1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
---|
2 | * |
---|
3 | * This file is a part of LEMON, a generic C++ optimization library. |
---|
4 | * |
---|
5 | * Copyright (C) 2003-2009 |
---|
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 <lemon/tolerance.h> |
---|
23 | #include <lemon/elevator.h> |
---|
24 | |
---|
25 | /// \file |
---|
26 | /// \ingroup max_flow |
---|
27 | /// \brief Implementation of the preflow algorithm. |
---|
28 | |
---|
29 | namespace lemon { |
---|
30 | |
---|
31 | /// \brief Default traits class of Preflow class. |
---|
32 | /// |
---|
33 | /// Default traits class of Preflow class. |
---|
34 | /// \tparam GR Digraph type. |
---|
35 | /// \tparam CAP Capacity map type. |
---|
36 | template <typename GR, typename CAP> |
---|
37 | struct PreflowDefaultTraits { |
---|
38 | |
---|
39 | /// \brief The type of the digraph the algorithm runs on. |
---|
40 | typedef GR Digraph; |
---|
41 | |
---|
42 | /// \brief The type of the map that stores the arc capacities. |
---|
43 | /// |
---|
44 | /// The type of the map that stores the arc capacities. |
---|
45 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
---|
46 | typedef CAP CapacityMap; |
---|
47 | |
---|
48 | /// \brief The type of the flow values. |
---|
49 | typedef typename CapacityMap::Value Value; |
---|
50 | |
---|
51 | /// \brief The type of the map that stores the flow values. |
---|
52 | /// |
---|
53 | /// The type of the map that stores the flow values. |
---|
54 | /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept. |
---|
55 | #ifdef DOXYGEN |
---|
56 | typedef GR::ArcMap<Value> FlowMap; |
---|
57 | #else |
---|
58 | typedef typename Digraph::template ArcMap<Value> FlowMap; |
---|
59 | #endif |
---|
60 | |
---|
61 | /// \brief Instantiates a FlowMap. |
---|
62 | /// |
---|
63 | /// This function instantiates a \ref FlowMap. |
---|
64 | /// \param digraph The digraph for which we would like to define |
---|
65 | /// the flow map. |
---|
66 | static FlowMap* createFlowMap(const Digraph& digraph) { |
---|
67 | return new FlowMap(digraph); |
---|
68 | } |
---|
69 | |
---|
70 | /// \brief The elevator type used by Preflow algorithm. |
---|
71 | /// |
---|
72 | /// The elevator type used by Preflow algorithm. |
---|
73 | /// |
---|
74 | /// \sa Elevator, LinkedElevator |
---|
75 | #ifdef DOXYGEN |
---|
76 | typedef lemon::Elevator<GR, GR::Node> Elevator; |
---|
77 | #else |
---|
78 | typedef lemon::Elevator<Digraph, typename Digraph::Node> Elevator; |
---|
79 | #endif |
---|
80 | |
---|
81 | /// \brief Instantiates an Elevator. |
---|
82 | /// |
---|
83 | /// This function instantiates an \ref Elevator. |
---|
84 | /// \param digraph The digraph for which we would like to define |
---|
85 | /// the elevator. |
---|
86 | /// \param max_level The maximum level of the elevator. |
---|
87 | static Elevator* createElevator(const Digraph& digraph, int max_level) { |
---|
88 | return new Elevator(digraph, max_level); |
---|
89 | } |
---|
90 | |
---|
91 | /// \brief The tolerance used by the algorithm |
---|
92 | /// |
---|
93 | /// The tolerance used by the algorithm to handle inexact computation. |
---|
94 | typedef lemon::Tolerance<Value> Tolerance; |
---|
95 | |
---|
96 | }; |
---|
97 | |
---|
98 | |
---|
99 | /// \ingroup max_flow |
---|
100 | /// |
---|
101 | /// \brief %Preflow algorithm class. |
---|
102 | /// |
---|
103 | /// This class provides an implementation of Goldberg-Tarjan's \e preflow |
---|
104 | /// \e push-relabel algorithm producing a \ref max_flow |
---|
105 | /// "flow of maximum value" in a digraph \ref clrs01algorithms, |
---|
106 | /// \ref amo93networkflows, \ref goldberg88newapproach. |
---|
107 | /// The preflow algorithms are the fastest known maximum |
---|
108 | /// flow algorithms. The current implementation uses a mixture of the |
---|
109 | /// \e "highest label" and the \e "bound decrease" heuristics. |
---|
110 | /// The worst case time complexity of the algorithm is \f$O(n^2\sqrt{e})\f$. |
---|
111 | /// |
---|
112 | /// The algorithm consists of two phases. After the first phase |
---|
113 | /// the maximum flow value and the minimum cut is obtained. The |
---|
114 | /// second phase constructs a feasible maximum flow on each arc. |
---|
115 | /// |
---|
116 | /// \warning This implementation cannot handle infinite or very large |
---|
117 | /// capacities (e.g. the maximum value of \c CAP::Value). |
---|
118 | /// |
---|
119 | /// \tparam GR The type of the digraph the algorithm runs on. |
---|
120 | /// \tparam CAP The type of the capacity map. The default map |
---|
