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_GOLDBERG_TARJAN_H |
---|
20 | #define LEMON_GOLDBERG_TARJAN_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 | #include <lemon/dynamic_tree.h> |
---|
31 | #include <limits> |
---|
32 | |
---|
33 | /// \file |
---|
34 | /// \ingroup max_flow |
---|
35 | /// \brief Implementation of the preflow algorithm. |
---|
36 | |
---|
37 | namespace lemon { |
---|
38 | |
---|
39 | /// \brief Default traits class of GoldbergTarjan class. |
---|
40 | /// |
---|
41 | /// Default traits class of GoldbergTarjan class. |
---|
42 | /// \param _Graph Graph type. |
---|
43 | /// \param _CapacityMap Type of capacity map. |
---|
44 | template <typename _Graph, typename _CapacityMap> |
---|
45 | struct GoldbergTarjanDefaultTraits { |
---|
46 | |
---|
47 | /// \brief The graph type the algorithm runs on. |
---|
48 | typedef _Graph Graph; |
---|
49 | |
---|
50 | /// \brief The type of the map that stores the edge capacities. |
---|
51 | /// |
---|
52 | /// The type of the map that stores the edge capacities. |
---|
53 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
---|
54 | typedef _CapacityMap CapacityMap; |
---|
55 | |
---|
56 | /// \brief The type of the length of the edges. |
---|
57 | typedef typename CapacityMap::Value Value; |
---|
58 | |
---|
59 | /// \brief The map type that stores the flow values. |
---|
60 | /// |
---|
61 | /// The map type that stores the flow values. |
---|
62 | /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept. |
---|
63 | typedef typename Graph::template EdgeMap<Value> FlowMap; |
---|
64 | |
---|
65 | /// \brief Instantiates a FlowMap. |
---|
66 | /// |
---|
67 | /// This function instantiates a \ref FlowMap. |
---|
68 | /// \param graph The graph, to which we would like to define the flow map. |
---|
69 | static FlowMap* createFlowMap(const Graph& graph) { |
---|
70 | return new FlowMap(graph); |
---|
71 | } |
---|
72 | |
---|
73 | /// \brief The eleavator type used by GoldbergTarjan algorithm. |
---|
74 | /// |
---|
75 | /// The elevator type used by GoldbergTarjan algorithm. |
---|
76 | /// |
---|
77 | /// \sa Elevator |
---|
78 | /// \sa LinkedElevator |
---|
79 | typedef LinkedElevator<Graph, typename Graph::Node> Elevator; |
---|
80 | |
---|
81 | /// \brief Instantiates an Elevator. |
---|
82 | /// |
---|
83 | /// This function instantiates a \ref Elevator. |
---|
84 | /// \param graph The graph, to which we would like to define the elevator. |
---|
85 | /// \param max_level The maximum level of the elevator. |
---|
86 | static Elevator* createElevator(const Graph& graph, int max_level) { |
---|
87 | return new Elevator(graph, max_level); |
---|
88 | } |
---|
89 | |
---|
90 | /// \brief The tolerance used by the algorithm |
---|
91 | /// |
---|
92 | /// The tolerance used by the algorithm to handle inexact computation. |
---|
93 | typedef Tolerance<Value> Tolerance; |
---|
94 | |
---|
95 | }; |
---|
96 | |
---|
97 | /// \ingroup max_flow |
---|
98 | /// \brief Goldberg-Tarjan algorithms class. |
---|
99 | /// |
---|
100 | /// This class provides an implementation of the \e GoldbergTarjan |
---|
101 | /// \e algorithm producing a flow of maximum value in a directed |
---|
102 | /// graph. The GoldbergTarjan algorithm is a theoretical improvement |
---|
103 | /// of the Goldberg's \ref Preflow "preflow" algorithm by using the \ref |
---|
104 | /// DynamicTree "dynamic tree" data structure of Sleator and Tarjan. |
---|
105 | /// |
---|
106 | /// The original preflow algorithm with \e highest \e label |
---|
107 | /// heuristic has \f$O(n^2\sqrt{e})\f$ or with \e FIFO heuristic has |
---|
108 | /// \f$O(n^3)\f$ time complexity. The current algorithm improved |
---|
109 | /// this complexity to \f$O(nm\log(\frac{n^2}{m}))\f$. The algorithm |
---|
110 | /// builds limited size dynamic trees on the residual graph, which |
---|
111 | /// can be used to make multilevel push operations and gives a |
---|
112 | /// better bound on the number of non-saturating pushes. |
---|
113 | /// |
---|
114 | /// \param Graph The directed graph type the algorithm runs on. |
---|
115 | /// \param CapacityMap The capacity map type. |
---|
116 | /// \param _Traits Traits class to set various data types used by |
---|
117 | /// the algorithm. The default traits class is \ref |
---|
118 | /// GoldbergTarjanDefaultTraits. See \ref |
---|
119 | /// GoldbergTarjanDefaultTraits for the documentation of a |
---|
120 | /// Goldberg-Tarjan traits class. |
---|
121 | /// |
