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_CANCEL_AND_TIGHTEN_H |
---|
20 | #define LEMON_CANCEL_AND_TIGHTEN_H |
---|
21 | |
---|
22 | /// \ingroup min_cost_flow |
---|
23 | /// |
---|
24 | /// \file |
---|
25 | /// \brief Cancel and Tighten algorithm for finding a minimum cost flow. |
---|
26 | |
---|
27 | #include <vector> |
---|
28 | |
---|
29 | #include <lemon/circulation.h> |
---|
30 | #include <lemon/bellman_ford.h> |
---|
31 | #include <lemon/howard.h> |
---|
32 | #include <lemon/adaptors.h> |
---|
33 | #include <lemon/tolerance.h> |
---|
34 | #include <lemon/math.h> |
---|
35 | |
---|
36 | #include <lemon/static_graph.h> |
---|
37 | |
---|
38 | namespace lemon { |
---|
39 | |
---|
40 | /// \addtogroup min_cost_flow |
---|
41 | /// @{ |
---|
42 | |
---|
43 | /// \brief Implementation of the Cancel and Tighten algorithm for |
---|
44 | /// finding a minimum cost flow. |
---|
45 | /// |
---|
46 | /// \ref CancelAndTighten implements the Cancel and Tighten algorithm for |
---|
47 | /// finding a minimum cost flow. |
---|
48 | /// |
---|
49 | /// \tparam Digraph The digraph type the algorithm runs on. |
---|
50 | /// \tparam LowerMap The type of the lower bound map. |
---|
51 | /// \tparam CapacityMap The type of the capacity (upper bound) map. |
---|
52 | /// \tparam CostMap The type of the cost (length) map. |
---|
53 | /// \tparam SupplyMap The type of the supply map. |
---|
54 | /// |
---|
55 | /// \warning |
---|
56 | /// - Arc capacities and costs should be \e non-negative \e integers. |
---|
57 | /// - Supply values should be \e signed \e integers. |
---|
58 | /// - The value types of the maps should be convertible to each other. |
---|
59 | /// - \c CostMap::Value must be signed type. |
---|
60 | /// |
---|
61 | /// \author Peter Kovacs |
---|
62 | template < typename Digraph, |
---|
63 | typename LowerMap = typename Digraph::template ArcMap<int>, |
---|
64 | typename CapacityMap = typename Digraph::template ArcMap<int>, |
---|
65 | typename CostMap = typename Digraph::template ArcMap<int>, |
---|
66 | typename SupplyMap = typename Digraph::template NodeMap<int> > |
---|
67 | class CancelAndTighten |
---|
68 | { |
---|
69 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
---|
70 | |
---|
71 | typedef typename CapacityMap::Value Capacity; |
---|
72 | typedef typename CostMap::Value Cost; |
---|
73 | typedef typename SupplyMap::Value Supply; |
---|
74 | typedef typename Digraph::template ArcMap<Capacity> CapacityArcMap; |
---|
75 | typedef typename Digraph::template NodeMap<Supply> SupplyNodeMap; |
---|
76 | |
---|
77 | typedef ResidualDigraph< const Digraph, |
---|
78 | CapacityArcMap, CapacityArcMap > ResDigraph; |
---|
79 | |
---|
80 | public: |
---|
81 | |
---|
82 | /// The type of the flow map. |
---|
83 | typedef typename Digraph::template ArcMap<Capacity> FlowMap; |
---|
84 | /// The type of the potential map. |
---|
85 | typedef typename Digraph::template NodeMap<Cost> PotentialMap; |
---|
86 | |
---|
87 | private: |
---|
88 | |
---|
89 | /// \brief Map adaptor class for handling residual arc costs. |
---|
90 | /// |
---|
91 | /// Map adaptor class for handling residual arc costs. |
---|
92 | class ResidualCostMap : public MapBase<typename ResDigraph::Arc, Cost> |
---|
93 | { |
---|
94 | typedef typename ResDigraph::Arc Arc; |
---|
95 | |
---|
96 | private: |
---|
97 | |
---|
98 | const CostMap &_cost_map; |
---|
99 | |
---|
100 | public: |
---|
101 | |
---|
102 | ///\e |
---|
103 | ResidualCostMap(const CostMap &cost_map) : _cost_map(cost_map) {} |
---|
104 | |