121 | /// type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
---|
122 | /// \tparam TR The traits class that defines various types used by the |
---|
123 | /// algorithm. By default, it is \ref PreflowDefaultTraits |
---|
124 | /// "PreflowDefaultTraits<GR, CAP>". |
---|
125 | /// In most cases, this parameter should not be set directly, |
---|
126 | /// consider to use the named template parameters instead. |
---|
127 | #ifdef DOXYGEN |
---|
128 | template <typename GR, typename CAP, typename TR> |
---|
129 | #else |
---|
130 | template <typename GR, |
---|
131 | typename CAP = typename GR::template ArcMap<int>, |
---|
132 | typename TR = PreflowDefaultTraits<GR, CAP> > |
---|
133 | #endif |
---|
134 | class Preflow { |
---|
135 | public: |
---|
136 | |
---|
137 | ///The \ref PreflowDefaultTraits "traits class" of the algorithm. |
---|
138 | typedef TR Traits; |
---|
139 | ///The type of the digraph the algorithm runs on. |
---|
140 | typedef typename Traits::Digraph Digraph; |
---|
141 | ///The type of the capacity map. |
---|
142 | typedef typename Traits::CapacityMap CapacityMap; |
---|
143 | ///The type of the flow values. |
---|
144 | typedef typename Traits::Value Value; |
---|
145 | |
---|
146 | ///The type of the flow map. |
---|
147 | typedef typename Traits::FlowMap FlowMap; |
---|
148 | ///The type of the elevator. |
---|
149 | typedef typename Traits::Elevator Elevator; |
---|
150 | ///The type of the tolerance. |
---|
151 | typedef typename Traits::Tolerance Tolerance; |
---|
152 | |
---|
153 | private: |
---|
154 | |
---|
155 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
---|
156 | |
---|
157 | const Digraph& _graph; |
---|
158 | const CapacityMap* _capacity; |
---|
159 | |
---|
160 | int _node_num; |
---|
161 | |
---|
162 | Node _source, _target; |
---|
163 | |
---|
164 | FlowMap* _flow; |
---|
165 | bool _local_flow; |
---|
166 | |
---|
167 | Elevator* _level; |
---|
168 | bool _local_level; |
---|
169 | |
---|
170 | typedef typename Digraph::template NodeMap<Value> ExcessMap; |
---|
171 | ExcessMap* _excess; |
---|
172 | |
---|
173 | Tolerance _tolerance; |
---|
174 | |
---|
175 | bool _phase; |
---|
176 | |
---|
177 | |
---|
178 | void createStructures() { |
---|
179 | _node_num = countNodes(_graph); |
---|
180 | |
---|
181 | if (!_flow) { |
---|
182 | _flow = Traits::createFlowMap(_graph); |
---|
183 | _local_flow = true; |
---|
184 | } |
---|
185 | if (!_level) { |
---|
186 | _level = Traits::createElevator(_graph, _node_num); |
---|
187 | _local_level = true; |
---|
188 | } |
---|
189 | if (!_excess) { |
---|
190 | _excess = new ExcessMap(_graph); |
---|
191 | } |
---|
192 | } |
---|
193 | |
---|
194 | void destroyStructures() { |
---|
195 | if (_local_flow) { |
---|
196 | delete _flow; |
---|
197 | } |
---|
198 | if (_local_level) { |
---|
199 | delete _level; |
---|
200 | } |
---|
201 | if (_excess) { |
---|
202 | delete _excess; |
---|
203 | } |
---|
204 | } |
---|
205 | |
---|
206 | public: |
---|
207 | |
---|
208 | typedef Preflow Create; |
---|
209 | |
---|
210 | ///\name Named Template Parameters |
---|
211 | |
---|
212 | ///@{ |
---|
213 | |
---|
214 | template <typename T> |
---|
215 | struct SetFlowMapTraits : public Traits { |
---|
216 | typedef T FlowMap; |
---|
217 | static FlowMap *createFlowMap(const Digraph&) { |
---|
218 | LEMON_ASSERT(false, "FlowMap is not initialized"); |
---|
219 | return 0; // ignore warnings |
---|
220 | } |
---|
221 | }; |
---|
222 | |
---|
223 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
224 | /// FlowMap type |
---|
225 | /// |
---|
226 | /// \ref named-templ-param "Named parameter" for setting FlowMap |
---|
227 | /// type. |
---|
228 | template <typename T> |
---|
229 | struct SetFlowMap |
---|
230 | : public Preflow<Digraph, CapacityMap, SetFlowMapTraits<T> > { |
---|
231 | typedef Preflow<Digraph, CapacityMap, |
---|
232 | SetFlowMapTraits<T> > Create; |
---|
233 | }; |
---|
234 | |
---|
235 | template <typename T> |
---|
236 | struct SetElevatorTraits : public Traits { |
---|
237 | typedef T Elevator; |
---|
238 | static Elevator *createElevator(const Digraph&, int) { |
---|
239 | LEMON_ASSERT(false, "Elevator is not initialized"); |
---|
240 | return 0; // ignore warnings |
---|
241 | } |
---|
242 | }; |
---|
243 | |
---|
244 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
245 | /// Elevator type |
---|
246 | /// |
---|
247 | /// \ref named-templ-param "Named parameter" for setting Elevator |
---|
248 | /// type. If this named parameter is used, then an external |
---|
249 | /// elevator object must be passed to the algorithm using the |