---|
122 | /// \author Tamas Hamori and Balazs Dezso |
---|
123 | #ifdef DOXYGEN |
---|
124 | template <typename _Graph, typename _CapacityMap, typename _Traits> |
---|
125 | #else |
---|
126 | template <typename _Graph, |
---|
127 | typename _CapacityMap = typename _Graph::template EdgeMap<int>, |
---|
128 | typename _Traits = |
---|
129 | GoldbergTarjanDefaultTraits<_Graph, _CapacityMap> > |
---|
130 | #endif |
---|
131 | class GoldbergTarjan { |
---|
132 | public: |
---|
133 | |
---|
134 | typedef _Traits Traits; |
---|
135 | typedef typename Traits::Graph Graph; |
---|
136 | typedef typename Traits::CapacityMap CapacityMap; |
---|
137 | typedef typename Traits::Value Value; |
---|
138 | |
---|
139 | typedef typename Traits::FlowMap FlowMap; |
---|
140 | typedef typename Traits::Elevator Elevator; |
---|
141 | typedef typename Traits::Tolerance Tolerance; |
---|
142 | |
---|
143 | protected: |
---|
144 | |
---|
145 | GRAPH_TYPEDEFS(typename Graph); |
---|
146 | |
---|
147 | typedef typename Graph::template NodeMap<Node> NodeNodeMap; |
---|
148 | typedef typename Graph::template NodeMap<int> IntNodeMap; |
---|
149 | |
---|
150 | typedef typename Graph::template NodeMap<Edge> EdgeNodeMap; |
---|
151 | typedef typename Graph::template EdgeMap<Edge> EdgeEdgeMap; |
---|
152 | |
---|
153 | typedef typename std::vector<Node> VecNode; |
---|
154 | |
---|
155 | typedef DynamicTree<Value,IntNodeMap,Tolerance> DynTree; |
---|
156 | |
---|
157 | const Graph& _graph; |
---|
158 | const CapacityMap* _capacity; |
---|
159 | int _node_num; //the number of nodes of G |
---|
160 | |
---|
161 | Node _source; |
---|
162 | Node _target; |
---|
163 | |
---|
164 | FlowMap* _flow; |
---|
165 | bool _local_flow; |
---|
166 | |
---|
167 | Elevator* _level; |
---|
168 | bool _local_level; |
---|
169 | |
---|
170 | typedef typename Graph::template NodeMap<Value> ExcessMap; |
---|
171 | ExcessMap* _excess; |
---|
172 | |
---|
173 | Tolerance _tolerance; |
---|
174 | |
---|
175 | bool _phase; |
---|
176 | |
---|
177 | // constant for treesize |
---|
178 | static const double _tree_bound = 2; |
---|
179 | int _max_tree_size; |
---|
180 | |
---|
181 | //tags for the dynamic tree |
---|
182 | DynTree *_dt; |
---|
183 | //datastructure of dyanamic tree |
---|
184 | IntNodeMap *_dt_index; |
---|
185 | //datastrucure for solution of the communication between the two class |
---|
186 | EdgeNodeMap *_dt_edges; |
---|
187 | //nodeMap for storing the outgoing edge from the node in the tree |
---|
188 | |
---|
189 | //max of the type Value |
---|
190 | const Value _max_value; |
---|
191 | |
---|
192 | public: |
---|
193 | |
---|
194 | typedef GoldbergTarjan Create; |
---|
195 | |
---|
196 | ///\name Named template parameters |
---|
197 | |
---|
198 | ///@{ |
---|
199 | |
---|
200 | template <typename _FlowMap> |
---|
201 | struct DefFlowMapTraits : public Traits { |
---|
202 | typedef _FlowMap FlowMap; |
---|
203 | static FlowMap *createFlowMap(const Graph&) { |
---|
204 | throw UninitializedParameter(); |
---|
205 | } |
---|
206 | }; |
---|
207 | |
---|
208 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
209 | /// FlowMap type |
---|
210 | /// |
---|
211 | /// \ref named-templ-param "Named parameter" for setting FlowMap |
---|
212 | /// type |
---|
213 | template <typename _FlowMap> |
---|
214 | struct DefFlowMap |
---|
215 | : public GoldbergTarjan<Graph, CapacityMap, |
---|
216 | DefFlowMapTraits<_FlowMap> > { |
---|
217 | typedef GoldbergTarjan<Graph, CapacityMap, |
---|
218 | DefFlowMapTraits<_FlowMap> > Create; |
---|
219 | }; |
---|
220 | |
---|
221 | template <typename _Elevator> |
---|
222 | struct DefElevatorTraits : public Traits { |
---|
223 | typedef _Elevator Elevator; |
---|
224 | static Elevator *createElevator(const Graph&, int) { |
---|
225 | throw UninitializedParameter(); |
---|
226 | } |
---|
227 | }; |
---|
228 | |
---|
229 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
230 | /// Elevator type |
---|
231 | /// |
---|
232 | /// \ref named-templ-param "Named parameter" for setting Elevator |
---|
233 | /// type |
---|
234 | template <typename _Elevator> |
---|
235 | struct DefElevator |
---|
236 | : public GoldbergTarjan<Graph, CapacityMap, |
---|
237 | DefElevatorTraits<_Elevator> > { |
---|
238 | typedef GoldbergTarjan<Graph, CapacityMap, |
---|
239 | DefElevatorTraits<_Elevator> > Create; |
---|
240 | }; |
---|
241 | |
---|
242 | template <typename _Elevator> |
---|
243 | struct DefStandardElevatorTraits : public Traits { |
