1 | /* -*- C++ -*- |
---|
2 | * |
---|
3 | * This file is a part of LEMON, a generic C++ optimization library |
---|
4 | * |
---|
5 | * Copyright (C) 2003-2007 |
---|
6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
8 | * |
---|
9 | * Permission to use, modify and distribute this software is granted |
---|
10 | * provided that this copyright notice appears in all copies. For |
---|
11 | * precise terms see the accompanying LICENSE file. |
---|
12 | * |
---|
13 | * This software is provided "AS IS" with no warranty of any kind, |
---|
14 | * express or implied, and with no claim as to its suitability for any |
---|
15 | * purpose. |
---|
16 | * |
---|
17 | */ |
---|
18 | |
---|
19 | #ifndef LEMON_PREFLOW_H |
---|
20 | #define LEMON_PREFLOW_H |
---|
21 | |
---|
22 | #include <vector> |
---|
23 | #include <queue> |
---|
24 | |
---|
25 | #include <lemon/error.h> |
---|
26 | #include <lemon/bits/invalid.h> |
---|
27 | #include <lemon/tolerance.h> |
---|
28 | #include <lemon/maps.h> |
---|
29 | #include <lemon/graph_utils.h> |
---|
30 | |
---|
31 | /// \file |
---|
32 | /// \ingroup max_flow |
---|
33 | /// \brief Implementation of the preflow algorithm. |
---|
34 | |
---|
35 | namespace lemon { |
---|
36 | |
---|
37 | ///\ingroup max_flow |
---|
38 | ///\brief %Preflow algorithms class. |
---|
39 | /// |
---|
40 | ///This class provides an implementation of the \e preflow \e |
---|
41 | ///algorithm producing a flow of maximum value in a directed |
---|
42 | ///graph. The preflow algorithms are the fastest known max flow algorithms. |
---|
43 | ///The \e source node, the \e target node, the \e |
---|
44 | ///capacity of the edges and the \e starting \e flow value of the |
---|
45 | ///edges should be passed to the algorithm through the |
---|
46 | ///constructor. It is possible to change these quantities using the |
---|
47 | ///functions \ref source, \ref target, \ref capacityMap and \ref |
---|
48 | ///flowMap. |
---|
49 | /// |
---|
50 | ///After running \ref lemon::Preflow::phase1() "phase1()" |
---|
51 | ///or \ref lemon::Preflow::run() "run()", the maximal flow |
---|
52 | ///value can be obtained by calling \ref flowValue(). The minimum |
---|
53 | ///value cut can be written into a <tt>bool</tt> node map by |
---|
54 | ///calling \ref minCut(). (\ref minMinCut() and \ref maxMinCut() writes |
---|
55 | ///the inclusionwise minimum and maximum of the minimum value cuts, |
---|
56 | ///resp.) |
---|
57 | /// |
---|
58 | ///\param Graph The directed graph type the algorithm runs on. |
---|
59 | ///\param Num The number type of the capacities and the flow values. |
---|
60 | ///\param CapacityMap The capacity map type. |
---|
61 | ///\param FlowMap The flow map type. |
---|
62 | ///\param Tol The tolerance type. |
---|
63 | /// |
---|
64 | ///\author Jacint Szabo |
---|
65 | ///\todo Second template parameter is superfluous |
---|
66 | template <typename Graph, typename Num, |
---|
67 | typename CapacityMap=typename Graph::template EdgeMap<Num>, |
---|
68 | typename FlowMap=typename Graph::template EdgeMap<Num>, |
---|
69 | typename Tol=Tolerance<Num> > |
---|
70 | class Preflow { |
---|
71 | protected: |
---|
72 | typedef typename Graph::Node Node; |
---|
73 | typedef typename Graph::NodeIt NodeIt; |
---|
74 | typedef typename Graph::EdgeIt EdgeIt; |
---|
75 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
---|
76 | typedef typename Graph::InEdgeIt InEdgeIt; |
---|
77 | |
---|
78 | typedef typename Graph::template NodeMap<Node> NNMap; |
---|
79 | typedef typename std::vector<Node> VecNode; |
---|
80 | |
---|
81 | const Graph* _g; |
---|
82 | Node _source; |
---|
83 | Node _target; |
---|
84 | const CapacityMap* _capacity; |
---|
85 | FlowMap* _flow; |
---|
86 | |
---|
87 | Tol _surely; |
---|
88 | |
---|
89 | int _node_num; //the number of nodes of G |
---|
90 | |
---|
91 | typename Graph::template NodeMap<int> level; |
---|
92 | typename Graph::template NodeMap<Num> excess; |
---|
93 | |
---|
94 | // constants used for heuristics |
---|
95 | static const int H0=20; |
---|
96 | static const int H1=1; |
---|
97 | |
---|
98 | public: |
---|
99 | |
---|
100 | ///\ref Exception for the case when s=t. |
---|
