * member is useful for iterating over neighbors, and contains the index of this Neighbor entry in the
63 * corresponding BipartiteGraph::Neighbors variable. The \a dual member is useful to find the dual Neighbor
64 * element: a pair of neighboring nodes can be either specified as a node of type 1 and a neighbor of type
65 * 2, or as a node of type 2 and a neighbor of type 1; the \a dual member contains the index of the dual
66 * Neighbor element (see the example for another explanation of the dual member).
67 */
68 struct Neighbor {
69 /// Corresponds to the index of this Neighbor entry in the vector of neighbors
70 size_t iter;
71 /// Contains the number of the neighboring node
72 size_t node;
73 /// Contains the "dual" iter
74 size_t dual;
76 /// Default constructor
77 Neighbor() {}
78 /// Constructor that sets the Neighbor members according to the parameters
79 Neighbor( size_t iter, size_t node, size_t dual ) : iter(iter), node(node), dual(dual) {}
81 /// Cast to size_t returns node member
82 operator size_t () const { return node; }
83 };
85 /// Describes the neighbors of some node.
86 typedef std::vector<Neighbor> Neighbors;
88 /// 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.
89 typedef std::pair<size_t,size_t> Edge;
91 private:
92 /// Contains for each node of type 1 a vector of its neighbors
93 std::vector<Neighbors> _nb1;
95 /// Contains for each node of type 2 a vector of its neighbors
96 std::vector<Neighbors> _nb2;
98 /// Used internally by isTree()
99 struct levelType {
100 std::vector<size_t> ind1; // indices of nodes of type 1
101 std::vector<size_t> ind2; // indices of nodes of type 2
102 };
104 public:
105 /// Default constructor (creates an empty bipartite graph)
106 BipartiteGraph() : _nb1(), _nb2() {}
108 /// Constructs BipartiteGraph from a range of edges.
109 /** \tparam EdgeInputIterator Iterator that iterates over instances of BipartiteGraph::Edge.
110 * \param nr1 The number of nodes of type 1.
111 * \param nr2 The number of nodes of type 2.
112 * \param begin Points to the first edge.
113 * \param end Points just beyond the last edge.
114 */
115 template<typename EdgeInputIterator>
116 BipartiteGraph( size_t nr1, size_t nr2, EdgeInputIterator begin, EdgeInputIterator end ) : _nb1( nr1 ), _nb2( nr2 ) {
117 construct( nr1, nr2, begin, end );
118 }
120 /// (Re)constructs BipartiteGraph from a range of edges.
121 /** \tparam EdgeInputIterator Iterator that iterates over instances of BipartiteGraph::Edge.
122 * \param nr1 The number of nodes of type 1.
123 * \param nr2 The number of nodes of type 2.
124 * \param begin Points to the first edge.
125 * \param end Points just beyond the last edge.
126 */
127 template<typename EdgeInputIterator>
128 void construct( size_t nr1, size_t nr2, EdgeInputIterator begin, EdgeInputIterator end );
130 /// Returns constant reference to the _i2'th neighbor of node i1 of type 1
131 const Neighbor & nb1( size_t i1, size_t _i2 ) const {
132 #ifdef DAI_DEBUG
133 assert( i1 < _nb1.size() );
134 assert( _i2 < _nb1[i1].size() );
135 #endif
136 return _nb1[i1][_i2];
137 }
138 /// Returns reference to the _i2'th neighbor of node i1 of type 1
139 Neighbor & nb1( size_t i1, size_t _i2 ) {
140 #ifdef DAI_DEBUG
141 assert( i1 < _nb1.size() );
142 assert( _i2 < _nb1[i1].size() );
143 #endif
144 return _nb1[i1][_i2];
145 }
147 /// Returns constant reference to the _i1'th neighbor of node i2 of type 2
148 const Neighbor & nb2( size_t i2, size_t _i1 ) const {
149 #ifdef DAI_DEBUG
150 assert( i2 < _nb2.size() );
151 assert( _i1 < _nb2[i2].size() );
152 #endif
153 return _nb2[i2][_i1];
154 }
155 /// Returns reference to the _i1'th neighbor of node i2 of type 2
156 Neighbor & nb2( size_t i2, size_t _i1 ) {
