1 | /* -*- C++ -*- |
---|
2 | * |
---|
3 | * This file is a part of LEMON, a generic C++ optimization library |
---|
4 | * |
---|
5 | * Copyright (C) 2003-2008 |
---|
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_EDMONDS_KARP_H |
---|
20 | #define LEMON_EDMONDS_KARP_H |
---|
21 | |
---|
22 | /// \file |
---|
23 | /// \ingroup max_flow |
---|
24 | /// \brief Implementation of the Edmonds-Karp algorithm. |
---|
25 | |
---|
26 | #include <lemon/tolerance.h> |
---|
27 | #include <vector> |
---|
28 | |
---|
29 | namespace lemon { |
---|
30 | |
---|
31 | /// \brief Default traits class of EdmondsKarp class. |
---|
32 | /// |
---|
33 | /// Default traits class of EdmondsKarp class. |
---|
34 | /// \param _Graph Graph type. |
---|
35 | /// \param _CapacityMap Type of capacity map. |
---|
36 | template <typename _Graph, typename _CapacityMap> |
---|
37 | struct EdmondsKarpDefaultTraits { |
---|
38 | |
---|
39 | /// \brief The graph type the algorithm runs on. |
---|
40 | typedef _Graph Graph; |
---|
41 | |
---|
42 | /// \brief The type of the map that stores the edge capacities. |
---|
43 | /// |
---|
44 | /// The type of the map that stores the edge capacities. |
---|
45 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
---|
46 | typedef _CapacityMap CapacityMap; |
---|
47 | |
---|
48 | /// \brief The type of the length of the edges. |
---|
49 | typedef typename CapacityMap::Value Value; |
---|
50 | |
---|
51 | /// \brief The map type that stores the flow values. |
---|
52 | /// |
---|
53 | /// The map type that stores the flow values. |
---|
54 | /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept. |
---|
55 | typedef typename Graph::template EdgeMap<Value> FlowMap; |
---|
56 | |
---|
57 | /// \brief Instantiates a FlowMap. |
---|
58 | /// |
---|
59 | /// This function instantiates a \ref FlowMap. |
---|
60 | /// \param graph The graph, to which we would like to define the flow map. |
---|
61 | static FlowMap* createFlowMap(const Graph& graph) { |
---|
62 | return new FlowMap(graph); |
---|
63 | } |
---|
64 | |
---|
65 | /// \brief The tolerance used by the algorithm |
---|
66 | /// |
---|
67 | /// The tolerance used by the algorithm to handle inexact computation. |
---|
68 | typedef Tolerance<Value> Tolerance; |
---|
69 | |
---|
70 | }; |
---|
71 | |
---|
72 | /// \ingroup max_flow |
---|
73 | /// |
---|
74 | /// \brief Edmonds-Karp algorithms class. |
---|
75 | /// |
---|
76 | /// This class provides an implementation of the \e Edmonds-Karp \e |
---|
77 | /// algorithm producing a flow of maximum value in a directed |
---|
78 | /// graphs. The Edmonds-Karp algorithm is slower than the Preflow |
---|
79 | /// algorithm but it has an advantage of the step-by-step execution |
---|
80 | /// control with feasible flow solutions. The \e source node, the \e |
---|
81 | /// target node, the \e capacity of the edges and the \e starting \e |
---|
82 | /// flow value of the edges should be passed to the algorithm |
---|
83 | /// through the constructor. |
---|
84 | /// |
---|
85 | /// The time complexity of the algorithm is \f$ O(nm^2) \f$ in |
---|
86 | /// worst case. Always try the preflow algorithm instead of this if |
---|
87 | /// you just want to compute the optimal flow. |
---|
88 | /// |
---|
89 | /// \param _Graph The directed graph type the algorithm runs on. |
---|
90 | /// \param _CapacityMap The capacity map type. |
---|
91 | /// \param _Traits Traits class to set various data types used by |
---|
92 | /// the algorithm. The default traits class is \ref |
---|
93 | /// EdmondsKarpDefaultTraits. See \ref EdmondsKarpDefaultTraits for the |
---|
94 | /// documentation of a Edmonds-Karp traits class. |
---|
95 | /// |
---|
96 | /// \author Balazs Dezso |
---|
97 | #ifdef DOXYGEN |
---|
98 | template <typename _Graph, typename _CapacityMap, typename _Traits> |