101 | |
---|
102 | ///\ref Exception for the case when the source equals the target. |
---|
103 | class InvalidArgument : public lemon::LogicError { |
---|
104 | public: |
---|
105 | virtual const char* what() const throw() { |
---|
106 | return "lemon::Preflow::InvalidArgument"; |
---|
107 | } |
---|
108 | }; |
---|
109 | |
---|
110 | |
---|
111 | ///Indicates the property of the starting flow map. |
---|
112 | |
---|
113 | ///Indicates the property of the starting flow map. |
---|
114 | /// |
---|
115 | enum FlowEnum{ |
---|
116 | ///indicates an unspecified edge map. \c flow will be |
---|
117 | ///set to the constant zero flow in the beginning of |
---|
118 | ///the algorithm in this case. |
---|
119 | NO_FLOW, |
---|
120 | ///constant zero flow |
---|
121 | ZERO_FLOW, |
---|
122 | ///any flow, i.e. the sum of the in-flows equals to |
---|
123 | ///the sum of the out-flows in every node except the \c source and |
---|
124 | ///the \c target. |
---|
125 | GEN_FLOW, |
---|
126 | ///any preflow, i.e. the sum of the in-flows is at |
---|
127 | ///least the sum of the out-flows in every node except the \c source. |
---|
128 | PRE_FLOW |
---|
129 | }; |
---|
130 | |
---|
131 | ///Indicates the state of the preflow algorithm. |
---|
132 | |
---|
133 | ///Indicates the state of the preflow algorithm. |
---|
134 | /// |
---|
135 | enum StatusEnum { |
---|
136 | ///before running the algorithm or |
---|
137 | ///at an unspecified state. |
---|
138 | AFTER_NOTHING, |
---|
139 | ///right after running \ref phase1() |
---|
140 | AFTER_PREFLOW_PHASE_1, |
---|
141 | ///after running \ref phase2() |
---|
142 | AFTER_PREFLOW_PHASE_2 |
---|
143 | }; |
---|
144 | |
---|
145 | protected: |
---|
146 | FlowEnum flow_prop; |
---|
147 | StatusEnum status; // Do not needle this flag only if necessary. |
---|
148 | |
---|
149 | public: |
---|
150 | ///The constructor of the class. |
---|
151 | |
---|
152 | ///The constructor of the class. |
---|
153 | ///\param _gr The directed graph the algorithm runs on. |
---|
154 | ///\param _s The source node. |
---|
155 | ///\param _t The target node. |
---|
156 | ///\param _cap The capacity of the edges. |
---|
157 | ///\param _f The flow of the edges. |
---|
158 | ///\param _sr Tol class. |
---|
159 | ///Except the graph, all of these parameters can be reset by |
---|
160 | ///calling \ref source, \ref target, \ref capacityMap and \ref |
---|
161 | ///flowMap, resp. |
---|
162 | Preflow(const Graph& _gr, Node _s, Node _t, |
---|
163 | const CapacityMap& _cap, FlowMap& _f, |
---|
164 | const Tol &_sr=Tol()) : |
---|
165 | _g(&_gr), _source(_s), _target(_t), _capacity(&_cap), |
---|
166 | _flow(&_f), _surely(_sr), |
---|
167 | _node_num(countNodes(_gr)), level(_gr), excess(_gr,0), |
---|
168 | flow_prop(NO_FLOW), status(AFTER_NOTHING) { |
---|
169 | if ( _source==_target ) |
---|
170 | throw InvalidArgument(); |
---|
171 | } |
---|
172 | |
---|
173 | ///Give a reference to the tolerance handler class |
---|
174 | |
---|
175 | ///Give a reference to the tolerance handler class |
---|
176 | ///\sa Tolerance |
---|
177 | Tol &tolerance() { return _surely; } |
---|
178 | |
---|
179 | ///Runs the preflow algorithm. |
---|
180 | |
---|
181 | ///Runs the preflow algorithm. |
---|
182 | /// |
---|
183 | void run() { |
---|
184 | phase1(flow_prop); |
---|
185 | phase2(); |
---|
186 | } |
---|
187 | |
---|
188 | ///Runs the preflow algorithm. |
---|
189 | |
---|
190 | ///Runs the preflow algorithm. |
---|
191 | ///\pre The starting flow map must be |
---|
192 | /// - a constant zero flow if \c fp is \c ZERO_FLOW, |
---|
193 | /// - an arbitrary flow if \c fp is \c GEN_FLOW, |
---|
194 | /// - an arbitrary preflow if \c fp is \c PRE_FLOW, |
---|
195 | /// - any map if \c fp is NO_FLOW. |
---|
196 | ///If the starting flow map is a flow or a preflow then |
---|
197 | ///the algorithm terminates faster. |
---|
198 | void run(FlowEnum fp) { |
---|
199 | flow_prop=fp; |
---|
200 | run(); |
---|
201 | } |
---|
202 | |
---|
203 | ///Runs the first phase of the preflow algorithm. |
---|
204 | |
---|
205 | ///The preflow algorithm consists of two phases, this method runs |
---|
206 | ///the first phase. After the first phase the maximum flow value |