---|
105 | ///\e |
---|
106 | Cost operator[](const Arc &e) const { |
---|
107 | return ResDigraph::forward(e) ? _cost_map[e] : -_cost_map[e]; |
---|
108 | } |
---|
109 | |
---|
110 | }; //class ResidualCostMap |
---|
111 | |
---|
112 | /// \brief Map adaptor class for handling reduced arc costs. |
---|
113 | /// |
---|
114 | /// Map adaptor class for handling reduced arc costs. |
---|
115 | class ReducedCostMap : public MapBase<Arc, Cost> |
---|
116 | { |
---|
117 | private: |
---|
118 | |
---|
119 | const Digraph &_gr; |
---|
120 | const CostMap &_cost_map; |
---|
121 | const PotentialMap &_pot_map; |
---|
122 | |
---|
123 | public: |
---|
124 | |
---|
125 | ///\e |
---|
126 | ReducedCostMap( const Digraph &gr, |
---|
127 | const CostMap &cost_map, |
---|
128 | const PotentialMap &pot_map ) : |
---|
129 | _gr(gr), _cost_map(cost_map), _pot_map(pot_map) {} |
---|
130 | |
---|
131 | ///\e |
---|
132 | inline Cost operator[](const Arc &e) const { |
---|
133 | return _cost_map[e] + _pot_map[_gr.source(e)] |
---|
134 | - _pot_map[_gr.target(e)]; |
---|
135 | } |
---|
136 | |
---|
137 | }; //class ReducedCostMap |
---|
138 | |
---|
139 | struct BFOperationTraits { |
---|
140 | static double zero() { return 0; } |
---|
141 | |
---|
142 | static double infinity() { |
---|
143 | return std::numeric_limits<double>::infinity(); |
---|
144 | } |
---|
145 | |
---|
146 | static double plus(const double& left, const double& right) { |
---|
147 | return left + right; |
---|
148 | } |
---|
149 | |
---|
150 | static bool less(const double& left, const double& right) { |
---|
151 | return left + 1e-6 < right; |
---|
152 | } |
---|
153 | }; // class BFOperationTraits |
---|
154 | |
---|
155 | private: |
---|
156 | |
---|
157 | // The digraph the algorithm runs on |
---|
158 | const Digraph &_graph; |
---|
159 | // The original lower bound map |
---|
160 | const LowerMap *_lower; |
---|
161 | // The modified capacity map |
---|
162 | CapacityArcMap _capacity; |
---|
163 | // The original cost map |
---|
164 | const CostMap &_cost; |
---|
165 | // The modified supply map |
---|
166 | SupplyNodeMap _supply; |
---|
167 | bool _valid_supply; |
---|
168 | |
---|
169 | // Arc map of the current flow |
---|
170 | FlowMap *_flow; |
---|
171 | bool _local_flow; |
---|
172 | // Node map of the current potentials |
---|
173 | PotentialMap *_potential; |
---|
174 | bool _local_potential; |
---|
175 | |
---|
176 | // The residual digraph |
---|
177 | ResDigraph *_res_graph; |
---|
178 | // The residual cost map |
---|
179 | ResidualCostMap _res_cost; |
---|
180 | |
---|
181 | public: |
---|
182 | |
---|
183 | /// \brief General constructor (with lower bounds). |
---|
184 | /// |
---|
185 | /// General constructor (with lower bounds). |
---|
186 | /// |
---|
187 | /// \param digraph The digraph the algorithm runs on. |
---|
188 | /// \param lower The lower bounds of the arcs. |
---|
189 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
190 | /// \param cost The cost (length) values of the arcs. |
---|
191 | /// \param supply The supply values of the nodes (signed). |
---|
192 | CancelAndTighten( const Digraph &digraph, |
---|
193 | const LowerMap &lower, |
---|
194 | const CapacityMap &capacity, |
---|
195 | const CostMap &cost, |
---|
196 | const SupplyMap &supply ) : |
---|
197 | _graph(digraph), _lower(&lower), _capacity(digraph), _cost(cost), |
---|
198 | _supply(digraph), _flow(NULL), _local_flow(false), |
---|
199 | _potential(NULL), _local_potential(false), |
---|
200 | _res_graph(NULL), _res_cost(_cost) |
---|
201 | { |