---|
99 | #else |
---|
100 | template <typename _Graph, |
---|
101 | typename _CapacityMap = typename _Graph::template EdgeMap<int>, |
---|
102 | typename _Traits = EdmondsKarpDefaultTraits<_Graph, _CapacityMap> > |
---|
103 | #endif |
---|
104 | class EdmondsKarp { |
---|
105 | public: |
---|
106 | |
---|
107 | typedef _Traits Traits; |
---|
108 | typedef typename Traits::Graph Graph; |
---|
109 | typedef typename Traits::CapacityMap CapacityMap; |
---|
110 | typedef typename Traits::Value Value; |
---|
111 | |
---|
112 | typedef typename Traits::FlowMap FlowMap; |
---|
113 | typedef typename Traits::Tolerance Tolerance; |
---|
114 | |
---|
115 | /// \brief \ref Exception for the case when the source equals the target. |
---|
116 | /// |
---|
117 | /// \ref Exception for the case when the source equals the target. |
---|
118 | /// |
---|
119 | class InvalidArgument : public lemon::LogicError { |
---|
120 | public: |
---|
121 | virtual const char* what() const throw() { |
---|
122 | return "lemon::EdmondsKarp::InvalidArgument"; |
---|
123 | } |
---|
124 | }; |
---|
125 | |
---|
126 | |
---|
127 | private: |
---|
128 | |
---|
129 | GRAPH_TYPEDEFS(typename Graph); |
---|
130 | typedef typename Graph::template NodeMap<Edge> PredMap; |
---|
131 | |
---|
132 | const Graph& _graph; |
---|
133 | const CapacityMap* _capacity; |
---|
134 | |
---|
135 | Node _source, _target; |
---|
136 | |
---|
137 | FlowMap* _flow; |
---|
138 | bool _local_flow; |
---|
139 | |
---|
140 | PredMap* _pred; |
---|
141 | std::vector<Node> _queue; |
---|
142 | |
---|
143 | Tolerance _tolerance; |
---|
144 | Value _flow_value; |
---|
145 | |
---|
146 | void createStructures() { |
---|
147 | if (!_flow) { |
---|
148 | _flow = Traits::createFlowMap(_graph); |
---|
149 | _local_flow = true; |
---|
150 | } |
---|
151 | if (!_pred) { |
---|
152 | _pred = new PredMap(_graph); |
---|
153 | } |
---|
154 | _queue.resize(countNodes(_graph)); |
---|
155 | } |
---|
156 | |
---|
157 | void destroyStructures() { |
---|
158 | if (_local_flow) { |
---|
159 | delete _flow; |
---|
160 | } |
---|
161 | if (_pred) { |
---|
162 | delete _pred; |
---|
163 | } |
---|
164 | } |
---|
165 | |
---|
166 | public: |
---|
167 | |
---|
168 | ///\name Named template parameters |
---|
169 | |
---|
170 | ///@{ |
---|
171 | |
---|
172 | template <typename _FlowMap> |
---|
173 | struct DefFlowMapTraits : public Traits { |
---|
174 | typedef _FlowMap FlowMap; |
---|
175 | static FlowMap *createFlowMap(const Graph&) { |
---|
176 | throw UninitializedParameter(); |
---|
177 | } |
---|
178 | }; |
---|
179 | |
---|
180 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
181 | /// FlowMap type |
---|
182 | /// |
---|
183 | /// \ref named-templ-param "Named parameter" for setting FlowMap |
---|
184 | /// type |
---|
185 | template <typename _FlowMap> |
---|
186 | struct DefFlowMap |
---|
187 | : public EdmondsKarp<Graph, CapacityMap, DefFlowMapTraits<_FlowMap> > { |
---|
188 | typedef EdmondsKarp<Graph, CapacityMap, DefFlowMapTraits<_FlowMap> > |
---|
189 | Create; |
---|
190 | }; |
---|
191 | |
---|
192 | |
---|
193 | /// @} |
---|
194 | |
---|
195 | protected: |
---|
196 | |
---|
197 | EdmondsKarp() {} |
---|
198 | |
---|
199 | public: |
---|
200 | |
---|
201 | /// \brief The constructor of the class. |
---|
202 | /// |
---|
203 | /// The constructor of the class. |
---|
204 | /// \param graph The directed graph the algorithm runs on. |
---|
205 | /// \param capacity The capacity of the edges. |
---|
206 | /// \param source The source node. |
---|
207 | /// \param target The target node. |
---|
208 | EdmondsKarp(const Graph& graph, const CapacityMap& capacity, |
---|
209 | Node source, Node target) |
---|
210 | : _graph(graph), _capacity(&capacity), _source(source), _target(target), |
---|