---|
207 | ///and a minimum value cut can already be computed, although a |
---|
208 | ///maximum flow is not yet obtained. So after calling this method |
---|
209 | ///\ref flowValue returns the value of a maximum flow and \ref |
---|
210 | ///minCut returns a minimum cut. |
---|
211 | ///\warning \ref minMinCut and \ref maxMinCut do not give minimum |
---|
212 | ///value cuts unless calling \ref phase2. |
---|
213 | ///\warning A real flow map (i.e. not \ref lemon::NullMap "NullMap") |
---|
214 | ///is needed for this phase. |
---|
215 | ///\pre The starting flow must be |
---|
216 | ///- a constant zero flow if \c fp is \c ZERO_FLOW, |
---|
217 | ///- an arbitary flow if \c fp is \c GEN_FLOW, |
---|
218 | ///- an arbitary preflow if \c fp is \c PRE_FLOW, |
---|
219 | ///- any map if \c fp is NO_FLOW. |
---|
220 | void phase1(FlowEnum fp) |
---|
221 | { |
---|
222 | flow_prop=fp; |
---|
223 | phase1(); |
---|
224 | } |
---|
225 | |
---|
226 | |
---|
227 | ///Runs the first phase of the preflow algorithm. |
---|
228 | |
---|
229 | ///The preflow algorithm consists of two phases, this method runs |
---|
230 | ///the first phase. After the first phase the maximum flow value |
---|
231 | ///and a minimum value cut can already be computed, although a |
---|
232 | ///maximum flow is not yet obtained. So after calling this method |
---|
233 | ///\ref flowValue returns the value of a maximum flow and \ref |
---|
234 | ///minCut returns a minimum cut. |
---|
235 | ///\warning \ref minMinCut() and \ref maxMinCut() do not |
---|
236 | ///give minimum value cuts unless calling \ref phase2(). |
---|
237 | ///\warning A real flow map (i.e. not \ref lemon::NullMap "NullMap") |
---|
238 | ///is needed for this phase. |
---|
239 | void phase1() |
---|
240 | { |
---|
241 | int heur0=int(H0*_node_num); //time while running 'bound decrease' |
---|
242 | int heur1=int(H1*_node_num); //time while running 'highest label' |
---|
243 | int heur=heur1; //starting time interval (#of relabels) |
---|
244 | int numrelabel=0; |
---|
245 | |
---|
246 | bool what_heur=1; |
---|
247 | //It is 0 in case 'bound decrease' and 1 in case 'highest label' |
---|
248 | |
---|
249 | bool end=false; |
---|
250 | //Needed for 'bound decrease', true means no active |
---|
251 | //nodes are above bound b. |
---|
252 | |
---|
253 | int k=_node_num-2; //bound on the highest level under n containing a node |
---|
254 | int b=k; //bound on the highest level under n containing an active node |
---|
255 | |
---|
256 | VecNode first(_node_num, INVALID); |
---|
257 | NNMap next(*_g, INVALID); |
---|
258 | |
---|
259 | NNMap left(*_g, INVALID); |
---|
260 | NNMap right(*_g, INVALID); |
---|
261 | VecNode level_list(_node_num,INVALID); |
---|
262 | //List of the nodes in level i<n, set to n. |
---|
263 | |
---|
264 | preflowPreproc(first, next, level_list, left, right); |
---|
265 | |
---|
266 | //Push/relabel on the highest level active nodes. |
---|
267 | while ( true ) { |
---|
268 | if ( b == 0 ) { |
---|
269 | if ( !what_heur && !end && k > 0 ) { |
---|
270 | b=k; |
---|
271 | end=true; |
---|
272 | } else break; |
---|
273 | } |
---|
274 | |
---|
275 | if ( first[b]==INVALID ) --b; |
---|
276 | else { |
---|
277 | end=false; |
---|
278 | Node w=first[b]; |
---|
279 | first[b]=next[w]; |
---|
280 | int newlevel=push(w, next, first); |
---|
281 | if ( excess[w] != 0 ) { |
---|
282 | relabel(w, newlevel, first, next, level_list, |
---|
283 | left, right, b, k, what_heur); |
---|
284 | } |
---|
285 | |
---|
286 | ++numrelabel; |
---|
287 | if ( numrelabel >= heur ) { |
---|
288 | numrelabel=0; |
---|
289 | if ( what_heur ) { |
---|
290 | what_heur=0; |
---|
291 | heur=heur0; |
---|
292 | end=false; |
---|
293 | } else { |
---|
294 | what_heur=1; |
---|
295 | heur=heur1; |
---|
296 | b=k; |
---|
297 | } |
---|
298 | } |
---|
299 | } |
---|
300 | } |
---|
301 | flow_prop=PRE_FLOW; |
---|
302 | status=AFTER_PREFLOW_PHASE_1; |
---|
303 | } |
---|
304 | // Heuristics: |
---|
305 | // 2 phase |
---|
306 | // gap |
---|
307 | // list 'level_list' on the nodes on level i implemented by hand |
---|
308 | // stack 'active' on the active nodes on level i |
