1 | /* -*- C++ -*- |
---|
2 | * lemon/preflow_matching.h - Part of LEMON, a generic C++ optimization library |
---|
3 | * |
---|
4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
6 | * |
---|
7 | * Permission to use, modify and distribute this software is granted |
---|
8 | * provided that this copyright notice appears in all copies. For |
---|
9 | * precise terms see the accompanying LICENSE file. |
---|
10 | * |
---|
11 | * This software is provided "AS IS" with no warranty of any kind, |
---|
12 | * express or implied, and with no claim as to its suitability for any |
---|
13 | * purpose. |
---|
14 | * |
---|
15 | */ |
---|
16 | |
---|
17 | #ifndef LEMON_BP_MATCHING |
---|
18 | #define LEMON_BP_MATCHING |
---|
19 | |
---|
20 | #include <lemon/graph_utils.h> |
---|
21 | #include <lemon/iterable_maps.h> |
---|
22 | #include <iostream> |
---|
23 | #include <queue> |
---|
24 | #include <lemon/counter.h> |
---|
25 | #include <lemon/elevator.h> |
---|
26 | |
---|
27 | ///\ingroup matching |
---|
28 | ///\file |
---|
29 | ///\brief Push-prelabel maximum matching algorithms in bipartite graphs. |
---|
30 | /// |
---|
31 | ///\todo This file slightly conflicts with \ref lemon/bipartite_matching.h |
---|
32 | ///\todo (Re)move the XYZ_TYPEDEFS macros |
---|
33 | namespace lemon { |
---|
34 | |
---|
35 | #define BIPARTITE_TYPEDEFS(Graph) \ |
---|
36 | GRAPH_TYPEDEFS(Graph) \ |
---|
37 | typedef Graph::ANodeIt ANodeIt; \ |
---|
38 | typedef Graph::BNodeIt BNodeIt; |
---|
39 | |
---|
40 | #define UNDIRBIPARTITE_TYPEDEFS(Graph) \ |
---|
41 | UNDIRGRAPH_TYPEDEFS(Graph) \ |
---|
42 | typedef Graph::ANodeIt ANodeIt; \ |
---|
43 | typedef Graph::BNodeIt BNodeIt; |
---|
44 | |
---|
45 | template<class Graph, |
---|
46 | class MT=typename Graph::template ANodeMap<typename Graph::UEdge> > |
---|
47 | class BpMatching { |
---|
48 | typedef typename Graph::Node Node; |
---|
49 | typedef typename Graph::ANodeIt ANodeIt; |
---|
50 | typedef typename Graph::BNodeIt BNodeIt; |
---|
51 | typedef typename Graph::UEdge UEdge; |
---|
52 | typedef typename Graph::IncEdgeIt IncEdgeIt; |
---|
53 | |
---|
54 | const Graph &_g; |
---|
55 | int _node_num; |
---|
56 | MT &_matching; |
---|
57 | Elevator<Graph,typename Graph::BNode> _levels; |
---|
58 | typename Graph::template BNodeMap<int> _cov; |
---|
59 | |
---|
60 | public: |
---|
61 | BpMatching(const Graph &g, MT &matching) : |
---|
62 | _g(g), |
---|
63 | _node_num(countBNodes(g)), |
---|
64 | _matching(matching), |
---|
65 | _levels(g,_node_num), |
---|
66 | _cov(g,0) |
---|
67 | { |
---|
68 | } |
---|
69 | |
---|
70 | private: |
---|
71 | void init() |
---|
72 | { |
---|
73 | // for(BNodeIt n(g);n!=INVALID;++n) cov[n]=0; |
---|
74 | for(ANodeIt n(_g);n!=INVALID;++n) |
---|
75 | if((_matching[n]=IncEdgeIt(_g,n))!=INVALID) |
---|
76 | ++_cov[_g.oppositeNode(n,_matching[n])]; |
---|
77 | |
---|
78 | std::queue<Node> q; |
---|
79 | _levels.initStart(); |
---|
80 | for(BNodeIt n(_g);n!=INVALID;++n) |
---|
81 | if(_cov[n]>1) { |
---|
82 | _levels.initAddItem(n); |
---|
83 | q.push(n); |
---|
84 | } |
---|
85 | int hlev=0; |
---|
86 | while(!q.empty()) { |
---|
87 | Node n=q.front(); |
---|
88 | q.pop(); |
---|
89 | int nlev=_levels[n]+1; |
---|
90 | for(IncEdgeIt e(_g,n);e!=INVALID;++e) { |
---|
91 | Node m=_g.runningNode(e); |
---|
92 | if(e==_matching[m]) { |
---|
93 | for(IncEdgeIt f(_g,m);f!=INVALID;++f) { |
---|
94 | Node r=_g.runningNode(f); |
---|
95 | if(_levels[r]>nlev) { |
---|
96 | for(;nlev>hlev;hlev++) |
---|
97 | _levels.initNewLevel(); |
---|
98 | _levels.initAddItem(r); |
---|
99 | q.push(r); |
---|
100 | } |
---|
101 | } |
---|
102 | } |
---|
103 | } |
---|
104 | } |
---|
105 | _levels.initFinish(); |