211 | _flow(0), _local_flow(false), _pred(0), _tolerance(), _flow_value() |
---|
212 | { |
---|
213 | if (_source == _target) { |
---|
214 | throw InvalidArgument(); |
---|
215 | } |
---|
216 | } |
---|
217 | |
---|
218 | /// \brief Destrcutor. |
---|
219 | /// |
---|
220 | /// Destructor. |
---|
221 | ~EdmondsKarp() { |
---|
222 | destroyStructures(); |
---|
223 | } |
---|
224 | |
---|
225 | /// \brief Sets the capacity map. |
---|
226 | /// |
---|
227 | /// Sets the capacity map. |
---|
228 | /// \return \c (*this) |
---|
229 | EdmondsKarp& capacityMap(const CapacityMap& map) { |
---|
230 | _capacity = ↦ |
---|
231 | return *this; |
---|
232 | } |
---|
233 | |
---|
234 | /// \brief Sets the flow map. |
---|
235 | /// |
---|
236 | /// Sets the flow map. |
---|
237 | /// \return \c (*this) |
---|
238 | EdmondsKarp& flowMap(FlowMap& map) { |
---|
239 | if (_local_flow) { |
---|
240 | delete _flow; |
---|
241 | _local_flow = false; |
---|
242 | } |
---|
243 | _flow = ↦ |
---|
244 | return *this; |
---|
245 | } |
---|
246 | |
---|
247 | /// \brief Returns the flow map. |
---|
248 | /// |
---|
249 | /// \return The flow map. |
---|
250 | const FlowMap& flowMap() { |
---|
251 | return *_flow; |
---|
252 | } |
---|
253 | |
---|
254 | /// \brief Sets the source node. |
---|
255 | /// |
---|
256 | /// Sets the source node. |
---|
257 | /// \return \c (*this) |
---|
258 | EdmondsKarp& source(const Node& node) { |
---|
259 | _source = node; |
---|
260 | return *this; |
---|
261 | } |
---|
262 | |
---|
263 | /// \brief Sets the target node. |
---|
264 | /// |
---|
265 | /// Sets the target node. |
---|
266 | /// \return \c (*this) |
---|
267 | EdmondsKarp& target(const Node& node) { |
---|
268 | _target = node; |
---|
269 | return *this; |
---|
270 | } |
---|
271 | |
---|
272 | /// \brief Sets the tolerance used by algorithm. |
---|
273 | /// |
---|
274 | /// Sets the tolerance used by algorithm. |
---|
275 | EdmondsKarp& tolerance(const Tolerance& tolerance) const { |
---|
276 | _tolerance = tolerance; |
---|
277 | return *this; |
---|
278 | } |
---|
279 | |
---|
280 | /// \brief Returns the tolerance used by algorithm. |
---|
281 | /// |
---|
282 | /// Returns the tolerance used by algorithm. |
---|
283 | const Tolerance& tolerance() const { |
---|
284 | return tolerance; |
---|
285 | } |
---|
286 | |
---|
287 | /// \name Execution control The simplest way to execute the |
---|
288 | /// algorithm is to use the \c run() member functions. |
---|
289 | /// \n |
---|
290 | /// If you need more control on initial solution or |
---|
291 | /// execution then you have to call one \ref init() function and then |
---|
292 | /// the start() or multiple times the \c augment() member function. |
---|
293 | |
---|
294 | ///@{ |
---|
295 | |
---|
296 | /// \brief Initializes the algorithm |
---|
297 | /// |
---|
298 | /// It sets the flow to empty flow. |
---|
299 | void init() { |
---|
300 | createStructures(); |
---|
301 | for (EdgeIt it(_graph); it != INVALID; ++it) { |
---|
302 | _flow->set(it, 0); |
---|
303 | } |
---|
304 | _flow_value = 0; |
---|
305 | } |
---|
306 | |
---|
307 | /// \brief Initializes the algorithm |
---|
308 | /// |
---|
309 | /// Initializes the flow to the \c flowMap. The \c flowMap should |
---|
310 | /// contain a feasible flow, ie. in each node excluding the source |
---|
311 | /// and the target the incoming flow should be equal to the |
---|
312 | /// outgoing flow. |
---|
313 | template <typename FlowMap> |
---|
314 | void flowInit(const FlowMap& flowMap) { |
---|
315 | createStructures(); |
---|
316 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
317 | _flow->set(e, flowMap[e]); |
---|
318 | } |
---|
319 | _flow_value = 0; |
---|
320 | for (OutEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
---|
321 | _flow_value += (*_flow)[jt]; |
---|
322 | } |
---|