---|
309 | // runs heuristic 'highest label' for H1*n relabels |
---|
310 | // runs heuristic 'bound decrease' for H0*n relabels, |
---|
311 | // starts with 'highest label' |
---|
312 | // Parameters H0 and H1 are initialized to 20 and 1. |
---|
313 | |
---|
314 | |
---|
315 | ///Runs the second phase of the preflow algorithm. |
---|
316 | |
---|
317 | ///The preflow algorithm consists of two phases, this method runs |
---|
318 | ///the second phase. After calling \ref phase1() and then |
---|
319 | ///\ref phase2(), |
---|
320 | /// \ref flowMap() return a maximum flow, \ref flowValue |
---|
321 | ///returns the value of a maximum flow, \ref minCut returns a |
---|
322 | ///minimum cut, while the methods \ref minMinCut and \ref |
---|
323 | ///maxMinCut return the inclusionwise minimum and maximum cuts of |
---|
324 | ///minimum value, resp. \pre \ref phase1 must be called before. |
---|
325 | /// |
---|
326 | /// \todo The inexact computation can cause positive excess on a set of |
---|
327 | /// unpushable nodes. We may have to watch the empty level in this case |
---|
328 | /// due to avoid the terrible long running time. |
---|
329 | void phase2() |
---|
330 | { |
---|
331 | |
---|
332 | int k=_node_num-2; //bound on the highest level under n containing a node |
---|
333 | int b=k; //bound on the highest level under n of an active node |
---|
334 | |
---|
335 | |
---|
336 | VecNode first(_node_num, INVALID); |
---|
337 | NNMap next(*_g, INVALID); |
---|
338 | level.set(_source,0); |
---|
339 | std::queue<Node> bfs_queue; |
---|
340 | bfs_queue.push(_source); |
---|
341 | |
---|
342 | while ( !bfs_queue.empty() ) { |
---|
343 | |
---|
344 | Node v=bfs_queue.front(); |
---|
345 | bfs_queue.pop(); |
---|
346 | int l=level[v]+1; |
---|
347 | |
---|
348 | for(InEdgeIt e(*_g,v); e!=INVALID; ++e) { |
---|
349 | if ( !_surely.positive((*_capacity)[e] - (*_flow)[e])) continue; |
---|
350 | Node u=_g->source(e); |
---|
351 | if ( level[u] >= _node_num ) { |
---|
352 | bfs_queue.push(u); |
---|
353 | level.set(u, l); |
---|
354 | if ( excess[u] != 0 ) { |
---|
355 | next.set(u,first[l]); |
---|
356 | first[l]=u; |
---|
357 | } |
---|
358 | } |
---|
359 | } |
---|
360 | |
---|
361 | for(OutEdgeIt e(*_g,v); e!=INVALID; ++e) { |
---|
362 | if ( !_surely.positive((*_flow)[e]) ) continue; |
---|
363 | Node u=_g->target(e); |
---|
364 | if ( level[u] >= _node_num ) { |
---|
365 | bfs_queue.push(u); |
---|
366 | level.set(u, l); |
---|
367 | if ( excess[u] != 0 ) { |
---|
368 | next.set(u,first[l]); |
---|
369 | first[l]=u; |
---|
370 | } |
---|
371 | } |
---|
372 | } |
---|
373 | } |
---|
374 | b=_node_num-2; |
---|
375 | |
---|
376 | while ( true ) { |
---|
377 | |
---|
378 | if ( b == 0 ) break; |
---|
379 | if ( first[b]==INVALID ) --b; |
---|
380 | else { |
---|
381 | Node w=first[b]; |
---|
382 | first[b]=next[w]; |
---|
383 | int newlevel=push(w,next, first); |
---|
384 | |
---|
385 | if ( newlevel == _node_num) { |
---|
386 | excess.set(w, 0); |
---|
387 | level.set(w,_node_num); |
---|
388 | } |
---|
389 | //relabel |
---|
390 | if ( excess[w] != 0 ) { |
---|
391 | level.set(w,++newlevel); |
---|
392 | next.set(w,first[newlevel]); |
---|
393 | first[newlevel]=w; |
---|
394 | b=newlevel; |
---|
395 | } |
---|
396 | } |
---|
397 | } // while(true) |
---|
398 | flow_prop=GEN_FLOW; |
---|
399 | status=AFTER_PREFLOW_PHASE_2; |
---|
400 | } |
---|
401 | |
---|
402 | /// Returns the value of the maximum flow. |
---|
403 | |
---|
404 | /// Returns the value of the maximum flow by returning the excess |
---|
405 | /// of the target node \c t. This value equals to the value of |
---|
406 | /// the maximum flow already after running \ref phase1. |
---|
407 | Num flowValue() const { |
---|
408 | return excess[_target]; |
---|
409 | } |
---|
410 | |
---|
411 | |
---|
412 | ///Returns a minimum value cut. |
---|
413 | |
---|
414 | ///Sets \c M to the characteristic vector of a minimum value |
---|
415 | ///cut. This method can be called both after running \ref |
---|
416 | ///phase1 and \ref phase2. It is much faster after |
---|
417 | ///\ref phase1. \pre M should be a bool-valued node-map. \pre |
---|