---|
244 | typedef _Elevator Elevator; |
---|
245 | static Elevator *createElevator(const Graph& graph, int max_level) { |
---|
246 | return new Elevator(graph, max_level); |
---|
247 | } |
---|
248 | }; |
---|
249 | |
---|
250 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
251 | /// Elevator type |
---|
252 | /// |
---|
253 | /// \ref named-templ-param "Named parameter" for setting Elevator |
---|
254 | /// type. The Elevator should be standard constructor interface, ie. |
---|
255 | /// the graph and the maximum level should be passed to it. |
---|
256 | template <typename _Elevator> |
---|
257 | struct DefStandardElevator |
---|
258 | : public GoldbergTarjan<Graph, CapacityMap, |
---|
259 | DefStandardElevatorTraits<_Elevator> > { |
---|
260 | typedef GoldbergTarjan<Graph, CapacityMap, |
---|
261 | DefStandardElevatorTraits<_Elevator> > Create; |
---|
262 | }; |
---|
263 | |
---|
264 | |
---|
265 | ///\ref Exception for the case when s=t. |
---|
266 | |
---|
267 | ///\ref Exception for the case when the source equals the target. |
---|
268 | class InvalidArgument : public lemon::LogicError { |
---|
269 | public: |
---|
270 | virtual const char* what() const throw() { |
---|
271 | return "lemon::GoldbergTarjan::InvalidArgument"; |
---|
272 | } |
---|
273 | }; |
---|
274 | |
---|
275 | protected: |
---|
276 | |
---|
277 | GoldbergTarjan() {} |
---|
278 | |
---|
279 | public: |
---|
280 | |
---|
281 | /// \brief The constructor of the class. |
---|
282 | /// |
---|
283 | /// The constructor of the class. |
---|
284 | /// \param graph The directed graph the algorithm runs on. |
---|
285 | /// \param capacity The capacity of the edges. |
---|
286 | /// \param source The source node. |
---|
287 | /// \param target The target node. |
---|
288 | /// Except the graph, all of these parameters can be reset by |
---|
289 | /// calling \ref source, \ref target, \ref capacityMap and \ref |
---|
290 | /// flowMap, resp. |
---|
291 | GoldbergTarjan(const Graph& graph, const CapacityMap& capacity, |
---|
292 | Node source, Node target) |
---|
293 | : _graph(graph), _capacity(&capacity), |
---|
294 | _node_num(), _source(source), _target(target), |
---|
295 | _flow(0), _local_flow(false), |
---|
296 | _level(0), _local_level(false), |
---|
297 | _excess(0), _tolerance(), |
---|
298 | _phase(), _max_tree_size(), |
---|
299 | _dt(0), _dt_index(0), _dt_edges(0), |
---|
300 | _max_value(std::numeric_limits<Value>::max()) { |
---|
301 | if (_source == _target) throw InvalidArgument(); |
---|
302 | } |
---|
303 | |
---|
304 | /// \brief Destrcutor. |
---|
305 | /// |
---|
306 | /// Destructor. |
---|
307 | ~GoldbergTarjan() { |
---|
308 | destroyStructures(); |
---|
309 | } |
---|
310 | |
---|
311 | /// \brief Sets the capacity map. |
---|
312 | /// |
---|
313 | /// Sets the capacity map. |
---|
314 | /// \return \c (*this) |
---|
315 | GoldbergTarjan& capacityMap(const CapacityMap& map) { |
---|
316 | _capacity = ↦ |
---|
317 | return *this; |
---|
318 | } |
---|
319 | |
---|
320 | /// \brief Sets the flow map. |
---|
321 | /// |
---|
322 | /// Sets the flow map. |
---|
323 | /// \return \c (*this) |
---|
324 | GoldbergTarjan& flowMap(FlowMap& map) { |
---|
325 | if (_local_flow) { |
---|
326 | delete _flow; |
---|
327 | _local_flow = false; |
---|
328 | } |
---|
329 | _flow = ↦ |
---|
330 | return *this; |
---|
331 | } |
---|
332 | |
---|
333 | /// \brief Returns the flow map. |
---|
334 | /// |
---|
335 | /// \return The flow map. |
---|
336 | const FlowMap& flowMap() { |
---|
337 | return *_flow; |
---|
338 | } |
---|
339 | |
---|
340 | /// \brief Sets the elevator. |
---|
341 | /// |
---|
342 | /// Sets the elevator. |
---|
343 | /// \return \c (*this) |
---|
344 | GoldbergTarjan& elevator(Elevator& elevator) { |
---|
345 | if (_local_level) { |
---|
346 | delete _level; |
---|
347 | _local_level = false; |
---|
348 | } |
---|
349 | _level = &elevator; |
---|
350 | return *this; |
---|
351 | } |
---|
352 | |
---|
353 | /// \brief Returns the elevator. |
---|
354 | /// |
---|
355 | /// \return The elevator. |
---|
356 | const Elevator& elevator() { |
---|
357 | return *_level; |
---|
358 | } |
---|
359 | |
---|
360 | /// \brief Sets the source node. |
---|
361 | /// |
---|
362 | /// Sets the source node. |
---|
363 | /// \return \c (*this) |
---|
364 | GoldbergTarjan& source(const Node& node) { |
---|
365 | _source = node; |
---|
366 | return *this; |
---|
367 | } |
---|
368 | |
---|
369 | /// \brief Sets the target node. |