157 #ifdef DAI_DEBUG
158 assert( i2 < _nb2.size() );
159 assert( _i1 < _nb2[i2].size() );
160 #endif
161 return _nb2[i2][_i1];
162 }
164 /// Returns constant reference to all neighbors of node i1 of type 1
165 const Neighbors & nb1( size_t i1 ) const {
166 #ifdef DAI_DEBUG
167 assert( i1 < _nb1.size() );
168 #endif
169 return _nb1[i1];
170 }
171 /// Returns reference to all neighbors of node of i1 type 1
172 Neighbors & nb1( size_t i1 ) {
173 #ifdef DAI_DEBUG
174 assert( i1 < _nb1.size() );
175 #endif
176 return _nb1[i1];
177 }
179 /// Returns constant reference to all neighbors of node i2 of type 2
180 const Neighbors & nb2( size_t i2 ) const {
181 #ifdef DAI_DEBUG
182 assert( i2 < _nb2.size() );
183 #endif
184 return _nb2[i2];
185 }
186 /// Returns reference to all neighbors of node i2 of type 2
187 Neighbors & nb2( size_t i2 ) {
188 #ifdef DAI_DEBUG
189 assert( i2 < _nb2.size() );
190 #endif
191 return _nb2[i2];
192 }
194 /// Returns number of nodes of type 1
195 size_t nr1() const { return _nb1.size(); }
196 /// Returns number of nodes of type 2
197 size_t nr2() const { return _nb2.size(); }
199 /// Calculates the number of edges, time complexity: O(nr1())
200 size_t nrEdges() const {
201 size_t sum = 0;
202 for( size_t i1 = 0; i1 < nr1(); i1++ )
203 sum += nb1(i1).size();
204 return sum;
205 }
207 /// Adds a node of type 1 without neighbors.
208 void add1() { _nb1.push_back( Neighbors() ); }
210 /// Adds a node of type 2 without neighbors.
211 void add2() { _nb2.push_back( Neighbors() ); }
213 /// Adds a node of type 1, with neighbors specified by a range of nodes of type 2.
214 /** \tparam NodeInputIterator Iterator that iterates over instances of size_t.
215 * \param begin Points to the first index of the nodes of type 2 that should become neighbors of the added node.
216 * \param end Points just beyond the last index of the nodes of type 2 that should become neighbors of the added node.
217 * \param sizeHint For improved efficiency, the size of the range may be specified by sizeHint.
218 */
219 template <typename NodeInputIterator>
220 void add1( NodeInputIterator begin, NodeInputIterator end, size_t sizeHint = 0 ) {
221 Neighbors nbs1new;
222 nbs1new.reserve( sizeHint );
223 size_t iter = 0;
224 for( NodeInputIterator it = begin; it != end; ++it ) {
225 assert( *it < nr2() );
226 Neighbor nb1new( iter, *it, nb2(*it).size() );
227 Neighbor nb2new( nb2(*it).size(), nr1(), iter++ );
228 nbs1new.push_back( nb1new );
229 nb2( *it ).push_back( nb2new );
230 }
231 _nb1.push_back( nbs1new );
232 }
234 /// Adds a node of type 2, with neighbors specified by a range of nodes of type 1.
235 /** \tparam NodeInputIterator Iterator that iterates over instances of size_t.
236 * \param begin Points to the first index of the nodes of type 1 that should become neighbors of the added node.
237 * \param end Points just beyond the last index of the nodes of type 1 that should become neighbors of the added node.
238 * \param sizeHint For improved efficiency, the size of the range may be specified by sizeHint.
239 */
240 template <typename NodeInputIterator>
241 void add2( NodeInputIterator begin, NodeInputIterator end, size_t sizeHint = 0 ) {
242 Neighbors nbs2new;
243 nbs2new.reserve( sizeHint );
244 size_t iter = 0;
245 for( NodeInputIterator it = begin; it != end; ++it ) {
246 assert( *it < nr1() );
247 Neighbor nb2new( iter, *it, nb1(*it).size() );
248 Neighbor nb1new( nb1(*it).size(), nr2(), iter++ );
249 nbs2new.push_back( nb2new );
250 nb1( *it ).push_back( nb1new );
251 }
252 _nb2.push_back( nbs2new );
253 }
255 /// Removes node n1 of type 1 and all incident edges.
256 void erase1( size_t n1 );
258 /// Removes node n2 of type 2 and all incident edges.