---|
250 | /// \ref elevator(Elevator&) "elevator()" function before calling |
---|
251 | /// \ref run() or \ref init(). |
---|
252 | /// \sa SetStandardElevator |
---|
253 | template <typename T> |
---|
254 | struct SetElevator |
---|
255 | : public Preflow<Digraph, CapacityMap, SetElevatorTraits<T> > { |
---|
256 | typedef Preflow<Digraph, CapacityMap, |
---|
257 | SetElevatorTraits<T> > Create; |
---|
258 | }; |
---|
259 | |
---|
260 | template <typename T> |
---|
261 | struct SetStandardElevatorTraits : public Traits { |
---|
262 | typedef T Elevator; |
---|
263 | static Elevator *createElevator(const Digraph& digraph, int max_level) { |
---|
264 | return new Elevator(digraph, max_level); |
---|
265 | } |
---|
266 | }; |
---|
267 | |
---|
268 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
269 | /// Elevator type with automatic allocation |
---|
270 | /// |
---|
271 | /// \ref named-templ-param "Named parameter" for setting Elevator |
---|
272 | /// type with automatic allocation. |
---|
273 | /// The Elevator should have standard constructor interface to be |
---|
274 | /// able to automatically created by the algorithm (i.e. the |
---|
275 | /// digraph and the maximum level should be passed to it). |
---|
276 | /// However, an external elevator object could also be passed to the |
---|
277 | /// algorithm with the \ref elevator(Elevator&) "elevator()" function |
---|
278 | /// before calling \ref run() or \ref init(). |
---|
279 | /// \sa SetElevator |
---|
280 | template <typename T> |
---|
281 | struct SetStandardElevator |
---|
282 | : public Preflow<Digraph, CapacityMap, |
---|
283 | SetStandardElevatorTraits<T> > { |
---|
284 | typedef Preflow<Digraph, CapacityMap, |
---|
285 | SetStandardElevatorTraits<T> > Create; |
---|
286 | }; |
---|
287 | |
---|
288 | /// @} |
---|
289 | |
---|
290 | protected: |
---|
291 | |
---|
292 | Preflow() {} |
---|
293 | |
---|
294 | public: |
---|
295 | |
---|
296 | |
---|
297 | /// \brief The constructor of the class. |
---|
298 | /// |
---|
299 | /// The constructor of the class. |
---|
300 | /// \param digraph The digraph the algorithm runs on. |
---|
301 | /// \param capacity The capacity of the arcs. |
---|
302 | /// \param source The source node. |
---|
303 | /// \param target The target node. |
---|
304 | Preflow(const Digraph& digraph, const CapacityMap& capacity, |
---|
305 | Node source, Node target) |
---|
306 | : _graph(digraph), _capacity(&capacity), |
---|
307 | _node_num(0), _source(source), _target(target), |
---|
308 | _flow(0), _local_flow(false), |
---|
309 | _level(0), _local_level(false), |
---|
310 | _excess(0), _tolerance(), _phase() {} |
---|
311 | |
---|
312 | /// \brief Destructor. |
---|
313 | /// |
---|
314 | /// Destructor. |
---|
315 | ~Preflow() { |
---|
316 | destroyStructures(); |
---|
317 | } |
---|
318 | |
---|
319 | /// \brief Sets the capacity map. |
---|
320 | /// |
---|
321 | /// Sets the capacity map. |
---|
322 | /// \return <tt>(*this)</tt> |
---|
323 | Preflow& capacityMap(const CapacityMap& map) { |
---|
324 | _capacity = ↦ |
---|
325 | return *this; |
---|
326 | } |
---|
327 | |
---|
328 | /// \brief Sets the flow map. |
---|
329 | /// |
---|
330 | /// Sets the flow map. |
---|
331 | /// If you don't use this function before calling \ref run() or |
---|
332 | /// \ref init(), an instance will be allocated automatically. |
---|
333 | /// The destructor deallocates this automatically allocated map, |
---|
334 | /// of course. |
---|
335 | /// \return <tt>(*this)</tt> |
---|
336 | Preflow& flowMap(FlowMap& map) { |
---|
337 | if (_local_flow) { |
---|
338 | delete _flow; |
---|
339 | _local_flow = false; |
---|
340 | } |
---|
341 | _flow = ↦ |
---|
342 | return *this; |
---|
343 | } |
---|
344 | |
---|
345 | /// \brief Sets the source node. |
---|
346 | /// |
---|
347 | /// Sets the source node. |
---|
348 | /// \return <tt>(*this)</tt> |
---|
349 | Preflow& source(const Node& node) { |
---|
350 | _source = node; |
---|
351 | return *this; |
---|
352 | } |
---|
353 | |
---|
354 | /// \brief Sets the target node. |
---|
355 | /// |
---|
356 | /// Sets the target node. |
---|
357 | /// \return <tt>(*this)</tt> |
---|
358 | Preflow& target(const Node& node) { |
---|
359 | _target = node; |
---|
360 | return *this; |
---|
361 | } |
---|
362 | |
---|
363 | /// \brief Sets the elevator used by algorithm. |
---|
364 | /// |
---|
365 | /// Sets the elevator used by algorithm. |
---|
366 | /// If you don't use this function before calling \ref run() or |
---|
367 | /// \ref init(), an instance will be allocated automatically. |