---|
202 | // Check the sum of supply values |
---|
203 | Supply sum = 0; |
---|
204 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
205 | _supply[n] = supply[n]; |
---|
206 | sum += _supply[n]; |
---|
207 | } |
---|
208 | _valid_supply = sum == 0; |
---|
209 | |
---|
210 | // Remove non-zero lower bounds |
---|
211 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
212 | _capacity[e] = capacity[e]; |
---|
213 | if (lower[e] != 0) { |
---|
214 | _capacity[e] -= lower[e]; |
---|
215 | _supply[_graph.source(e)] -= lower[e]; |
---|
216 | _supply[_graph.target(e)] += lower[e]; |
---|
217 | } |
---|
218 | } |
---|
219 | } |
---|
220 | /* |
---|
221 | /// \brief General constructor (without lower bounds). |
---|
222 | /// |
---|
223 | /// General constructor (without lower bounds). |
---|
224 | /// |
---|
225 | /// \param digraph The digraph the algorithm runs on. |
---|
226 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
227 | /// \param cost The cost (length) values of the arcs. |
---|
228 | /// \param supply The supply values of the nodes (signed). |
---|
229 | CancelAndTighten( const Digraph &digraph, |
---|
230 | const CapacityMap &capacity, |
---|
231 | const CostMap &cost, |
---|
232 | const SupplyMap &supply ) : |
---|
233 | _graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost), |
---|
234 | _supply(supply), _flow(NULL), _local_flow(false), |
---|
235 | _potential(NULL), _local_potential(false), |
---|
236 | _res_graph(NULL), _res_cost(_cost) |
---|
237 | { |
---|
238 | // Check the sum of supply values |
---|
239 | Supply sum = 0; |
---|
240 | for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n]; |
---|
241 | _valid_supply = sum == 0; |
---|
242 | } |
---|
243 | |
---|
244 | /// \brief Simple constructor (with lower bounds). |
---|
245 | /// |
---|
246 | /// Simple constructor (with lower bounds). |
---|
247 | /// |
---|
248 | /// \param digraph The digraph the algorithm runs on. |
---|
249 | /// \param lower The lower bounds of the arcs. |
---|
250 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
251 | /// \param cost The cost (length) values of the arcs. |
---|
252 | /// \param s The source node. |
---|
253 | /// \param t The target node. |
---|
254 | /// \param flow_value The required amount of flow from node \c s |
---|
255 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
---|
256 | CancelAndTighten( const Digraph &digraph, |
---|
257 | const LowerMap &lower, |
---|
258 | const CapacityMap &capacity, |
---|
259 | const CostMap &cost, |
---|
260 | Node s, Node t, |
---|
261 | Supply flow_value ) : |
---|
262 | _graph(digraph), _lower(&lower), _capacity(capacity), _cost(cost), |
---|
263 | _supply(digraph, 0), _flow(NULL), _local_flow(false), |
---|
264 | _potential(NULL), _local_potential(false), |
---|
265 | _res_graph(NULL), _res_cost(_cost) |
---|
266 | { |
---|
267 | // Remove non-zero lower bounds |
---|
268 | _supply[s] = flow_value; |
---|
269 | _supply[t] = -flow_value; |
---|
270 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
271 | if (lower[e] != 0) { |
---|
272 | _capacity[e] -= lower[e]; |
---|
273 | _supply[_graph.source(e)] -= lower[e]; |
---|
274 | _supply[_graph.target(e)] += lower[e]; |
---|
275 | } |
---|
276 | } |
---|
277 | _valid_supply = true; |
---|
278 | } |
---|
279 | |
---|
280 | /// \brief Simple constructor (without lower bounds). |
---|
281 | /// |
---|
282 | /// Simple constructor (without lower bounds). |
---|
283 | /// |
---|
284 | /// \param digraph The digraph the algorithm runs on. |
---|