418 | ///If \ref minCut() is called after \ref phase2() then M should |
---|
419 | ///be initialized to false. |
---|
420 | template<typename _CutMap> |
---|
421 | void minCut(_CutMap& M) const { |
---|
422 | switch ( status ) { |
---|
423 | case AFTER_PREFLOW_PHASE_1: |
---|
424 | for(NodeIt v(*_g); v!=INVALID; ++v) { |
---|
425 | if (level[v] < _node_num) { |
---|
426 | M.set(v, false); |
---|
427 | } else { |
---|
428 | M.set(v, true); |
---|
429 | } |
---|
430 | } |
---|
431 | break; |
---|
432 | case AFTER_PREFLOW_PHASE_2: |
---|
433 | minMinCut(M); |
---|
434 | break; |
---|
435 | case AFTER_NOTHING: |
---|
436 | break; |
---|
437 | } |
---|
438 | } |
---|
439 | |
---|
440 | ///Returns the inclusionwise minimum of the minimum value cuts. |
---|
441 | |
---|
442 | ///Sets \c M to the characteristic vector of the minimum value cut |
---|
443 | ///which is inclusionwise minimum. It is computed by processing a |
---|
444 | ///bfs from the source node \c s in the residual graph. \pre M |
---|
445 | ///should be a node map of bools initialized to false. \pre \ref |
---|
446 | ///phase2 should already be run. |
---|
447 | template<typename _CutMap> |
---|
448 | void minMinCut(_CutMap& M) const { |
---|
449 | |
---|
450 | std::queue<Node> queue; |
---|
451 | M.set(_source,true); |
---|
452 | queue.push(_source); |
---|
453 | |
---|
454 | while (!queue.empty()) { |
---|
455 | Node w=queue.front(); |
---|
456 | queue.pop(); |
---|
457 | |
---|
458 | for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
---|
459 | Node v=_g->target(e); |
---|
460 | if (!M[v] && _surely.positive((*_capacity)[e] -(*_flow)[e]) ) { |
---|
461 | queue.push(v); |
---|
462 | M.set(v, true); |
---|
463 | } |
---|
464 | } |
---|
465 | |
---|
466 | for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
---|
467 | Node v=_g->source(e); |
---|
468 | if (!M[v] && _surely.positive((*_flow)[e]) ) { |
---|
469 | queue.push(v); |
---|
470 | M.set(v, true); |
---|
471 | } |
---|
472 | } |
---|
473 | } |
---|
474 | } |
---|
475 | |
---|
476 | ///Returns the inclusionwise maximum of the minimum value cuts. |
---|
477 | |
---|
478 | ///Sets \c M to the characteristic vector of the minimum value cut |
---|
479 | ///which is inclusionwise maximum. It is computed by processing a |
---|
480 | ///backward bfs from the target node \c t in the residual graph. |
---|
481 | ///\pre \ref phase2() or run() should already be run. |
---|
482 | template<typename _CutMap> |
---|
483 | void maxMinCut(_CutMap& M) const { |
---|
484 | |
---|
485 | for(NodeIt v(*_g) ; v!=INVALID; ++v) M.set(v, true); |
---|
486 | |
---|
487 | std::queue<Node> queue; |
---|
488 | |
---|
489 | M.set(_target,false); |
---|
490 | queue.push(_target); |
---|
491 | |
---|
492 | while (!queue.empty()) { |
---|
493 | Node w=queue.front(); |
---|
494 | queue.pop(); |
---|
495 | |
---|
496 | for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
---|
497 | Node v=_g->source(e); |
---|
498 | if (M[v] && _surely.positive((*_capacity)[e] - (*_flow)[e]) ) { |
---|
499 | queue.push(v); |
---|
500 | M.set(v, false); |
---|
501 | } |
---|
502 | } |
---|
503 | |
---|
504 | for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
---|
505 | Node v=_g->target(e); |
---|
506 | if (M[v] && _surely.positive((*_flow)[e]) ) { |
---|
507 | queue.push(v); |
---|
508 | M.set(v, false); |
---|
509 | } |
---|
510 | } |
---|
511 | } |
---|
512 | } |
---|
513 | |
---|
514 | ///Sets the source node to \c _s. |
---|
515 | |
---|
516 | ///Sets the source node to \c _s. |
---|
517 | /// |
---|
518 | void source(Node _s) { |
---|
519 | _source=_s; |
---|
520 | if ( flow_prop != ZERO_FLOW ) flow_prop=NO_FLOW; |
---|
521 | status=AFTER_NOTHING; |
---|
522 | } |
---|
523 | |
---|
524 | ///Returns the source node. |
---|
525 | |
---|
526 | ///Returns the source node. |
---|
527 | /// |
---|
528 | Node source() const { |
---|
529 | return _source; |
---|
530 | } |
---|
531 | |
---|
532 | ///Sets the target node to \c _t. |
---|
533 | |
---|
534 | ///Sets the target node to \c _t. |
---|
535 | /// |
---|
536 | void target(Node _t) { |
---|
537 | _target=_t; |
---|
538 | if ( flow_prop == GEN_FLOW ) flow_prop=PRE_FLOW; |
---|
539 | status=AFTER_NOTHING; |