---|
106 | for(BNodeIt n(_g);n!=INVALID;++n) |
---|
107 | if(_cov[n]<1&&_levels[n]<_node_num) |
---|
108 | _levels.activate(n); |
---|
109 | } |
---|
110 | public: |
---|
111 | int run() |
---|
112 | { |
---|
113 | init(); |
---|
114 | |
---|
115 | Node act; |
---|
116 | Node bact=INVALID; |
---|
117 | Node last_activated=INVALID; |
---|
118 | // while((act=last_activated!=INVALID? |
---|
119 | // last_activated:_levels.highestActive()) |
---|
120 | // !=INVALID) |
---|
121 | while((act=_levels.highestActive())!=INVALID) { |
---|
122 | last_activated=INVALID; |
---|
123 | int actlevel=_levels[act]; |
---|
124 | |
---|
125 | UEdge bedge=INVALID; |
---|
126 | int nlevel=_node_num; |
---|
127 | { |
---|
128 | int nnlevel; |
---|
129 | for(IncEdgeIt tbedge(_g,act); |
---|
130 | tbedge!=INVALID && nlevel>=actlevel; |
---|
131 | ++tbedge) |
---|
132 | if((nnlevel=_levels[_g.bNode(_matching[_g.runningNode(tbedge)])])< |
---|
133 | nlevel) |
---|
134 | { |
---|
135 | nlevel=nnlevel; |
---|
136 | bedge=tbedge; |
---|
137 | } |
---|
138 | } |
---|
139 | if(nlevel<_node_num) { |
---|
140 | if(nlevel>=actlevel) |
---|
141 | _levels.liftHighestActiveTo(nlevel+1); |
---|
142 | // _levels.liftTo(act,nlevel+1); |
---|
143 | bact=_g.bNode(_matching[_g.aNode(bedge)]); |
---|
144 | if(--_cov[bact]<1) { |
---|
145 | _levels.activate(bact); |
---|
146 | last_activated=bact; |
---|
147 | } |
---|
148 | _matching[_g.aNode(bedge)]=bedge; |
---|
149 | _cov[act]=1; |
---|
150 | _levels.deactivate(act); |
---|
151 | } |
---|
152 | else { |
---|
153 | if(_node_num>actlevel) |
---|
154 | _levels.liftHighestActiveTo(_node_num); |
---|
155 | // _levels.liftTo(act,_node_num); |
---|
156 | _levels.deactivate(act); |
---|
157 | } |
---|
158 | |
---|
159 | if(_levels.onLevel(actlevel)==0) |
---|
160 | _levels.liftToTop(actlevel); |
---|
161 | } |
---|
162 | |
---|
163 | int ret=_node_num; |
---|
164 | for(ANodeIt n(_g);n!=INVALID;++n) |
---|
165 | if(_matching[n]==INVALID) ret--; |
---|
166 | else if (_cov[_g.bNode(_matching[n])]>1) { |
---|
167 | _cov[_g.bNode(_matching[n])]--; |
---|
168 | ret--; |
---|
169 | _matching[n]=INVALID; |
---|
170 | } |
---|
171 | return ret; |
---|
172 | } |
---|
173 | |
---|
174 | ///\returns -1 if there is a perfect matching, or an empty level |
---|
175 | ///if it doesn't exists |
---|
176 | int runPerfect() |
---|
177 | { |
---|
178 | init(); |
---|
179 | |
---|
180 | Node act; |
---|
181 | Node bact=INVALID; |
---|
182 | Node last_activated=INVALID; |
---|
183 | while((act=_levels.highestActive())!=INVALID) { |
---|
184 | last_activated=INVALID; |
---|
185 | int actlevel=_levels[act]; |
---|
186 | |
---|
187 | UEdge bedge=INVALID; |
---|
188 | int nlevel=_node_num; |
---|
189 | { |
---|
190 | int nnlevel; |
---|
191 | for(IncEdgeIt tbedge(_g,act); |
---|
192 | tbedge!=INVALID && nlevel>=actlevel; |
---|
193 | ++tbedge) |
---|
194 | if((nnlevel=_levels[_g.bNode(_matching[_g.runningNode(tbedge)])])< |
---|
195 | nlevel) |
---|
196 | { |
---|
197 | nlevel=nnlevel; |
---|
198 | bedge=tbedge; |
---|
199 | } |
---|
200 | } |
---|
201 | if(nlevel<_node_num) { |
---|
202 | if(nlevel>=actlevel) |
---|
203 | _levels.liftHighestActiveTo(nlevel+1); |
---|
204 | bact=_g.bNode(_matching[_g.aNode(bedge)]); |
---|
205 | if(--_cov[bact]<1) { |
---|
206 | _levels.activate(bact); |
---|
207 | last_activated=bact; |
---|
208 | } |
---|
209 | _matching[_g.aNode(bedge)]=bedge; |
---|
210 | _cov[act]=1; |
---|
211 | _levels.deactivate(act); |
---|
212 | } |
---|
213 | else { |
---|
214 | if(_node_num>actlevel) |
---|
215 | _levels.liftHighestActiveTo(_node_num); |
---|
216 | _levels.deactivate(act); |
---|
217 | } |
---|
218 | |
---|