285 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
286 | /// \param cost The cost (length) values of the arcs. |
---|
287 | /// \param s The source node. |
---|
288 | /// \param t The target node. |
---|
289 | /// \param flow_value The required amount of flow from node \c s |
---|
290 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
---|
291 | CancelAndTighten( const Digraph &digraph, |
---|
292 | const CapacityMap &capacity, |
---|
293 | const CostMap &cost, |
---|
294 | Node s, Node t, |
---|
295 | Supply flow_value ) : |
---|
296 | _graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost), |
---|
297 | _supply(digraph, 0), _flow(NULL), _local_flow(false), |
---|
298 | _potential(NULL), _local_potential(false), |
---|
299 | _res_graph(NULL), _res_cost(_cost) |
---|
300 | { |
---|
301 | _supply[s] = flow_value; |
---|
302 | _supply[t] = -flow_value; |
---|
303 | _valid_supply = true; |
---|
304 | } |
---|
305 | */ |
---|
306 | /// Destructor. |
---|
307 | ~CancelAndTighten() { |
---|
308 | if (_local_flow) delete _flow; |
---|
309 | if (_local_potential) delete _potential; |
---|
310 | delete _res_graph; |
---|
311 | } |
---|
312 | |
---|
313 | /// \brief Set the flow map. |
---|
314 | /// |
---|
315 | /// Set the flow map. |
---|
316 | /// |
---|
317 | /// \return \c (*this) |
---|
318 | CancelAndTighten& flowMap(FlowMap &map) { |
---|
319 | if (_local_flow) { |
---|
320 | delete _flow; |
---|
321 | _local_flow = false; |
---|
322 | } |
---|
323 | _flow = ↦ |
---|
324 | return *this; |
---|
325 | } |
---|
326 | |
---|
327 | /// \brief Set the potential map. |
---|
328 | /// |
---|
329 | /// Set the potential map. |
---|
330 | /// |
---|
331 | /// \return \c (*this) |
---|
332 | CancelAndTighten& potentialMap(PotentialMap &map) { |
---|
333 | if (_local_potential) { |
---|
334 | delete _potential; |
---|
335 | _local_potential = false; |
---|
336 | } |
---|
337 | _potential = ↦ |
---|
338 | return *this; |
---|
339 | } |
---|
340 | |
---|
341 | /// \name Execution control |
---|
342 | |
---|
343 | /// @{ |
---|
344 | |
---|
345 | /// \brief Run the algorithm. |
---|
346 | /// |
---|
347 | /// Run the algorithm. |
---|
348 | /// |
---|
349 | /// \return \c true if a feasible flow can be found. |
---|
350 | bool run() { |
---|
351 | return init() && start(); |
---|
352 | } |
---|
353 | |
---|
354 | /// @} |
---|
355 | |
---|
356 | /// \name Query Functions |
---|
357 | /// The result of the algorithm can be obtained using these |
---|
358 | /// functions.\n |
---|
359 | /// \ref lemon::CancelAndTighten::run() "run()" must be called before |
---|
360 | /// using them. |
---|
361 | |
---|
362 | /// @{ |
---|
363 | |
---|
364 | /// \brief Return a const reference to the arc map storing the |
---|
365 | /// found flow. |
---|
366 | /// |
---|
367 | /// Return a const reference to the arc map storing the found flow. |
---|
368 | /// |
---|
369 | /// \pre \ref run() must be called before using this function. |
---|
370 | const FlowMap& flowMap() const { |
---|
371 | return *_flow; |
---|
372 | } |
---|
373 | |
---|
374 | /// \brief Return a const reference to the node map storing the |
---|
375 | /// found potentials (the dual solution). |
---|
376 | /// |
---|
377 | /// Return a const reference to the node map storing the found |
---|
378 | /// potentials (the dual solution). |
---|
379 | /// |
---|
380 | /// \pre \ref run() must be called before using this function. |
---|
381 | const PotentialMap& potentialMap() const { |
---|
382 | return *_potential; |
---|
383 | } |
---|
384 | |
---|