---|
370 | /// |
---|
371 | /// Sets the target node. |
---|
372 | /// \return \c (*this) |
---|
373 | GoldbergTarjan& target(const Node& node) { |
---|
374 | _target = node; |
---|
375 | return *this; |
---|
376 | } |
---|
377 | |
---|
378 | /// \brief Sets the tolerance used by algorithm. |
---|
379 | /// |
---|
380 | /// Sets the tolerance used by algorithm. |
---|
381 | GoldbergTarjan& tolerance(const Tolerance& tolerance) const { |
---|
382 | _tolerance = tolerance; |
---|
383 | if (_dt) { |
---|
384 | _dt->tolerance(_tolerance); |
---|
385 | } |
---|
386 | return *this; |
---|
387 | } |
---|
388 | |
---|
389 | /// \brief Returns the tolerance used by algorithm. |
---|
390 | /// |
---|
391 | /// Returns the tolerance used by algorithm. |
---|
392 | const Tolerance& tolerance() const { |
---|
393 | return tolerance; |
---|
394 | } |
---|
395 | |
---|
396 | |
---|
397 | private: |
---|
398 | |
---|
399 | void createStructures() { |
---|
400 | _node_num = countNodes(_graph); |
---|
401 | |
---|
402 | _max_tree_size = int((double(_node_num) * double(_node_num)) / |
---|
403 | double(countEdges(_graph))); |
---|
404 | |
---|
405 | if (!_flow) { |
---|
406 | _flow = Traits::createFlowMap(_graph); |
---|
407 | _local_flow = true; |
---|
408 | } |
---|
409 | if (!_level) { |
---|
410 | _level = Traits::createElevator(_graph, _node_num); |
---|
411 | _local_level = true; |
---|
412 | } |
---|
413 | if (!_excess) { |
---|
414 | _excess = new ExcessMap(_graph); |
---|
415 | } |
---|
416 | if (!_dt_index && !_dt) { |
---|
417 | _dt_index = new IntNodeMap(_graph); |
---|
418 | _dt = new DynTree(*_dt_index, _tolerance); |
---|
419 | } |
---|
420 | if (!_dt_edges) { |
---|
421 | _dt_edges = new EdgeNodeMap(_graph); |
---|
422 | } |
---|
423 | } |
---|
424 | |
---|
425 | void destroyStructures() { |
---|
426 | if (_local_flow) { |
---|
427 | delete _flow; |
---|
428 | } |
---|
429 | if (_local_level) { |
---|
430 | delete _level; |
---|
431 | } |
---|
432 | if (_excess) { |
---|
433 | delete _excess; |
---|
434 | } |
---|
435 | if (_dt) { |
---|
436 | delete _dt; |
---|
437 | } |
---|
438 | if (_dt_index) { |
---|
439 | delete _dt_index; |
---|
440 | } |
---|
441 | if (_dt_edges) { |
---|
442 | delete _dt_edges; |
---|
443 | } |
---|
444 | } |
---|
445 | |
---|
446 | bool sendOut(Node n, Value& excess) { |
---|
447 | |
---|
448 | Node w = _dt->findRoot(n); |
---|
449 | |
---|
450 | while (w != n) { |
---|
451 | |
---|
452 | Value rem; |
---|
453 | Node u = _dt->findCost(n, rem); |
---|
454 | |
---|
455 | if (_tolerance.positive(rem) && !_level->active(w) && w != _target) { |
---|
456 | _level->activate(w); |
---|
457 | } |
---|
458 | |
---|
459 | if (!_tolerance.less(rem, excess)) { |
---|
460 | _dt->addCost(n, - excess); |
---|
461 | _excess->set(w, (*_excess)[w] + excess); |
---|
462 | excess = 0; |
---|
463 | return true; |
---|
464 | } |
---|
465 | |
---|
466 | |
---|
467 | _dt->addCost(n, - rem); |
---|
468 | |
---|
469 | excess -= rem; |
---|
470 | _excess->set(w, (*_excess)[w] + rem); |
---|
471 | |
---|
472 | _dt->cut(u); |
---|
473 | _dt->addCost(u, _max_value); |
---|
474 | |
---|
475 | Edge e = (*_dt_edges)[u]; |
---|
476 | _dt_edges->set(u, INVALID); |
---|
477 | |
---|
478 | if (u == _graph.source(e)) { |
---|
479 | _flow->set(e, (*_capacity)[e]); |
---|
480 | } else { |
---|
481 | _flow->set(e, 0); |
---|
482 | } |
---|
483 | |
---|
484 | w = _dt->findRoot(n); |
---|
485 | } |
---|
486 | return false; |
---|
487 | } |
---|
488 | |
---|
489 | bool sendIn(Node n, Value& excess) { |
---|
490 | |
---|
491 | Node w = _dt->findRoot(n); |
---|
492 | |
---|
493 | while (w != n) { |
---|
494 | |
---|
495 | Value rem; |
---|
496 | Node u = _dt->findCost(n, rem); |
---|
497 | |
---|
498 | if (_tolerance.positive(rem) && !_level->active(w) && w != _source) { |
---|
499 | _level->activate(w); |
---|
500 | } |
---|
501 | |
---|
502 | if (!_tolerance.less(rem, excess)) { |
---|
503 | _dt->addCost(n, - excess); |
---|
504 | _excess->set(w, (*_excess)[w] + excess); |
---|
505 | excess = 0; |
---|
506 | return true; |
---|
507 | } |
---|
508 | |
---|
509 | |
---|
510 | _dt->addCost(n, - rem); |
---|
511 | |
---|
512 | excess -= rem; |
---|
513 | _excess->set(w, (*_excess)[w] + rem); |
---|
514 | |
---|
515 | _dt->cut(u); |
---|
516 | _dt->addCost(u, _max_value); |
---|
517 | |
---|
518 | Edge e = (*_dt_edges)[u]; |
---|
519 | _dt_edges->set(u, INVALID); |
---|
520 | |
---|
521 | if (u == _graph.source(e)) { |
---|
522 | _flow->set(e, (*_capacity)[e]); |