323 | for (InEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
---|
324 | _flow_value -= (*_flow)[jt]; |
---|
325 | } |
---|
326 | } |
---|
327 | |
---|
328 | /// \brief Initializes the algorithm |
---|
329 | /// |
---|
330 | /// Initializes the flow to the \c flowMap. The \c flowMap should |
---|
331 | /// contain a feasible flow, ie. in each node excluding the source |
---|
332 | /// and the target the incoming flow should be equal to the |
---|
333 | /// outgoing flow. |
---|
334 | /// \return %False when the given flowMap does not contain |
---|
335 | /// feasible flow. |
---|
336 | template <typename FlowMap> |
---|
337 | bool checkedFlowInit(const FlowMap& flowMap) { |
---|
338 | createStructures(); |
---|
339 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
340 | _flow->set(e, flowMap[e]); |
---|
341 | } |
---|
342 | for (NodeIt it(_graph); it != INVALID; ++it) { |
---|
343 | if (it == _source || it == _target) continue; |
---|
344 | Value outFlow = 0; |
---|
345 | for (OutEdgeIt jt(_graph, it); jt != INVALID; ++jt) { |
---|
346 | outFlow += (*_flow)[jt]; |
---|
347 | } |
---|
348 | Value inFlow = 0; |
---|
349 | for (InEdgeIt jt(_graph, it); jt != INVALID; ++jt) { |
---|
350 | inFlow += (*_flow)[jt]; |
---|
351 | } |
---|
352 | if (_tolerance.different(outFlow, inFlow)) { |
---|
353 | return false; |
---|
354 | } |
---|
355 | } |
---|
356 | for (EdgeIt it(_graph); it != INVALID; ++it) { |
---|
357 | if (_tolerance.less((*_flow)[it], 0)) return false; |
---|
358 | if (_tolerance.less((*_capacity)[it], (*_flow)[it])) return false; |
---|
359 | } |
---|
360 | _flow_value = 0; |
---|
361 | for (OutEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
---|
362 | _flow_value += (*_flow)[jt]; |
---|
363 | } |
---|
364 | for (InEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
---|
365 | _flow_value -= (*_flow)[jt]; |
---|
366 | } |
---|
367 | return true; |
---|
368 | } |
---|
369 | |
---|
370 | /// \brief Augment the solution on an edge shortest path. |
---|
371 | /// |
---|
372 | /// Augment the solution on an edge shortest path. It search an |
---|
373 | /// edge shortest path between the source and the target |
---|
374 | /// in the residual graph with the bfs algoritm. |
---|
375 | /// Then it increase the flow on this path with the minimal residual |
---|
376 | /// capacity on the path. If there is not such path it gives back |
---|
377 | /// false. |
---|
378 | /// \return %False when the augmenting is not success so the |
---|
379 | /// current flow is a feasible and optimal solution. |
---|
380 | bool augment() { |
---|
381 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
382 | _pred->set(n, INVALID); |
---|
383 | } |
---|
384 | |
---|
385 | int first = 0, last = 1; |
---|
386 | |
---|
387 | _queue[0] = _source; |
---|
388 | _pred->set(_source, OutEdgeIt(_graph, _source)); |
---|
389 | |
---|
390 | while (first != last && (*_pred)[_target] == INVALID) { |
---|
391 | Node n = _queue[first++]; |
---|
392 | |
---|
393 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
394 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
395 | Node t = _graph.target(e); |
---|
396 | if (_tolerance.positive(rem) && (*_pred)[t] == INVALID) { |
---|
397 | _pred->set(t, e); |
---|
398 | _queue[last++] = t; |
---|
399 | } |
---|
400 | } |
---|
401 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
402 | Value rem = (*_flow)[e]; |
---|
403 | Node t = _graph.source(e); |
---|
404 | if (_tolerance.positive(rem) && (*_pred)[t] == INVALID) { |
---|
405 | _pred->set(t, e); |
---|
406 | _queue[last++] = t; |
---|
407 | } |
---|
408 | } |
---|
409 | } |
---|
410 | |
---|
411 | if ((*_pred)[_target] != INVALID) { |
---|
412 | Node n = _target; |
---|
413 | Edge e = (*_pred)[n]; |
---|
414 | |
---|
415 | Value prem = (*_capacity)[e] - (*_flow)[e]; |
---|
416 | n = _graph.source(e); |