---|
368 | /// The destructor deallocates this automatically allocated elevator, |
---|
369 | /// of course. |
---|
370 | /// \return <tt>(*this)</tt> |
---|
371 | Preflow& elevator(Elevator& elevator) { |
---|
372 | if (_local_level) { |
---|
373 | delete _level; |
---|
374 | _local_level = false; |
---|
375 | } |
---|
376 | _level = &elevator; |
---|
377 | return *this; |
---|
378 | } |
---|
379 | |
---|
380 | /// \brief Returns a const reference to the elevator. |
---|
381 | /// |
---|
382 | /// Returns a const reference to the elevator. |
---|
383 | /// |
---|
384 | /// \pre Either \ref run() or \ref init() must be called before |
---|
385 | /// using this function. |
---|
386 | const Elevator& elevator() const { |
---|
387 | return *_level; |
---|
388 | } |
---|
389 | |
---|
390 | /// \brief Sets the tolerance used by the algorithm. |
---|
391 | /// |
---|
392 | /// Sets the tolerance object used by the algorithm. |
---|
393 | /// \return <tt>(*this)</tt> |
---|
394 | Preflow& tolerance(const Tolerance& tolerance) { |
---|
395 | _tolerance = tolerance; |
---|
396 | return *this; |
---|
397 | } |
---|
398 | |
---|
399 | /// \brief Returns a const reference to the tolerance. |
---|
400 | /// |
---|
401 | /// Returns a const reference to the tolerance object used by |
---|
402 | /// the algorithm. |
---|
403 | const Tolerance& tolerance() const { |
---|
404 | return _tolerance; |
---|
405 | } |
---|
406 | |
---|
407 | /// \name Execution Control |
---|
408 | /// The simplest way to execute the preflow algorithm is to use |
---|
409 | /// \ref run() or \ref runMinCut().\n |
---|
410 | /// If you need better control on the initial solution or the execution, |
---|
411 | /// you have to call one of the \ref init() functions first, then |
---|
412 | /// \ref startFirstPhase() and if you need it \ref startSecondPhase(). |
---|
413 | |
---|
414 | ///@{ |
---|
415 | |
---|
416 | /// \brief Initializes the internal data structures. |
---|
417 | /// |
---|
418 | /// Initializes the internal data structures and sets the initial |
---|
419 | /// flow to zero on each arc. |
---|
420 | void init() { |
---|
421 | createStructures(); |
---|
422 | |
---|
423 | _phase = true; |
---|
424 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
425 | (*_excess)[n] = 0; |
---|
426 | } |
---|
427 | |
---|
428 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
429 | _flow->set(e, 0); |
---|
430 | } |
---|
431 | |
---|
432 | typename Digraph::template NodeMap<bool> reached(_graph, false); |
---|
433 | |
---|
434 | _level->initStart(); |
---|
435 | _level->initAddItem(_target); |
---|
436 | |
---|
437 | std::vector<Node> queue; |
---|
438 | reached[_source] = true; |
---|
439 | |
---|
440 | queue.push_back(_target); |
---|
441 | reached[_target] = true; |
---|
442 | while (!queue.empty()) { |
---|
443 | _level->initNewLevel(); |
---|
444 | std::vector<Node> nqueue; |
---|
445 | for (int i = 0; i < int(queue.size()); ++i) { |
---|
446 | Node n = queue[i]; |
---|
447 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
448 | Node u = _graph.source(e); |
---|
449 | if (!reached[u] && _tolerance.positive((*_capacity)[e])) { |
---|
450 | reached[u] = true; |
---|
451 | _level->initAddItem(u); |
---|
452 | nqueue.push_back(u); |
---|
453 | } |
---|
454 | } |
---|
455 | } |
---|
456 | queue.swap(nqueue); |
---|
457 | } |
---|
458 | _level->initFinish(); |
---|
459 | |
---|
460 | for (OutArcIt e(_graph, _source); e != INVALID; ++e) { |
---|
461 | if (_tolerance.positive((*_capacity)[e])) { |
---|
462 | Node u = _graph.target(e); |
---|
463 | if ((*_level)[u] == _level->maxLevel()) continue; |
---|
464 | _flow->set(e, (*_capacity)[e]); |
---|
465 | (*_excess)[u] += (*_capacity)[e]; |
---|
466 | if (u != _target && !_level->active(u)) { |
---|
467 | _level->activate(u); |
---|
468 | } |
---|
469 | } |
---|
470 | } |
---|
471 | } |
---|
472 | |
---|
473 | /// \brief Initializes the internal data structures using the |
---|
474 | /// given flow map. |
---|
475 | /// |
---|
476 | /// Initializes the internal data structures and sets the initial |
---|
477 | /// flow to the given \c flowMap. The \c flowMap should contain a |
---|
478 | /// flow or at least a preflow, i.e. at each node excluding the |
---|
479 | /// source node the incoming flow should greater or equal to the |
---|
480 | /// outgoing flow. |
---|
481 | /// \return \c false if the given \c flowMap is not a preflow. |
---|
482 | template <typename FlowMap> |
---|
483 | bool init(const FlowMap& flowMap) { |
---|
484 | createStructures(); |
---|
485 | |
---|