---|
523 | } else { |
---|
524 | _flow->set(e, 0); |
---|
525 | } |
---|
526 | |
---|
527 | w = _dt->findRoot(n); |
---|
528 | } |
---|
529 | return false; |
---|
530 | } |
---|
531 | |
---|
532 | void cutChildren(Node n) { |
---|
533 | |
---|
534 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
535 | |
---|
536 | Node v = _graph.target(e); |
---|
537 | |
---|
538 | if ((*_dt_edges)[v] != INVALID && (*_dt_edges)[v] == e) { |
---|
539 | _dt->cut(v); |
---|
540 | _dt_edges->set(v, INVALID); |
---|
541 | Value rem; |
---|
542 | _dt->findCost(v, rem); |
---|
543 | _dt->addCost(v, - rem); |
---|
544 | _dt->addCost(v, _max_value); |
---|
545 | _flow->set(e, rem); |
---|
546 | |
---|
547 | } |
---|
548 | } |
---|
549 | |
---|
550 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
551 | |
---|
552 | Node v = _graph.source(e); |
---|
553 | |
---|
554 | if ((*_dt_edges)[v] != INVALID && (*_dt_edges)[v] == e) { |
---|
555 | _dt->cut(v); |
---|
556 | _dt_edges->set(v, INVALID); |
---|
557 | Value rem; |
---|
558 | _dt->findCost(v, rem); |
---|
559 | _dt->addCost(v, - rem); |
---|
560 | _dt->addCost(v, _max_value); |
---|
561 | _flow->set(e, (*_capacity)[e] - rem); |
---|
562 | |
---|
563 | } |
---|
564 | } |
---|
565 | } |
---|
566 | |
---|
567 | void extractTrees() { |
---|
568 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
569 | |
---|
570 | Node w = _dt->findRoot(n); |
---|
571 | |
---|
572 | while (w != n) { |
---|
573 | |
---|
574 | Value rem; |
---|
575 | Node u = _dt->findCost(n, rem); |
---|
576 | |
---|
577 | _dt->cut(u); |
---|
578 | _dt->addCost(u, - rem); |
---|
579 | _dt->addCost(u, _max_value); |
---|
580 | |
---|
581 | Edge e = (*_dt_edges)[u]; |
---|
582 | _dt_edges->set(u, INVALID); |
---|
583 | |
---|
584 | if (u == _graph.source(e)) { |
---|
585 | _flow->set(e, (*_capacity)[e] - rem); |
---|
586 | } else { |
---|
587 | _flow->set(e, rem); |
---|
588 | } |
---|
589 | |
---|
590 | w = _dt->findRoot(n); |
---|
591 | } |
---|
592 | } |
---|
593 | } |
---|
594 | |
---|
595 | public: |
---|
596 | |
---|
597 | /// \name Execution control The simplest way to execute the |
---|
598 | /// algorithm is to use one of the member functions called \c |
---|
599 | /// run(). |
---|
600 | /// \n |
---|
601 | /// If you need more control on initial solution or |
---|
602 | /// execution then you have to call one \ref init() function and then |
---|
603 | /// the startFirstPhase() and if you need the startSecondPhase(). |
---|
604 | |
---|
605 | ///@{ |
---|
606 | |
---|
607 | /// \brief Initializes the internal data structures. |
---|
608 | /// |
---|
609 | /// Initializes the internal data structures. |
---|
610 | /// |
---|
611 | void init() { |
---|
612 | createStructures(); |
---|
613 | |
---|
614 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
615 | _excess->set(n, 0); |
---|
616 | } |
---|
617 | |
---|
618 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
619 | _flow->set(e, 0); |
---|
620 | } |
---|
621 | |
---|
622 | _dt->clear(); |
---|
623 | for (NodeIt v(_graph); v != INVALID; ++v) { |
---|
624 | (*_dt_edges)[v] = INVALID; |
---|
625 | _dt->makeTree(v); |
---|
626 | _dt->addCost(v, _max_value); |
---|
627 | } |
---|
628 | |
---|
629 | typename Graph::template NodeMap<bool> reached(_graph, false); |
---|
630 | |
---|
631 | _level->initStart(); |
---|
632 | _level->initAddItem(_target); |
---|
633 | |
---|
634 | std::vector<Node> queue; |
---|
635 | reached.set(_source, true); |
---|
636 | |
---|
637 | queue.push_back(_target); |
---|
638 | reached.set(_target, true); |
---|
639 | while (!queue.empty()) { |
---|
640 | _level->initNewLevel(); |
---|
641 | std::vector<Node> nqueue; |
---|
642 | for (int i = 0; i < int(queue.size()); ++i) { |
---|
643 | Node n = queue[i]; |
---|
644 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
645 | Node u = _graph.source(e); |
---|
646 | if (!reached[u] && _tolerance.positive((*_capacity)[e])) { |
---|
647 | reached.set(u, true); |
---|
648 | _level->initAddItem(u); |
---|
649 | nqueue.push_back(u); |
---|
650 | } |
---|
651 | } |
---|
652 | } |
---|
653 | queue.swap(nqueue); |
---|
654 | } |
---|
655 | _level->initFinish(); |
---|
656 | |
---|
657 | for (OutEdgeIt e(_graph, _source); e != INVALID; ++e) { |
---|
658 | if (_tolerance.positive((*_capacity)[e])) { |
---|
659 | Node u = _graph.target(e); |
---|
660 | if ((*_level)[u] == _level->maxLevel()) continue; |
---|
661 | _flow->set(e, (*_capacity)[e]); |
---|