---|
417 | while (n != _source) { |
---|
418 | e = (*_pred)[n]; |
---|
419 | if (_graph.target(e) == n) { |
---|
420 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
421 | if (rem < prem) prem = rem; |
---|
422 | n = _graph.source(e); |
---|
423 | } else { |
---|
424 | Value rem = (*_flow)[e]; |
---|
425 | if (rem < prem) prem = rem; |
---|
426 | n = _graph.target(e); |
---|
427 | } |
---|
428 | } |
---|
429 | |
---|
430 | n = _target; |
---|
431 | e = (*_pred)[n]; |
---|
432 | |
---|
433 | _flow->set(e, (*_flow)[e] + prem); |
---|
434 | n = _graph.source(e); |
---|
435 | while (n != _source) { |
---|
436 | e = (*_pred)[n]; |
---|
437 | if (_graph.target(e) == n) { |
---|
438 | _flow->set(e, (*_flow)[e] + prem); |
---|
439 | n = _graph.source(e); |
---|
440 | } else { |
---|
441 | _flow->set(e, (*_flow)[e] - prem); |
---|
442 | n = _graph.target(e); |
---|
443 | } |
---|
444 | } |
---|
445 | |
---|
446 | _flow_value += prem; |
---|
447 | return true; |
---|
448 | } else { |
---|
449 | return false; |
---|
450 | } |
---|
451 | } |
---|
452 | |
---|
453 | /// \brief Executes the algorithm |
---|
454 | /// |
---|
455 | /// It runs augmenting phases until the optimal solution is reached. |
---|
456 | void start() { |
---|
457 | while (augment()) {} |
---|
458 | } |
---|
459 | |
---|
460 | /// \brief runs the algorithm. |
---|
461 | /// |
---|
462 | /// It is just a shorthand for: |
---|
463 | /// |
---|
464 | ///\code |
---|
465 | /// ek.init(); |
---|
466 | /// ek.start(); |
---|
467 | ///\endcode |
---|
468 | void run() { |
---|
469 | init(); |
---|
470 | start(); |
---|
471 | } |
---|
472 | |
---|
473 | /// @} |
---|
474 | |
---|
475 | /// \name Query Functions |
---|
476 | /// The result of the Edmonds-Karp algorithm can be obtained using these |
---|
477 | /// functions.\n |
---|
478 | /// Before the use of these functions, |
---|
479 | /// either run() or start() must be called. |
---|
480 | |
---|
481 | ///@{ |
---|
482 | |
---|
483 | /// \brief Returns the value of the maximum flow. |
---|
484 | /// |
---|
485 | /// Returns the value of the maximum flow by returning the excess |
---|
486 | /// of the target node \c t. This value equals to the value of |
---|
487 | /// the maximum flow already after the first phase. |
---|
488 | Value flowValue() const { |
---|
489 | return _flow_value; |
---|
490 | } |
---|
491 | |
---|
492 | |
---|
493 | /// \brief Returns the flow on the edge. |
---|
494 | /// |
---|
495 | /// Sets the \c flowMap to the flow on the edges. This method can |
---|
496 | /// be called after the second phase of algorithm. |
---|
497 | Value flow(const Edge& edge) const { |
---|
498 | return (*_flow)[edge]; |
---|
499 | } |
---|
500 | |
---|
501 | /// \brief Returns true when the node is on the source side of minimum cut. |
---|
502 | /// |
---|
503 | |
---|
504 | /// Returns true when the node is on the source side of minimum |
---|
505 | /// cut. This method can be called both after running \ref |
---|
506 | /// startFirstPhase() and \ref startSecondPhase(). |
---|
507 | bool minCut(const Node& node) const { |
---|
508 | return (*_pred)[node] != INVALID; |
---|
509 | } |
---|
510 | |
---|
511 | /// \brief Returns a minimum value cut. |
---|
512 | /// |
---|
513 | /// Sets \c cut to the characteristic vector of a minimum value cut |
---|
514 | /// It simply calls the minMinCut member. |
---|
515 | /// \retval cut Write node bool map. |
---|
516 | template <typename CutMap> |
---|
517 | void minCutMap(CutMap& cutMap) const { |
---|
518 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
519 | cutMap.set(n, (*_pred)[n] != INVALID); |
---|
520 | } |
---|
521 | cutMap.set(_source, true); |
---|
522 | } |
---|
523 | |
---|
524 | /// @} |
---|
525 | |
---|
526 | }; |
---|
527 | |
---|
528 | } |
---|
529 | |
---|
530 | #endif |
---|