---|
540 | } |
---|
541 | |
---|
542 | ///Returns the target node. |
---|
543 | |
---|
544 | ///Returns the target node. |
---|
545 | /// |
---|
546 | Node target() const { |
---|
547 | return _target; |
---|
548 | } |
---|
549 | |
---|
550 | /// Sets the edge map of the capacities to _cap. |
---|
551 | |
---|
552 | /// Sets the edge map of the capacities to _cap. |
---|
553 | /// |
---|
554 | void capacityMap(const CapacityMap& _cap) { |
---|
555 | _capacity=&_cap; |
---|
556 | status=AFTER_NOTHING; |
---|
557 | } |
---|
558 | /// Returns a reference to capacity map. |
---|
559 | |
---|
560 | /// Returns a reference to capacity map. |
---|
561 | /// |
---|
562 | const CapacityMap &capacityMap() const { |
---|
563 | return *_capacity; |
---|
564 | } |
---|
565 | |
---|
566 | /// Sets the edge map of the flows to _flow. |
---|
567 | |
---|
568 | /// Sets the edge map of the flows to _flow. |
---|
569 | /// |
---|
570 | void flowMap(FlowMap& _f) { |
---|
571 | _flow=&_f; |
---|
572 | flow_prop=NO_FLOW; |
---|
573 | status=AFTER_NOTHING; |
---|
574 | } |
---|
575 | |
---|
576 | /// Returns a reference to flow map. |
---|
577 | |
---|
578 | /// Returns a reference to flow map. |
---|
579 | /// |
---|
580 | const FlowMap &flowMap() const { |
---|
581 | return *_flow; |
---|
582 | } |
---|
583 | |
---|
584 | private: |
---|
585 | |
---|
586 | int push(Node w, NNMap& next, VecNode& first) { |
---|
587 | |
---|
588 | int lev=level[w]; |
---|
589 | Num exc=excess[w]; |
---|
590 | int newlevel=_node_num; //bound on the next level of w |
---|
591 | |
---|
592 | for(OutEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
---|
593 | if ( !_surely.positive((*_capacity)[e] - (*_flow)[e])) continue; |
---|
594 | Node v=_g->target(e); |
---|
595 | |
---|
596 | if( lev > level[v] ) { //Push is allowed now |
---|
597 | |
---|
598 | if ( excess[v] == 0 && v!=_target && v!=_source ) { |
---|
599 | next.set(v,first[level[v]]); |
---|
600 | first[level[v]]=v; |
---|
601 | } |
---|
602 | |
---|
603 | Num cap=(*_capacity)[e]; |
---|
604 | Num flo=(*_flow)[e]; |
---|
605 | Num remcap=cap-flo; |
---|
606 | |
---|
607 | if ( ! _surely.less(remcap, exc) ) { //A nonsaturating push. |
---|
608 | |
---|
609 | _flow->set(e, flo+exc); |
---|
610 | excess.set(v, excess[v]+exc); |
---|
611 | exc=0; |
---|
612 | break; |
---|
613 | |
---|
614 | } else { //A saturating push. |
---|
615 | _flow->set(e, cap); |
---|
616 | excess.set(v, excess[v]+remcap); |
---|
617 | exc-=remcap; |
---|
618 | } |
---|
619 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
---|
620 | } //for out edges wv |
---|
621 | |
---|
622 | if ( exc != 0 ) { |
---|
623 | for(InEdgeIt e(*_g,w) ; e!=INVALID; ++e) { |
---|
624 | |
---|
625 | if ( !_surely.positive((*_flow)[e]) ) continue; |
---|
626 | Node v=_g->source(e); |
---|
627 | |
---|
628 | if( lev > level[v] ) { //Push is allowed now |
---|
629 | |
---|
630 | if ( excess[v] == 0 && v!=_target && v!=_source ) { |
---|
631 | next.set(v,first[level[v]]); |
---|
632 | first[level[v]]=v; |
---|
633 | } |
---|
634 | |
---|
635 | Num flo=(*_flow)[e]; |
---|
636 | |
---|
637 | if ( !_surely.less(flo, exc) ) { //A nonsaturating push. |
---|
638 | |
---|
639 | _flow->set(e, flo-exc); |
---|
640 | excess.set(v, excess[v]+exc); |
---|
641 | exc=0; |
---|
642 | break; |
---|
643 | } else { //A saturating push. |
---|
644 | |
---|
645 | excess.set(v, excess[v]+flo); |
---|
646 | exc-=flo; |
---|
647 | _flow->set(e,0); |
---|
648 | } |
---|
649 | } else if ( newlevel > level[v] ) newlevel = level[v]; |
---|
650 | } //for in edges vw |
---|
651 | |
---|
652 | } // if w still has excess after the out edge for cycle |
---|
653 | |
---|
654 | excess.set(w, exc); |
---|
655 | |
---|
656 | return newlevel; |
---|
657 | } |
---|
658 | |
---|
659 | |
---|
660 | |
---|
661 | void preflowPreproc(VecNode& first, NNMap& next, |
---|
662 | VecNode& level_list, NNMap& left, NNMap& right) |
---|
663 | { |
---|
664 | for(NodeIt v(*_g); v!=INVALID; ++v) level.set(v,_node_num); |
---|
665 | std::queue<Node> bfs_queue; |
---|
666 | |
---|
667 | if ( flow_prop == GEN_FLOW || flow_prop == PRE_FLOW ) { |
---|
668 | //Reverse_bfs from t in the residual graph, |