662 | _excess->set(u, (*_excess)[u] + (*_capacity)[e]); |
---|
663 | if (u != _target && !_level->active(u)) { |
---|
664 | _level->activate(u); |
---|
665 | } |
---|
666 | } |
---|
667 | } |
---|
668 | } |
---|
669 | |
---|
670 | /// \brief Starts the first phase of the preflow algorithm. |
---|
671 | /// |
---|
672 | /// The preflow algorithm consists of two phases, this method runs |
---|
673 | /// the first phase. After the first phase the maximum flow value |
---|
674 | /// and a minimum value cut can already be computed, although a |
---|
675 | /// maximum flow is not yet obtained. So after calling this method |
---|
676 | /// \ref flowValue() returns the value of a maximum flow and \ref |
---|
677 | /// minCut() returns a minimum cut. |
---|
678 | /// \pre One of the \ref init() functions should be called. |
---|
679 | void startFirstPhase() { |
---|
680 | _phase = true; |
---|
681 | Node n; |
---|
682 | |
---|
683 | while ((n = _level->highestActive()) != INVALID) { |
---|
684 | Value excess = (*_excess)[n]; |
---|
685 | int level = _level->highestActiveLevel(); |
---|
686 | int new_level = _level->maxLevel(); |
---|
687 | |
---|
688 | if (_dt->findRoot(n) != n) { |
---|
689 | if (sendOut(n, excess)) goto no_more_push; |
---|
690 | } |
---|
691 | |
---|
692 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
693 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
694 | Node v = _graph.target(e); |
---|
695 | |
---|
696 | if (!_tolerance.positive(rem) && (*_dt_edges)[v] != e) continue; |
---|
697 | |
---|
698 | if ((*_level)[v] < level) { |
---|
699 | |
---|
700 | if (_dt->findSize(n) + _dt->findSize(v) < |
---|
701 | _tree_bound * _max_tree_size) { |
---|
702 | _dt->addCost(n, -_max_value); |
---|
703 | _dt->addCost(n, rem); |
---|
704 | _dt->link(n, v); |
---|
705 | _dt_edges->set(n, e); |
---|
706 | if (sendOut(n, excess)) goto no_more_push; |
---|
707 | } else { |
---|
708 | if (!_level->active(v) && v != _target) { |
---|
709 | _level->activate(v); |
---|
710 | } |
---|
711 | if (!_tolerance.less(rem, excess)) { |
---|
712 | _flow->set(e, (*_flow)[e] + excess); |
---|
713 | _excess->set(v, (*_excess)[v] + excess); |
---|
714 | excess = 0; |
---|
715 | goto no_more_push; |
---|
716 | } else { |
---|
717 | excess -= rem; |
---|
718 | _excess->set(v, (*_excess)[v] + rem); |
---|
719 | _flow->set(e, (*_capacity)[e]); |
---|
720 | } |
---|
721 | } |
---|
722 | } else if (new_level > (*_level)[v]) { |
---|
723 | new_level = (*_level)[v]; |
---|
724 | } |
---|
725 | } |
---|
726 | |
---|
727 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
728 | Value rem = (*_flow)[e]; |
---|
729 | Node v = _graph.source(e); |
---|
730 | if (!_tolerance.positive(rem) && (*_dt_edges)[v] != e) continue; |
---|
731 | |
---|
732 | if ((*_level)[v] < level) { |
---|
733 | |
---|
734 | if (_dt->findSize(n) + _dt->findSize(v) < |
---|
735 | _tree_bound * _max_tree_size) { |
---|
736 | _dt->addCost(n, - _max_value); |
---|
737 | _dt->addCost(n, rem); |
---|
738 | _dt->link(n, v); |
---|
739 | _dt_edges->set(n, e); |
---|
740 | if (sendOut(n, excess)) goto no_more_push; |
---|
741 | } else { |
---|
742 | if (!_level->active(v) && v != _target) { |
---|
743 | _level->activate(v); |
---|
744 | } |
---|
745 | if (!_tolerance.less(rem, excess)) { |
---|
746 | _flow->set(e, (*_flow)[e] - excess); |
---|
747 | _excess->set(v, (*_excess)[v] + excess); |
---|
748 | excess = 0; |
---|
749 | goto no_more_push; |
---|
750 | } else { |
---|
751 | excess -= rem; |
---|
752 | _excess->set(v, (*_excess)[v] + rem); |
---|
753 | _flow->set(e, 0); |
---|
754 | } |
---|
755 | } |
---|
756 | } else if (new_level > (*_level)[v]) { |
---|
757 | new_level = (*_level)[v]; |
---|
758 | } |
---|
759 | } |
---|
760 | |
---|
761 | no_more_push: |
---|
762 | |
---|
763 | _excess->set(n, excess); |
---|
764 | |
---|
765 | if (excess != 0) { |
---|
766 | cutChildren(n); |
---|
767 | if (new_level + 1 < _level->maxLevel()) { |
---|
768 | _level->liftHighestActive(new_level + 1); |
---|
769 | } else { |
---|
770 | _level->liftHighestActiveToTop(); |
---|
771 | } |
---|
772 | if (_level->emptyLevel(level)) { |
---|
773 | _level->liftToTop(level); |
---|
774 | } |
---|
775 | } else { |
---|
776 | _level->deactivate(n); |
---|
777 | } |
---|
778 | } |
---|
779 | extractTrees(); |
---|
780 | } |
---|
781 | |
---|
782 | /// \brief Starts the second phase of the preflow algorithm. |
---|
783 | /// |
---|
784 | /// The preflow algorithm consists of two phases, this method runs |
---|