486 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
487 | _flow->set(e, flowMap[e]); |
---|
488 | } |
---|
489 | |
---|
490 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
491 | Value excess = 0; |
---|
492 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
493 | excess += (*_flow)[e]; |
---|
494 | } |
---|
495 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
496 | excess -= (*_flow)[e]; |
---|
497 | } |
---|
498 | if (excess < 0 && n != _source) return false; |
---|
499 | (*_excess)[n] = excess; |
---|
500 | } |
---|
501 | |
---|
502 | typename Digraph::template NodeMap<bool> reached(_graph, false); |
---|
503 | |
---|
504 | _level->initStart(); |
---|
505 | _level->initAddItem(_target); |
---|
506 | |
---|
507 | std::vector<Node> queue; |
---|
508 | reached[_source] = true; |
---|
509 | |
---|
510 | queue.push_back(_target); |
---|
511 | reached[_target] = true; |
---|
512 | while (!queue.empty()) { |
---|
513 | _level->initNewLevel(); |
---|
514 | std::vector<Node> nqueue; |
---|
515 | for (int i = 0; i < int(queue.size()); ++i) { |
---|
516 | Node n = queue[i]; |
---|
517 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
518 | Node u = _graph.source(e); |
---|
519 | if (!reached[u] && |
---|
520 | _tolerance.positive((*_capacity)[e] - (*_flow)[e])) { |
---|
521 | reached[u] = true; |
---|
522 | _level->initAddItem(u); |
---|
523 | nqueue.push_back(u); |
---|
524 | } |
---|
525 | } |
---|
526 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
527 | Node v = _graph.target(e); |
---|
528 | if (!reached[v] && _tolerance.positive((*_flow)[e])) { |
---|
529 | reached[v] = true; |
---|
530 | _level->initAddItem(v); |
---|
531 | nqueue.push_back(v); |
---|
532 | } |
---|
533 | } |
---|
534 | } |
---|
535 | queue.swap(nqueue); |
---|
536 | } |
---|
537 | _level->initFinish(); |
---|
538 | |
---|
539 | for (OutArcIt e(_graph, _source); e != INVALID; ++e) { |
---|
540 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
541 | if (_tolerance.positive(rem)) { |
---|
542 | Node u = _graph.target(e); |
---|
543 | if ((*_level)[u] == _level->maxLevel()) continue; |
---|
544 | _flow->set(e, (*_capacity)[e]); |
---|
545 | (*_excess)[u] += rem; |
---|
546 | if (u != _target && !_level->active(u)) { |
---|
547 | _level->activate(u); |
---|
548 | } |
---|
549 | } |
---|
550 | } |
---|
551 | for (InArcIt e(_graph, _source); e != INVALID; ++e) { |
---|
552 | Value rem = (*_flow)[e]; |
---|
553 | if (_tolerance.positive(rem)) { |
---|
554 | Node v = _graph.source(e); |
---|
555 | if ((*_level)[v] == _level->maxLevel()) continue; |
---|
556 | _flow->set(e, 0); |
---|
557 | (*_excess)[v] += rem; |
---|
558 | if (v != _target && !_level->active(v)) { |
---|
559 | _level->activate(v); |
---|
560 | } |
---|
561 | } |
---|
562 | } |
---|
563 | return true; |
---|
564 | } |
---|
565 | |
---|
566 | /// \brief Starts the first phase of the preflow algorithm. |
---|
567 | /// |
---|
568 | /// The preflow algorithm consists of two phases, this method runs |
---|
569 | /// the first phase. After the first phase the maximum flow value |
---|
570 | /// and a minimum value cut can already be computed, although a |
---|
571 | /// maximum flow is not yet obtained. So after calling this method |
---|
572 | /// \ref flowValue() returns the value of a maximum flow and \ref |
---|
573 | /// minCut() returns a minimum cut. |
---|
574 | /// \pre One of the \ref init() functions must be called before |
---|
575 | /// using this function. |
---|
576 | void startFirstPhase() { |
---|
577 | _phase = true; |
---|
578 | |
---|
579 | Node n = _level->highestActive(); |
---|
580 | int level = _level->highestActiveLevel(); |
---|
581 | while (n != INVALID) { |
---|
582 | int num = _node_num; |
---|
583 | |
---|
584 | while (num > 0 && n != INVALID) { |
---|
585 | Value excess = (*_excess)[n]; |
---|
586 | int new_level = _level->maxLevel(); |
---|
587 | |
---|
588 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
589 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
590 | if (!_tolerance.positive(rem)) continue; |
---|
591 | Node v = _graph.target(e); |
---|
592 | if ((*_level)[v] < level) { |
---|
593 | if (!_level->active(v) && v != _target) { |
---|
594 | _level->activate(v); |
---|
595 | } |
---|
596 | if (!_tolerance.less(rem, excess)) { |
---|
597 | _flow->set(e, (*_flow)[e] + excess); |
---|
598 | (*_excess)[v] += excess; |
---|
599 | excess = 0; |
---|
600 | goto no_more_push_1; |
---|
601 | } else { |
---|
602 | excess -= rem; |
---|
603 | (*_excess)[v] += rem; |
---|
604 | _flow->set(e, (*_capacity)[e]); |
---|
605 | } |