219 | if(_levels.onLevel(actlevel)==0) |
---|
220 | return actlevel; |
---|
221 | } |
---|
222 | return -1; |
---|
223 | } |
---|
224 | |
---|
225 | template<class GT> |
---|
226 | void aBarrier(GT &bar,int empty_level=-1) |
---|
227 | { |
---|
228 | if(empty_level==-1) |
---|
229 | for(empty_level=0;_levels.onLevel(empty_level);empty_level++) ; |
---|
230 | for(ANodeIt n(_g);n!=INVALID;++n) |
---|
231 | bar[n] = _matching[n]==INVALID || |
---|
232 | _levels[_g.bNode(_matching[n])]<empty_level; |
---|
233 | } |
---|
234 | template<class GT> |
---|
235 | void bBarrier(GT &bar, int empty_level=-1) |
---|
236 | { |
---|
237 | if(empty_level==-1) |
---|
238 | for(empty_level=0;_levels.onLevel(empty_level);empty_level++) ; |
---|
239 | for(BNodeIt n(_g);n!=INVALID;++n) bar[n]=(_levels[n]>empty_level); |
---|
240 | } |
---|
241 | |
---|
242 | }; |
---|
243 | |
---|
244 | |
---|
245 | ///Maximum cardinality of the matchings in a bipartite graph |
---|
246 | |
---|
247 | ///\ingroup matching |
---|
248 | ///This function finds the maximum cardinality of the matchings |
---|
249 | ///in a bipartite graph \c g. |
---|
250 | ///\param g An undirected bipartite graph. |
---|
251 | ///\return The cardinality of the maximum matching. |
---|
252 | /// |
---|
253 | ///\note The the implementation is based |
---|
254 | ///on the push-relabel principle. |
---|
255 | template<class Graph> |
---|
256 | int maxBpMatching(const Graph &g) |
---|
257 | { |
---|
258 | typename Graph::template ANodeMap<typename Graph::UEdge> matching(g); |
---|
259 | return maxBpMatching(g,matching); |
---|
260 | } |
---|
261 | |
---|
262 | ///Maximum cardinality matching in a bipartite graph |
---|
263 | |
---|
264 | ///\ingroup matching |
---|
265 | ///This function finds a maximum cardinality matching |
---|
266 | ///in a bipartite graph \c g. |
---|
267 | ///\param g An undirected bipartite graph. |
---|
268 | ///\retval matching A readwrite ANodeMap of value type \c Edge. |
---|
269 | /// The found edges will be returned in this map, |
---|
270 | /// i.e. for an \c ANode \c n, |
---|
271 | /// the edge <tt>matching[n]</tt> is the one that covers the node \c n, or |
---|
272 | /// \ref INVALID if it is uncovered. |
---|
273 | ///\return The cardinality of the maximum matching. |
---|
274 | /// |
---|
275 | ///\note The the implementation is based |
---|
276 | ///on the push-relabel principle. |
---|
277 | template<class Graph,class MT> |
---|
278 | int maxBpMatching(const Graph &g,MT &matching) |
---|
279 | { |
---|
280 | return BpMatching<Graph,MT>(g,matching).run(); |
---|
281 | } |
---|
282 | |
---|
283 | ///Maximum cardinality matching in a bipartite graph |
---|
284 | |
---|
285 | ///\ingroup matching |
---|
286 | ///This function finds a maximum cardinality matching |
---|
287 | ///in a bipartite graph \c g. |
---|
288 | ///\param g An undirected bipartite graph. |
---|
289 | ///\retval matching A readwrite ANodeMap of value type \c Edge. |
---|
290 | /// The found edges will be returned in this map, |
---|
291 | /// i.e. for an \c ANode \c n, |
---|
292 | /// the edge <tt>matching[n]</tt> is the one that covers the node \c n, or |
---|
293 | /// \ref INVALID if it is uncovered. |
---|
294 | ///\retval barrier A \c bool WriteMap on the BNodes. The map will be set |
---|
295 | /// exactly once for each BNode. The nodes with \c true value represent |
---|
296 | /// a barrier \e B, i.e. the cardinality of \e B minus the number of its |
---|
297 | /// neighbor is equal to the number of the <tt>BNode</tt>s minus the |
---|
298 | /// cardinality of the maximum matching. |
---|
299 | ///\return The cardinality of the maximum matching. |
---|
300 | /// |
---|