385 | /// \brief Return the flow on the given arc. |
---|
386 | /// |
---|
387 | /// Return the flow on the given arc. |
---|
388 | /// |
---|
389 | /// \pre \ref run() must be called before using this function. |
---|
390 | Capacity flow(const Arc& arc) const { |
---|
391 | return (*_flow)[arc]; |
---|
392 | } |
---|
393 | |
---|
394 | /// \brief Return the potential of the given node. |
---|
395 | /// |
---|
396 | /// Return the potential of the given node. |
---|
397 | /// |
---|
398 | /// \pre \ref run() must be called before using this function. |
---|
399 | Cost potential(const Node& node) const { |
---|
400 | return (*_potential)[node]; |
---|
401 | } |
---|
402 | |
---|
403 | /// \brief Return the total cost of the found flow. |
---|
404 | /// |
---|
405 | /// Return the total cost of the found flow. The complexity of the |
---|
406 | /// function is \f$ O(e) \f$. |
---|
407 | /// |
---|
408 | /// \pre \ref run() must be called before using this function. |
---|
409 | Cost totalCost() const { |
---|
410 | Cost c = 0; |
---|
411 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
412 | c += (*_flow)[e] * _cost[e]; |
---|
413 | return c; |
---|
414 | } |
---|
415 | |
---|
416 | /// @} |
---|
417 | |
---|
418 | private: |
---|
419 | |
---|
420 | /// Initialize the algorithm. |
---|
421 | bool init() { |
---|
422 | if (!_valid_supply) return false; |
---|
423 | |
---|
424 | // Initialize flow and potential maps |
---|
425 | if (!_flow) { |
---|
426 | _flow = new FlowMap(_graph); |
---|
427 | _local_flow = true; |
---|
428 | } |
---|
429 | if (!_potential) { |
---|
430 | _potential = new PotentialMap(_graph); |
---|
431 | _local_potential = true; |
---|
432 | } |
---|
433 | |
---|
434 | _res_graph = new ResDigraph(_graph, _capacity, *_flow); |
---|
435 | |
---|
436 | // Find a feasible flow using Circulation |
---|
437 | Circulation< Digraph, ConstMap<Arc, Capacity>, |
---|
438 | CapacityArcMap, SupplyMap > |
---|
439 | circulation( _graph, constMap<Arc>(Capacity(0)), |
---|
440 | _capacity, _supply ); |
---|
441 | return circulation.flowMap(*_flow).run(); |
---|
442 | } |
---|
443 | |
---|
444 | bool start() { |
---|
445 | const double LIMIT_FACTOR = 0.01; |
---|
446 | const int MIN_LIMIT = 3; |
---|
447 | |
---|
448 | typedef typename Digraph::template NodeMap<double> FloatPotentialMap; |
---|
449 | typedef typename Digraph::template NodeMap<int> LevelMap; |
---|
450 | typedef typename Digraph::template NodeMap<bool> BoolNodeMap; |
---|
451 | typedef typename Digraph::template NodeMap<Node> PredNodeMap; |
---|
452 | typedef typename Digraph::template NodeMap<Arc> PredArcMap; |
---|
453 | typedef typename ResDigraph::template ArcMap<double> ResShiftCostMap; |
---|
454 | FloatPotentialMap pi(_graph); |
---|
455 | LevelMap level(_graph); |
---|
456 | BoolNodeMap reached(_graph); |
---|
457 | BoolNodeMap processed(_graph); |
---|
458 | PredNodeMap pred_node(_graph); |
---|
459 | PredArcMap pred_arc(_graph); |
---|
460 | int node_num = countNodes(_graph); |
---|
461 | typedef std::pair<Arc, bool> pair; |
---|
462 | std::vector<pair> stack(node_num); |
---|
463 | std::vector<Node> proc_vector(node_num); |
---|
464 | ResShiftCostMap shift_cost(*_res_graph); |
---|
465 | |
---|
466 | Tolerance<double> tol; |
---|
467 | tol.epsilon(1e-6); |
---|
468 | |
---|
469 | Timer t1, t2, t3; |
---|
470 | t1.reset(); |
---|
471 | t2.reset(); |
---|
472 | t3.reset(); |
---|
473 | |
---|
474 | // Initialize epsilon and the node potentials |
---|
475 | double epsilon = 0; |
---|
476 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