---|
606 | } else if (new_level > (*_level)[v]) { |
---|
607 | new_level = (*_level)[v]; |
---|
608 | } |
---|
609 | } |
---|
610 | |
---|
611 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
612 | Value rem = (*_flow)[e]; |
---|
613 | if (!_tolerance.positive(rem)) continue; |
---|
614 | Node v = _graph.source(e); |
---|
615 | if ((*_level)[v] < level) { |
---|
616 | if (!_level->active(v) && v != _target) { |
---|
617 | _level->activate(v); |
---|
618 | } |
---|
619 | if (!_tolerance.less(rem, excess)) { |
---|
620 | _flow->set(e, (*_flow)[e] - excess); |
---|
621 | (*_excess)[v] += excess; |
---|
622 | excess = 0; |
---|
623 | goto no_more_push_1; |
---|
624 | } else { |
---|
625 | excess -= rem; |
---|
626 | (*_excess)[v] += rem; |
---|
627 | _flow->set(e, 0); |
---|
628 | } |
---|
629 | } else if (new_level > (*_level)[v]) { |
---|
630 | new_level = (*_level)[v]; |
---|
631 | } |
---|
632 | } |
---|
633 | |
---|
634 | no_more_push_1: |
---|
635 | |
---|
636 | (*_excess)[n] = excess; |
---|
637 | |
---|
638 | if (excess != 0) { |
---|
639 | if (new_level + 1 < _level->maxLevel()) { |
---|
640 | _level->liftHighestActive(new_level + 1); |
---|
641 | } else { |
---|
642 | _level->liftHighestActiveToTop(); |
---|
643 | } |
---|
644 | if (_level->emptyLevel(level)) { |
---|
645 | _level->liftToTop(level); |
---|
646 | } |
---|
647 | } else { |
---|
648 | _level->deactivate(n); |
---|
649 | } |
---|
650 | |
---|
651 | n = _level->highestActive(); |
---|
652 | level = _level->highestActiveLevel(); |
---|
653 | --num; |
---|
654 | } |
---|
655 | |
---|
656 | num = _node_num * 20; |
---|
657 | while (num > 0 && n != INVALID) { |
---|
658 | Value excess = (*_excess)[n]; |
---|
659 | int new_level = _level->maxLevel(); |
---|
660 | |
---|
661 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
662 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
663 | if (!_tolerance.positive(rem)) continue; |
---|
664 | Node v = _graph.target(e); |
---|
665 | if ((*_level)[v] < level) { |
---|
666 | if (!_level->active(v) && v != _target) { |
---|
667 | _level->activate(v); |
---|
668 | } |
---|
669 | if (!_tolerance.less(rem, excess)) { |
---|
670 | _flow->set(e, (*_flow)[e] + excess); |
---|
671 | (*_excess)[v] += excess; |
---|
672 | excess = 0; |
---|
673 | goto no_more_push_2; |
---|
674 | } else { |
---|
675 | excess -= rem; |
---|
676 | (*_excess)[v] += rem; |
---|
677 | _flow->set(e, (*_capacity)[e]); |
---|
678 | } |
---|
679 | } else if (new_level > (*_level)[v]) { |
---|
680 | new_level = (*_level)[v]; |
---|
681 | } |
---|
682 | } |
---|
683 | |
---|
684 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
685 | Value rem = (*_flow)[e]; |
---|
686 | if (!_tolerance.positive(rem)) continue; |
---|
687 | Node v = _graph.source(e); |
---|
688 | if ((*_level)[v] < level) { |
---|
689 | if (!_level->active(v) && v != _target) { |
---|
690 | _level->activate(v); |
---|
691 | } |
---|
692 | if (!_tolerance.less(rem, excess)) { |
---|
693 | _flow->set(e, (*_flow)[e] - excess); |
---|
694 | (*_excess)[v] += excess; |
---|
695 | excess = 0; |
---|
696 | goto no_more_push_2; |
---|
697 | } else { |
---|
698 | excess -= rem; |
---|
699 | (*_excess)[v] += rem; |
---|
700 | _flow->set(e, 0); |
---|
701 | } |
---|
702 | } else if (new_level > (*_level)[v]) { |
---|
703 | new_level = (*_level)[v]; |
---|
704 | } |
---|
705 | } |
---|
706 | |
---|
707 | no_more_push_2: |
---|
708 | |
---|
709 | (*_excess)[n] = excess; |
---|
710 | |
---|
711 | if (excess != 0) { |
---|
712 | if (new_level + 1 < _level->maxLevel()) { |
---|
713 | _level->liftActiveOn(level, new_level + 1); |
---|
714 | } else { |
---|
715 | _level->liftActiveToTop(level); |
---|
716 | } |
---|
717 | if (_level->emptyLevel(level)) { |
---|
718 | _level->liftToTop(level); |
---|
719 | } |
---|
720 | } else { |
---|
721 | _level->deactivate(n); |
---|
722 | } |
---|
723 | |
---|
724 | while (level >= 0 && _level->activeFree(level)) { |
---|
725 | --level; |
---|
726 | } |
---|
727 | if (level == -1) { |
---|
728 | n = _level->highestActive(); |
---|
729 | level = _level->highestActiveLevel(); |
---|
730 | } else { |
---|
731 | n = _level->activeOn(level); |
---|
732 | } |
---|
733 | --num; |
---|
734 | } |
---|
735 | } |
---|
736 | } |
---|
737 | |
---|
738 | /// \brief Starts the second phase of the preflow algorithm. |
---|
739 | /// |
---|
740 | /// The preflow algorithm consists of two phases, this method runs |
---|
741 | /// the second phase. After calling one of the \ref init() functions |
---|
742 | /// and \ref startFirstPhase() and then \ref startSecondPhase(), |