301 | ///\note The the implementation is based |
---|
302 | ///on the push-relabel principle. |
---|
303 | template<class Graph,class MT, class GT> |
---|
304 | int maxBpMatching(const Graph &g,MT &matching,GT &barrier) |
---|
305 | { |
---|
306 | BpMatching<Graph,MT> bpm(g,matching); |
---|
307 | int ret=bpm.run(); |
---|
308 | bpm.barrier(barrier); |
---|
309 | return ret; |
---|
310 | } |
---|
311 | |
---|
312 | ///Perfect matching in a bipartite graph |
---|
313 | |
---|
314 | ///\ingroup matching |
---|
315 | ///This function checks whether the bipartite graph \c g |
---|
316 | ///has a perfect matching. |
---|
317 | ///\param g An undirected bipartite graph. |
---|
318 | ///\return \c true iff \c g has a perfect matching. |
---|
319 | /// |
---|
320 | ///\note The the implementation is based |
---|
321 | ///on the push-relabel principle. |
---|
322 | template<class Graph> |
---|
323 | bool perfectBpMatching(const Graph &g) |
---|
324 | { |
---|
325 | typename Graph::template ANodeMap<typename Graph::UEdge> matching(g); |
---|
326 | return perfectBpMatching(g,matching); |
---|
327 | } |
---|
328 | |
---|
329 | ///Perfect matching in a bipartite graph |
---|
330 | |
---|
331 | ///\ingroup matching |
---|
332 | ///This function finds a perfect matching in a bipartite graph \c g. |
---|
333 | ///\param g An undirected bipartite graph. |
---|
334 | ///\retval matching A readwrite ANodeMap of value type \c Edge. |
---|
335 | /// The found edges will be returned in this map, |
---|
336 | /// i.e. for an \c ANode \c n, |
---|
337 | /// the edge <tt>matching[n]</tt> is the one that covers the node \c n. |
---|
338 | /// The values are unspecified if the graph |
---|
339 | /// has no perfect matching. |
---|
340 | ///\return \c true iff \c g has a perfect matching. |
---|
341 | /// |
---|
342 | ///\note The the implementation is based |
---|
343 | ///on the push-relabel principle. |
---|
344 | template<class Graph,class MT> |
---|
345 | bool perfectBpMatching(const Graph &g,MT &matching) |
---|
346 | { |
---|
347 | return BpMatching<Graph,MT>(g,matching).runPerfect()<0; |
---|
348 | } |
---|
349 | |
---|
350 | ///Perfect matching in a bipartite graph |
---|
351 | |
---|
352 | ///\ingroup matching |
---|
353 | ///This function finds a perfect matching in a bipartite graph \c g. |
---|
354 | ///\param g An undirected bipartite graph. |
---|
355 | ///\retval matching A readwrite ANodeMap of value type \c Edge. |
---|
356 | /// The found edges will be returned in this map, |
---|
357 | /// i.e. for an \c ANode \c n, |
---|
358 | /// the edge <tt>matching[n]</tt> is the one that covers the node \c n. |
---|
359 | /// The values are unspecified if the graph |
---|
360 | /// has no perfect matching. |
---|
361 | ///\retval barrier A \c bool WriteMap on the BNodes. The map will only |
---|
362 | /// be set if \c g has no perfect matching. In this case it is set |
---|
363 | /// exactly once for each BNode. The nodes with \c true value represent |
---|
364 | /// a barrier, i.e. a subset \e B a of BNodes with the property that |
---|
365 | /// the cardinality of \e B is greater than the numner of its neighbors. |
---|
366 | ///\return \c true iff \c g has a perfect matching. |
---|
367 | /// |
---|
368 | ///\note The the implementation is based |
---|
369 | ///on the push-relabel principle. |
---|
370 | template<class Graph,class MT, class GT> |
---|
371 | int perfectBpMatching(const Graph &g,MT &matching,GT &barrier) |
---|
372 | { |
---|
373 | BpMatching<Graph,MT> bpm(g,matching); |
---|
374 | int ret=bpm.run(); |
---|
375 | if(ret>=0) |
---|
376 | bpm.barrier(barrier,ret); |
---|
377 | return ret<0; |
---|
378 | } |
---|
379 | } |
---|
380 | |
---|
381 | #endif |
---|