785 | /// the second phase. After calling \ref init() and \ref |
---|
786 | /// startFirstPhase() and then \ref startSecondPhase(), \ref |
---|
787 | /// flowMap() return a maximum flow, \ref flowValue() returns the |
---|
788 | /// value of a maximum flow, \ref minCut() returns a minimum cut |
---|
789 | /// \pre The \ref init() and startFirstPhase() functions should be |
---|
790 | /// called before. |
---|
791 | void startSecondPhase() { |
---|
792 | _phase = false; |
---|
793 | |
---|
794 | typename Graph::template NodeMap<bool> reached(_graph, false); |
---|
795 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
796 | reached.set(n, (*_level)[n] < _level->maxLevel()); |
---|
797 | } |
---|
798 | |
---|
799 | _level->initStart(); |
---|
800 | _level->initAddItem(_source); |
---|
801 | |
---|
802 | std::vector<Node> queue; |
---|
803 | queue.push_back(_source); |
---|
804 | reached.set(_source, true); |
---|
805 | |
---|
806 | while (!queue.empty()) { |
---|
807 | _level->initNewLevel(); |
---|
808 | std::vector<Node> nqueue; |
---|
809 | for (int i = 0; i < int(queue.size()); ++i) { |
---|
810 | Node n = queue[i]; |
---|
811 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
812 | Node v = _graph.target(e); |
---|
813 | if (!reached[v] && _tolerance.positive((*_flow)[e])) { |
---|
814 | reached.set(v, true); |
---|
815 | _level->initAddItem(v); |
---|
816 | nqueue.push_back(v); |
---|
817 | } |
---|
818 | } |
---|
819 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
820 | Node u = _graph.source(e); |
---|
821 | if (!reached[u] && |
---|
822 | _tolerance.positive((*_capacity)[e] - (*_flow)[e])) { |
---|
823 | reached.set(u, true); |
---|
824 | _level->initAddItem(u); |
---|
825 | nqueue.push_back(u); |
---|
826 | } |
---|
827 | } |
---|
828 | } |
---|
829 | queue.swap(nqueue); |
---|
830 | } |
---|
831 | _level->initFinish(); |
---|
832 | |
---|
833 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
834 | if (!reached[n]) { |
---|
835 | _level->markToBottom(n); |
---|
836 | } else if ((*_excess)[n] > 0 && _target != n) { |
---|
837 | _level->activate(n); |
---|
838 | } |
---|
839 | } |
---|
840 | |
---|
841 | Node n; |
---|
842 | |
---|
843 | while ((n = _level->highestActive()) != INVALID) { |
---|
844 | Value excess = (*_excess)[n]; |
---|
845 | int level = _level->highestActiveLevel(); |
---|
846 | int new_level = _level->maxLevel(); |
---|
847 | |
---|
848 | if (_dt->findRoot(n) != n) { |
---|
849 | if (sendIn(n, excess)) goto no_more_push; |
---|
850 | } |
---|
851 | |
---|
852 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
853 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
854 | Node v = _graph.target(e); |
---|
855 | |
---|
856 | if (!_tolerance.positive(rem) && (*_dt_edges)[v] != e) continue; |
---|
857 | |
---|
858 | if ((*_level)[v] < level) { |
---|
859 | |
---|
860 | if (_dt->findSize(n) + _dt->findSize(v) < |
---|
861 | _tree_bound * _max_tree_size) { |
---|
862 | _dt->addCost(n, -_max_value); |
---|
863 | _dt->addCost(n, rem); |
---|
864 | _dt->link(n, v); |
---|
865 | _dt_edges->set(n, e); |
---|
866 | if (sendIn(n, excess)) goto no_more_push; |
---|
867 | } else { |
---|
868 | if (!_level->active(v) && v != _source) { |
---|
869 | _level->activate(v); |
---|
870 | } |
---|
871 | if (!_tolerance.less(rem, excess)) { |
---|
872 | _flow->set(e, (*_flow)[e] + excess); |
---|
873 | _excess->set(v, (*_excess)[v] + excess); |
---|
874 | excess = 0; |
---|
875 | goto no_more_push; |
---|
876 | } else { |
---|
877 | excess -= rem; |
---|
878 | _excess->set(v, (*_excess)[v] + rem); |
---|
879 | _flow->set(e, (*_capacity)[e]); |
---|
880 | } |
---|
881 | } |
---|
882 | } else if (new_level > (*_level)[v]) { |
---|
883 | new_level = (*_level)[v]; |
---|
884 | } |
---|
885 | } |
---|
886 | |
---|
887 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
888 | Value rem = (*_flow)[e]; |
---|
889 | Node v = _graph.source(e); |
---|
890 | if (!_tolerance.positive(rem) && (*_dt_edges)[v] != e) continue; |
---|
891 | |
---|
892 | if ((*_level)[v] < level) { |
---|
893 | |
---|
894 | if (_dt->findSize(n) + _dt->findSize(v) < |
---|
895 | _tree_bound * _max_tree_size) { |
---|
896 | _dt->addCost(n, - _max_value); |
---|
897 | _dt->addCost(n, rem); |
---|
898 | _dt->link(n, v); |
---|
899 | _dt_edges->set(n, e); |
---|
900 | if (sendIn(n, excess)) goto no_more_push; |
---|
901 | } else { |
---|
902 | if (!_level->active(v) && v != _source) { |
---|
903 | _level->activate(v); |
---|
904 | } |
---|