---|
743 | /// \ref flowMap() returns a maximum flow, \ref flowValue() returns the |
---|
744 | /// value of a maximum flow, \ref minCut() returns a minimum cut |
---|
745 | /// \pre One of the \ref init() functions and \ref startFirstPhase() |
---|
746 | /// must be called before using this function. |
---|
747 | void startSecondPhase() { |
---|
748 | _phase = false; |
---|
749 | |
---|
750 | typename Digraph::template NodeMap<bool> reached(_graph); |
---|
751 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
752 | reached[n] = (*_level)[n] < _level->maxLevel(); |
---|
753 | } |
---|
754 | |
---|
755 | _level->initStart(); |
---|
756 | _level->initAddItem(_source); |
---|
757 | |
---|
758 | std::vector<Node> queue; |
---|
759 | queue.push_back(_source); |
---|
760 | reached[_source] = true; |
---|
761 | |
---|
762 | while (!queue.empty()) { |
---|
763 | _level->initNewLevel(); |
---|
764 | std::vector<Node> nqueue; |
---|
765 | for (int i = 0; i < int(queue.size()); ++i) { |
---|
766 | Node n = queue[i]; |
---|
767 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
768 | Node v = _graph.target(e); |
---|
769 | if (!reached[v] && _tolerance.positive((*_flow)[e])) { |
---|
770 | reached[v] = true; |
---|
771 | _level->initAddItem(v); |
---|
772 | nqueue.push_back(v); |
---|
773 | } |
---|
774 | } |
---|
775 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
776 | Node u = _graph.source(e); |
---|
777 | if (!reached[u] && |
---|
778 | _tolerance.positive((*_capacity)[e] - (*_flow)[e])) { |
---|
779 | reached[u] = true; |
---|
780 | _level->initAddItem(u); |
---|
781 | nqueue.push_back(u); |
---|
782 | } |
---|
783 | } |
---|
784 | } |
---|
785 | queue.swap(nqueue); |
---|
786 | } |
---|
787 | _level->initFinish(); |
---|
788 | |
---|
789 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
790 | if (!reached[n]) { |
---|
791 | _level->dirtyTopButOne(n); |
---|
792 | } else if ((*_excess)[n] > 0 && _target != n) { |
---|
793 | _level->activate(n); |
---|
794 | } |
---|
795 | } |
---|
796 | |
---|
797 | Node n; |
---|
798 | while ((n = _level->highestActive()) != INVALID) { |
---|
799 | Value excess = (*_excess)[n]; |
---|
800 | int level = _level->highestActiveLevel(); |
---|
801 | int new_level = _level->maxLevel(); |
---|
802 | |
---|
803 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
804 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
805 | if (!_tolerance.positive(rem)) continue; |
---|
806 | Node v = _graph.target(e); |
---|
807 | if ((*_level)[v] < level) { |
---|
808 | if (!_level->active(v) && v != _source) { |
---|
809 | _level->activate(v); |
---|
810 | } |
---|
811 | if (!_tolerance.less(rem, excess)) { |
---|
812 | _flow->set(e, (*_flow)[e] + excess); |
---|
813 | (*_excess)[v] += excess; |
---|
814 | excess = 0; |
---|
815 | goto no_more_push; |
---|
816 | } else { |
---|
817 | excess -= rem; |
---|
818 | (*_excess)[v] += rem; |
---|
819 | _flow->set(e, (*_capacity)[e]); |
---|
820 | } |
---|
821 | } else if (new_level > (*_level)[v]) { |
---|
822 | new_level = (*_level)[v]; |
---|
823 | } |
---|
824 | } |
---|
825 | |
---|
826 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
827 | Value rem = (*_flow)[e]; |
---|
828 | if (!_tolerance.positive(rem)) continue; |
---|
829 | Node v = _graph.source(e); |
---|
830 | if ((*_level)[v] < level) { |
---|
831 | if (!_level->active(v) && v != _source) { |
---|
832 | _level->activate(v); |
---|
833 | } |
---|
834 | if (!_tolerance.less(rem, excess)) { |
---|
835 | _flow->set(e, (*_flow)[e] - excess); |
---|
836 | (*_excess)[v] += excess; |
---|
837 | excess = 0; |
---|
838 | goto no_more_push; |
---|
839 | } else { |
---|
840 | excess -= rem; |
---|
841 | (*_excess)[v] += rem; |
---|
842 | _flow->set(e, 0); |
---|
843 | } |
---|
844 | } else if (new_level > (*_level)[v]) { |
---|
845 | new_level = (*_level)[v]; |
---|
846 | } |
---|
847 | } |
---|
848 | |
---|
849 | no_more_push: |
---|
850 | |
---|
851 | (*_excess)[n] = excess; |
---|
852 | |
---|
853 | if (excess != 0) { |
---|
854 | if (new_level + 1 < _level->maxLevel()) { |
---|
855 | _level->liftHighestActive(new_level + 1); |
---|
856 | } else { |
---|
857 | // Calculation error |
---|
858 | _level->liftHighestActiveToTop(); |
---|
859 | } |
---|
860 | if (_level->emptyLevel(level)) { |
---|
861 | // Calculation error |
---|
862 | _level->liftToTop(level); |
---|
863 | } |
---|
864 | } else { |
---|
865 | _level->deactivate(n); |
---|
866 | } |
---|
867 | |
---|
868 | } |
---|
869 | } |
---|
870 | |
---|
871 | /// \brief Runs the preflow algorithm. |
---|
872 | /// |