---|
669 | //to find the starting level. |
---|
670 | level.set(_target,0); |
---|
671 | bfs_queue.push(_target); |
---|
672 | |
---|
673 | while ( !bfs_queue.empty() ) { |
---|
674 | |
---|
675 | Node v=bfs_queue.front(); |
---|
676 | bfs_queue.pop(); |
---|
677 | int l=level[v]+1; |
---|
678 | |
---|
679 | for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) { |
---|
680 | if ( !_surely.positive((*_capacity)[e] - (*_flow)[e] )) continue; |
---|
681 | Node w=_g->source(e); |
---|
682 | if ( level[w] == _node_num && w != _source ) { |
---|
683 | bfs_queue.push(w); |
---|
684 | Node z=level_list[l]; |
---|
685 | if ( z!=INVALID ) left.set(z,w); |
---|
686 | right.set(w,z); |
---|
687 | level_list[l]=w; |
---|
688 | level.set(w, l); |
---|
689 | } |
---|
690 | } |
---|
691 | |
---|
692 | for(OutEdgeIt e(*_g,v) ; e!=INVALID; ++e) { |
---|
693 | if ( !_surely.positive((*_flow)[e]) ) continue; |
---|
694 | Node w=_g->target(e); |
---|
695 | if ( level[w] == _node_num && w != _source ) { |
---|
696 | bfs_queue.push(w); |
---|
697 | Node z=level_list[l]; |
---|
698 | if ( z!=INVALID ) left.set(z,w); |
---|
699 | right.set(w,z); |
---|
700 | level_list[l]=w; |
---|
701 | level.set(w, l); |
---|
702 | } |
---|
703 | } |
---|
704 | } //while |
---|
705 | } //if |
---|
706 | |
---|
707 | |
---|
708 | switch (flow_prop) { |
---|
709 | case NO_FLOW: |
---|
710 | for(EdgeIt e(*_g); e!=INVALID; ++e) _flow->set(e,0); |
---|
711 | case ZERO_FLOW: |
---|
712 | for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0); |
---|
713 | |
---|
714 | //Reverse_bfs from t, to find the starting level. |
---|
715 | level.set(_target,0); |
---|
716 | bfs_queue.push(_target); |
---|
717 | |
---|
718 | while ( !bfs_queue.empty() ) { |
---|
719 | |
---|
720 | Node v=bfs_queue.front(); |
---|
721 | bfs_queue.pop(); |
---|
722 | int l=level[v]+1; |
---|
723 | |
---|
724 | for(InEdgeIt e(*_g,v) ; e!=INVALID; ++e) { |
---|
725 | Node w=_g->source(e); |
---|
726 | if ( level[w] == _node_num && w != _source ) { |
---|
727 | bfs_queue.push(w); |
---|
728 | Node z=level_list[l]; |
---|
729 | if ( z!=INVALID ) left.set(z,w); |
---|
730 | right.set(w,z); |
---|
731 | level_list[l]=w; |
---|
732 | level.set(w, l); |
---|
733 | } |
---|
734 | } |
---|
735 | } |
---|
736 | |
---|
737 | //the starting flow |
---|
738 | for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) { |
---|
739 | Num c=(*_capacity)[e]; |
---|
740 | if ( !_surely.positive(c) ) continue; |
---|
741 | Node w=_g->target(e); |
---|
742 | if ( level[w] < _node_num ) { |
---|
743 | if ( excess[w] == 0 && w!=_target ) { //putting into the stack |
---|
744 | next.set(w,first[level[w]]); |
---|
745 | first[level[w]]=w; |
---|
746 | } |
---|
747 | _flow->set(e, c); |
---|
748 | excess.set(w, excess[w]+c); |
---|
749 | } |
---|
750 | } |
---|
751 | break; |
---|
752 | |
---|
753 | case GEN_FLOW: |
---|
754 | for(NodeIt v(*_g); v!=INVALID; ++v) excess.set(v,0); |
---|
755 | { |
---|
756 | Num exc=0; |
---|
757 | for(InEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc+=(*_flow)[e]; |
---|
758 | for(OutEdgeIt e(*_g,_target) ; e!=INVALID; ++e) exc-=(*_flow)[e]; |
---|
759 | if (!_surely.positive(exc)) { |
---|
760 | exc = 0; |
---|
761 | } |
---|
762 | excess.set(_target,exc); |
---|
763 | } |
---|
764 | |
---|
765 | //the starting flow |
---|
766 | for(OutEdgeIt e(*_g,_source); e!=INVALID; ++e) { |
---|
767 | Num rem=(*_capacity)[e]-(*_flow)[e]; |
---|
768 | if ( !_surely.positive(rem) ) continue; |
---|
769 | Node w=_g->target(e); |
---|
770 | if ( level[w] < _node_num ) { |
---|
771 | if ( excess[w] == 0 && w!=_target ) { //putting into the stack |
---|
772 | next.set(w,first[level[w]]); |
---|
773 | first[level[w]]=w; |
---|
774 | } |
---|
775 | _flow->set(e, (*_capacity)[e]); |
---|
776 | excess.set(w, excess[w]+rem); |
---|
777 | } |
---|
778 | } |
---|
779 | |
---|
780 | for(InEdgeIt e(*_g,_source); e!=INVALID; ++e) { |
---|
781 | if ( !_surely.positive((*_flow)[e]) ) continue; |
---|
782 | Node w=_g->source(e); |
---|
783 | if ( level[w] < _node_num ) { |
---|
784 | if ( excess[w] == 0 && w!=_target ) { |
---|
785 | next.set(w,first[level[w]]); |
---|
786 | first[level[w]]=w; |