905 | if (!_tolerance.less(rem, excess)) { |
---|
906 | _flow->set(e, (*_flow)[e] - excess); |
---|
907 | _excess->set(v, (*_excess)[v] + excess); |
---|
908 | excess = 0; |
---|
909 | goto no_more_push; |
---|
910 | } else { |
---|
911 | excess -= rem; |
---|
912 | _excess->set(v, (*_excess)[v] + rem); |
---|
913 | _flow->set(e, 0); |
---|
914 | } |
---|
915 | } |
---|
916 | } else if (new_level > (*_level)[v]) { |
---|
917 | new_level = (*_level)[v]; |
---|
918 | } |
---|
919 | } |
---|
920 | |
---|
921 | no_more_push: |
---|
922 | |
---|
923 | _excess->set(n, excess); |
---|
924 | |
---|
925 | if (excess != 0) { |
---|
926 | cutChildren(n); |
---|
927 | if (new_level + 1 < _level->maxLevel()) { |
---|
928 | _level->liftHighestActive(new_level + 1); |
---|
929 | } else { |
---|
930 | _level->liftHighestActiveToTop(); |
---|
931 | } |
---|
932 | if (_level->emptyLevel(level)) { |
---|
933 | _level->liftToTop(level); |
---|
934 | } |
---|
935 | } else { |
---|
936 | _level->deactivate(n); |
---|
937 | } |
---|
938 | } |
---|
939 | extractTrees(); |
---|
940 | } |
---|
941 | |
---|
942 | /// \brief Runs the Goldberg-Tarjan algorithm. |
---|
943 | /// |
---|
944 | /// Runs the Goldberg-Tarjan algorithm. |
---|
945 | /// \note pf.run() is just a shortcut of the following code. |
---|
946 | /// \code |
---|
947 | /// pf.init(); |
---|
948 | /// pf.startFirstPhase(); |
---|
949 | /// pf.startSecondPhase(); |
---|
950 | /// \endcode |
---|
951 | void run() { |
---|
952 | init(); |
---|
953 | startFirstPhase(); |
---|
954 | startSecondPhase(); |
---|
955 | } |
---|
956 | |
---|
957 | /// \brief Runs the Goldberg-Tarjan algorithm to compute the minimum cut. |
---|
958 | /// |
---|
959 | /// Runs the Goldberg-Tarjan algorithm to compute the minimum cut. |
---|
960 | /// \note pf.runMinCut() is just a shortcut of the following code. |
---|
961 | /// \code |
---|
962 | /// pf.init(); |
---|
963 | /// pf.startFirstPhase(); |
---|
964 | /// \endcode |
---|
965 | void runMinCut() { |
---|
966 | init(); |
---|
967 | startFirstPhase(); |
---|
968 | } |
---|
969 | |
---|
970 | /// @} |
---|
971 | |
---|
972 | /// \name Query Functions |
---|
973 | /// The result of the Goldberg-Tarjan algorithm can be obtained |
---|
974 | /// using these functions. |
---|
975 | /// \n |
---|
976 | /// Before the use of these functions, either run() or start() must |
---|
977 | /// be called. |
---|
978 | |
---|
979 | ///@{ |
---|
980 | |
---|
981 | /// \brief Returns the value of the maximum flow. |
---|
982 | /// |
---|
983 | /// Returns the value of the maximum flow by returning the excess |
---|
984 | /// of the target node \c t. This value equals to the value of |
---|
985 | /// the maximum flow already after the first phase. |
---|
986 | Value flowValue() const { |
---|
987 | return (*_excess)[_target]; |
---|
988 | } |
---|
989 | |
---|
990 | /// \brief Returns true when the node is on the source side of minimum cut. |
---|
991 | /// |
---|
992 | /// Returns true when the node is on the source side of minimum |
---|
993 | /// cut. This method can be called both after running \ref |
---|
994 | /// startFirstPhase() and \ref startSecondPhase(). |
---|
995 | bool minCut(const Node& node) const { |
---|
996 | return ((*_level)[node] == _level->maxLevel()) == _phase; |
---|
997 | } |
---|
998 | |
---|
999 | /// \brief Returns a minimum value cut. |
---|
1000 | /// |
---|
1001 | /// Sets the \c cutMap to the characteristic vector of a minimum value |
---|
1002 | /// cut. This method can be called both after running \ref |
---|
1003 | /// startFirstPhase() and \ref startSecondPhase(). The result after second |
---|
1004 | /// phase could be changed slightly if inexact computation is used. |
---|
1005 | /// \pre The \c cutMap should be a bool-valued node-map. |
---|
1006 | template <typename CutMap> |
---|
1007 | void minCutMap(CutMap& cutMap) const { |
---|
1008 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
1009 | cutMap.set(n, minCut(n)); |
---|
1010 | } |
---|
1011 | } |
---|
1012 | |
---|
1013 | /// \brief Returns the flow on the edge. |
---|
1014 | /// |
---|
1015 | /// Sets the \c flowMap to the flow on the edges. This method can |
---|
1016 | /// be called after the second phase of algorithm. |
---|
1017 | Value flow(const Edge& edge) const { |
---|
1018 | return (*_flow)[edge]; |
---|
1019 | } |
---|
1020 | |
---|
1021 | /// @} |
---|
1022 | |
---|
1023 | }; |
---|
1024 | |
---|
1025 | } //namespace lemon |
---|
1026 | |
---|
1027 | #endif |
---|