---|
873 | /// Runs the preflow algorithm. |
---|
874 | /// \note pf.run() is just a shortcut of the following code. |
---|
875 | /// \code |
---|
876 | /// pf.init(); |
---|
877 | /// pf.startFirstPhase(); |
---|
878 | /// pf.startSecondPhase(); |
---|
879 | /// \endcode |
---|
880 | void run() { |
---|
881 | init(); |
---|
882 | startFirstPhase(); |
---|
883 | startSecondPhase(); |
---|
884 | } |
---|
885 | |
---|
886 | /// \brief Runs the preflow algorithm to compute the minimum cut. |
---|
887 | /// |
---|
888 | /// Runs the preflow algorithm to compute the minimum cut. |
---|
889 | /// \note pf.runMinCut() is just a shortcut of the following code. |
---|
890 | /// \code |
---|
891 | /// pf.init(); |
---|
892 | /// pf.startFirstPhase(); |
---|
893 | /// \endcode |
---|
894 | void runMinCut() { |
---|
895 | init(); |
---|
896 | startFirstPhase(); |
---|
897 | } |
---|
898 | |
---|
899 | /// @} |
---|
900 | |
---|
901 | /// \name Query Functions |
---|
902 | /// The results of the preflow algorithm can be obtained using these |
---|
903 | /// functions.\n |
---|
904 | /// Either one of the \ref run() "run*()" functions or one of the |
---|
905 | /// \ref startFirstPhase() "start*()" functions should be called |
---|
906 | /// before using them. |
---|
907 | |
---|
908 | ///@{ |
---|
909 | |
---|
910 | /// \brief Returns the value of the maximum flow. |
---|
911 | /// |
---|
912 | /// Returns the value of the maximum flow by returning the excess |
---|
913 | /// of the target node. This value equals to the value of |
---|
914 | /// the maximum flow already after the first phase of the algorithm. |
---|
915 | /// |
---|
916 | /// \pre Either \ref run() or \ref init() must be called before |
---|
917 | /// using this function. |
---|
918 | Value flowValue() const { |
---|
919 | return (*_excess)[_target]; |
---|
920 | } |
---|
921 | |
---|
922 | /// \brief Returns the flow value on the given arc. |
---|
923 | /// |
---|
924 | /// Returns the flow value on the given arc. This method can |
---|
925 | /// be called after the second phase of the algorithm. |
---|
926 | /// |
---|
927 | /// \pre Either \ref run() or \ref init() must be called before |
---|
928 | /// using this function. |
---|
929 | Value flow(const Arc& arc) const { |
---|
930 | return (*_flow)[arc]; |
---|
931 | } |
---|
932 | |
---|
933 | /// \brief Returns a const reference to the flow map. |
---|
934 | /// |
---|
935 | /// Returns a const reference to the arc map storing the found flow. |
---|
936 | /// This method can be called after the second phase of the algorithm. |
---|
937 | /// |
---|
938 | /// \pre Either \ref run() or \ref init() must be called before |
---|
939 | /// using this function. |
---|
940 | const FlowMap& flowMap() const { |
---|
941 | return *_flow; |
---|
942 | } |
---|
943 | |
---|
944 | /// \brief Returns \c true when the node is on the source side of the |
---|
945 | /// minimum cut. |
---|
946 | /// |
---|
947 | /// Returns true when the node is on the source side of the found |
---|
948 | /// minimum cut. This method can be called both after running \ref |
---|
949 | /// startFirstPhase() and \ref startSecondPhase(). |
---|
950 | /// |
---|
951 | /// \pre Either \ref run() or \ref init() must be called before |
---|
952 | /// using this function. |
---|
953 | bool minCut(const Node& node) const { |
---|
954 | return ((*_level)[node] == _level->maxLevel()) == _phase; |
---|
955 | } |
---|
956 | |
---|
957 | /// \brief Gives back a minimum value cut. |
---|
958 | /// |
---|
959 | /// Sets \c cutMap to the characteristic vector of a minimum value |
---|
960 | /// cut. \c cutMap should be a \ref concepts::WriteMap "writable" |
---|
961 | /// node map with \c bool (or convertible) value type. |
---|
962 | /// |
---|
963 | /// This method can be called both after running \ref startFirstPhase() |
---|
964 | /// and \ref startSecondPhase(). The result after the second phase |
---|
965 | /// could be slightly different if inexact computation is used. |
---|
966 | /// |
---|
967 | /// \note This function calls \ref minCut() for each node, so it runs in |
---|
968 | /// O(n) time. |
---|
969 | /// |
---|
970 | /// \pre Either \ref run() or \ref init() must be called before |
---|
971 | /// using this function. |
---|
972 | template <typename CutMap> |
---|
973 | void minCutMap(CutMap& cutMap) const { |
---|
974 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
975 | cutMap.set(n, minCut(n)); |
---|
976 | } |
---|
977 | } |
---|
978 | |
---|
979 | /// @} |
---|
980 | }; |
---|
981 | } |
---|
982 | |
---|
983 | #endif |
---|