259 void erase2( size_t n2 );
261 /// Removes edge between node n1 of type 1 and node n2 of type 2.
262 void eraseEdge( size_t n1, size_t n2 ) {
263 assert( n1 < nr1() );
264 assert( n2 < nr2() );
265 for( Neighbors::iterator i1 = _nb1[n1].begin(); i1 != _nb1[n1].end(); i1++ )
266 if( i1->node == n2 ) {
267 _nb1[n1].erase( i1 );
268 break;
269 }
270 for( Neighbors::iterator i2 = _nb2[n2].begin(); i2 != _nb2[n2].end(); i2++ )
271 if( i2->node == n1 ) {
272 _nb2[n2].erase( i2 );
273 break;
274 }
275 }
277 /// Adds an edge between node n1 of type 1 and node n2 of type 2.
278 /** If check == true, only adds the edge if it does not exist already.
279 */
280 void addEdge( size_t n1, size_t n2, bool check = true ) {
281 assert( n1 < nr1() );
282 assert( n2 < nr2() );
283 bool exists = false;
284 if( check ) {
285 // Check whether the edge already exists
286 foreach( const Neighbor &nb2, nb1(n1) )
287 if( nb2 == n2 ) {
288 exists = true;
289 break;
290 }
291 }
292 if( !exists ) { // Add edge
293 Neighbor nb_1( _nb1[n1].size(), n2, _nb2[n2].size() );
294 Neighbor nb_2( nb_1.dual, n1, nb_1.iter );
295 _nb1[n1].push_back( nb_1 );
296 _nb2[n2].push_back( nb_2 );
297 }
298 }
300 /// Calculates second-order neighbors (i.e., neighbors of neighbors) of node n1 of type 1.
301 /** If include == true, includes n1 itself, otherwise excludes n1.
302 */
303 std::vector<size_t> delta1( size_t n1, bool include = false ) const;
305 /// Calculates second-order neighbors (i.e., neighbors of neighbors) of node n2 of type 2.
306 /** If include == true, includes n2 itself, otherwise excludes n2.
307 */
308 std::vector<size_t> delta2( size_t n2, bool include = false ) const;
310 /// Returns true if the graph is connected
311 /** \todo Should be optimized by invoking boost::graph library
312 */
313 bool isConnected() const;
315 /// Returns true if the graph is a tree, i.e., if it is singly connected and connected.
316 bool isTree() const;
318 /// Writes this BipartiteGraph to an output stream in GraphViz .dot syntax
319 void printDot( std::ostream& os ) const;
321 private:
322 /// Checks internal consistency
323 void check() const;
324 };
327 template<typename EdgeInputIterator>
328 void BipartiteGraph::construct( size_t nr1, size_t nr2, EdgeInputIterator begin, EdgeInputIterator end ) {
329 _nb1.clear();
330 _nb1.resize( nr1 );
331 _nb2.clear();
332 _nb2.resize( nr2 );
334 for( EdgeInputIterator e = begin; e != end; e++ ) {
335 #ifdef DAI_DEBUG
336 addEdge( e->first, e->second, true );
337 #else
338 addEdge( e->first, e->second, false );
339 #endif
340 }
341 }
344 } // end of namespace dai
347 /** \example example_bipgraph.cpp
348 * This example deals with the following bipartite graph:
349 * \dot
350 * graph example {
351 * ordering=out;
352 * subgraph cluster_type1 {
353 * node[shape=circle,width=0.4,fixedsize=true,style=filled];
354 * 12 [label="2"];
355 * 11 [label="1"];
356 * 10 [label="0"];
357 * }
358 * subgraph cluster_type2 {
359 * node[shape=polygon,regular=true,sides=4,width=0.4,fixedsize=true,style=filled];
360 * 21 [label="1"];
361 * 20 [label="0"];
362 * }
363 * 10 -- 20;
364 * 11 -- 20;
365 * 12 -- 20;
366 * 11 -- 21;
367 * 12 -- 21;
368 * }
369 * \enddot
370 * It has three nodes of type 1 (drawn as circles) and two nodes of type 2 (drawn as rectangles).
371 * 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).
372 * The example code shows how to construct a BipartiteGraph object representing this bipartite graph and
373 * how to iterate over nodes and their neighbors.
374 *
375 * \section Output
376 * \verbinclude examples/example_bipgraph.out
377 *
378 * \section Source
379 */
382 #endif