---|
787 | } |
---|
788 | excess.set(w, excess[w]+(*_flow)[e]); |
---|
789 | _flow->set(e, 0); |
---|
790 | } |
---|
791 | } |
---|
792 | break; |
---|
793 | |
---|
794 | case PRE_FLOW: |
---|
795 | //the starting flow |
---|
796 | for(OutEdgeIt e(*_g,_source) ; e!=INVALID; ++e) { |
---|
797 | Num rem=(*_capacity)[e]-(*_flow)[e]; |
---|
798 | if ( !_surely.positive(rem) ) continue; |
---|
799 | Node w=_g->target(e); |
---|
800 | if ( level[w] < _node_num ) _flow->set(e, (*_capacity)[e]); |
---|
801 | } |
---|
802 | |
---|
803 | for(InEdgeIt e(*_g,_source) ; e!=INVALID; ++e) { |
---|
804 | if ( !_surely.positive((*_flow)[e]) ) continue; |
---|
805 | Node w=_g->source(e); |
---|
806 | if ( level[w] < _node_num ) _flow->set(e, 0); |
---|
807 | } |
---|
808 | |
---|
809 | //computing the excess |
---|
810 | for(NodeIt w(*_g); w!=INVALID; ++w) { |
---|
811 | Num exc=0; |
---|
812 | for(InEdgeIt e(*_g,w); e!=INVALID; ++e) exc+=(*_flow)[e]; |
---|
813 | for(OutEdgeIt e(*_g,w); e!=INVALID; ++e) exc-=(*_flow)[e]; |
---|
814 | if (!_surely.positive(exc)) { |
---|
815 | exc = 0; |
---|
816 | } |
---|
817 | excess.set(w,exc); |
---|
818 | |
---|
819 | //putting the active nodes into the stack |
---|
820 | int lev=level[w]; |
---|
821 | if ( exc != 0 && lev < _node_num && Node(w) != _target ) { |
---|
822 | next.set(w,first[lev]); |
---|
823 | first[lev]=w; |
---|
824 | } |
---|
825 | } |
---|
826 | break; |
---|
827 | } //switch |
---|
828 | } //preflowPreproc |
---|
829 | |
---|
830 | |
---|
831 | void relabel(Node w, int newlevel, VecNode& first, NNMap& next, |
---|
832 | VecNode& level_list, NNMap& left, |
---|
833 | NNMap& right, int& b, int& k, bool what_heur ) |
---|
834 | { |
---|
835 | |
---|
836 | int lev=level[w]; |
---|
837 | |
---|
838 | Node right_n=right[w]; |
---|
839 | Node left_n=left[w]; |
---|
840 | |
---|
841 | //unlacing starts |
---|
842 | if ( right_n!=INVALID ) { |
---|
843 | if ( left_n!=INVALID ) { |
---|
844 | right.set(left_n, right_n); |
---|
845 | left.set(right_n, left_n); |
---|
846 | } else { |
---|
847 | level_list[lev]=right_n; |
---|
848 | left.set(right_n, INVALID); |
---|
849 | } |
---|
850 | } else { |
---|
851 | if ( left_n!=INVALID ) { |
---|
852 | right.set(left_n, INVALID); |
---|
853 | } else { |
---|
854 | level_list[lev]=INVALID; |
---|
855 | } |
---|
856 | } |
---|
857 | //unlacing ends |
---|
858 | |
---|
859 | if ( level_list[lev]==INVALID ) { |
---|
860 | |
---|
861 | //gapping starts |
---|
862 | for (int i=lev; i!=k ; ) { |
---|
863 | Node v=level_list[++i]; |
---|
864 | while ( v!=INVALID ) { |
---|
865 | level.set(v,_node_num); |
---|
866 | v=right[v]; |
---|
867 | } |
---|
868 | level_list[i]=INVALID; |
---|
869 | if ( !what_heur ) first[i]=INVALID; |
---|
870 | } |
---|
871 | |
---|
872 | level.set(w,_node_num); |
---|
873 | b=lev-1; |
---|
874 | k=b; |
---|
875 | //gapping ends |
---|
876 | |
---|
877 | } else { |
---|
878 | |
---|
879 | if ( newlevel == _node_num ) level.set(w,_node_num); |
---|
880 | else { |
---|
881 | level.set(w,++newlevel); |
---|
882 | next.set(w,first[newlevel]); |
---|
883 | first[newlevel]=w; |
---|
884 | if ( what_heur ) b=newlevel; |
---|
885 | if ( k < newlevel ) ++k; //now k=newlevel |
---|
886 | Node z=level_list[newlevel]; |
---|
887 | if ( z!=INVALID ) left.set(z,w); |
---|
888 | right.set(w,z); |
---|
889 | left.set(w,INVALID); |
---|
890 | level_list[newlevel]=w; |
---|
891 | } |
---|
892 | } |
---|
893 | } //relabel |
---|
894 | |
---|
895 | }; |
---|
896 | |
---|
897 | ///\ingroup max_flow |
---|
898 | ///\brief Function type interface for Preflow algorithm. |
---|
899 | /// |
---|
900 | ///Function type interface for Preflow algorithm. |
---|
901 | ///\sa Preflow |
---|
902 | template<class GR, class CM, class FM> |
---|
903 | Preflow<GR,typename CM::Value,CM,FM> preflow(const GR &g, |
---|
904 | typename GR::Node source, |
---|
905 | typename GR::Node target, |
---|
906 | const CM &cap, |
---|
907 | FM &flow |
---|
908 | ) |
---|
909 | { |
---|
910 | return Preflow<GR,typename CM::Value,CM,FM>(g,source,target,cap,flow); |
---|
911 | } |
---|
912 | |
---|
913 | } //namespace lemon |
---|
914 | |
---|
915 | #endif //LEMON_PREFLOW_H |
---|