477 | if (_capacity[e] - (*_flow)[e] > 0 && _cost[e] < -epsilon) |
---|
478 | epsilon = -_cost[e]; |
---|
479 | else if ((*_flow)[e] > 0 && _cost[e] > epsilon) |
---|
480 | epsilon = _cost[e]; |
---|
481 | } |
---|
482 | for (NodeIt v(_graph); v != INVALID; ++v) { |
---|
483 | pi[v] = 0; |
---|
484 | } |
---|
485 | |
---|
486 | // Start phases |
---|
487 | int limit = int(LIMIT_FACTOR * node_num); |
---|
488 | if (limit < MIN_LIMIT) limit = MIN_LIMIT; |
---|
489 | int iter = limit; |
---|
490 | while (epsilon * node_num >= 1) { |
---|
491 | t1.start(); |
---|
492 | // Find and cancel cycles in the admissible digraph using DFS |
---|
493 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
494 | reached[n] = false; |
---|
495 | processed[n] = false; |
---|
496 | } |
---|
497 | int stack_head = -1; |
---|
498 | int proc_head = -1; |
---|
499 | |
---|
500 | for (NodeIt start(_graph); start != INVALID; ++start) { |
---|
501 | if (reached[start]) continue; |
---|
502 | |
---|
503 | // New start node |
---|
504 | reached[start] = true; |
---|
505 | pred_arc[start] = INVALID; |
---|
506 | pred_node[start] = INVALID; |
---|
507 | |
---|
508 | // Find the first admissible residual outgoing arc |
---|
509 | double p = pi[start]; |
---|
510 | Arc e; |
---|
511 | _graph.firstOut(e, start); |
---|
512 | while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 || |
---|
513 | !tol.negative(_cost[e] + p - pi[_graph.target(e)])) ) |
---|
514 | _graph.nextOut(e); |
---|
515 | if (e != INVALID) { |
---|
516 | stack[++stack_head] = pair(e, true); |
---|
517 | goto next_step_1; |
---|
518 | } |
---|
519 | _graph.firstIn(e, start); |
---|
520 | while ( e != INVALID && ((*_flow)[e] == 0 || |
---|
521 | !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) ) |
---|
522 | _graph.nextIn(e); |
---|
523 | if (e != INVALID) { |
---|
524 | stack[++stack_head] = pair(e, false); |
---|
525 | goto next_step_1; |
---|
526 | } |
---|
527 | processed[start] = true; |
---|
528 | proc_vector[++proc_head] = start; |
---|
529 | continue; |
---|
530 | next_step_1: |
---|
531 | |
---|
532 | while (stack_head >= 0) { |
---|
533 | Arc se = stack[stack_head].first; |
---|
534 | bool sf = stack[stack_head].second; |
---|
535 | Node u, v; |
---|
536 | if (sf) { |
---|
537 | u = _graph.source(se); |
---|
538 | v = _graph.target(se); |
---|
539 | } else { |
---|
540 | u = _graph.target(se); |
---|
541 | v = _graph.source(se); |
---|
542 | } |
---|
543 | |
---|
544 | if (!reached[v]) { |
---|
545 | // A new node is reached |
---|
546 | reached[v] = true; |
---|
547 | pred_node[v] = u; |
---|
548 | pred_arc[v] = se; |
---|
549 | // Find the first admissible residual outgoing arc |
---|
550 | double p = pi[v]; |
---|
551 | Arc e; |
---|
552 | _graph.firstOut(e, v); |
---|
553 | while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 || |
---|
554 | !tol.negative(_cost[e] + p - pi[_graph.target(e)])) ) |
---|
555 | _graph.nextOut(e); |
---|
556 | if (e != INVALID) { |
---|
557 | stack[++stack_head] = pair(e, true); |
---|
558 | goto next_step_2; |
---|
559 | } |
---|
560 | _graph.firstIn(e, v); |
---|
561 | while ( e != INVALID && ((*_flow)[e] == 0 || |
---|
562 | !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) ) |
---|
563 | _graph.nextIn(e); |
---|
564 | stack[++stack_head] = pair(e, false); |
---|
565 | next_step_2: ; |
---|
566 | } else { |
---|
567 | if (!processed[v]) { |
---|
568 | // A cycle is found |
---|
569 | Node n, w = u; |
---|
570 | Capacity d, delta = sf ? _capacity[se] - (*_flow)[se] : |
---|
571 | (*_flow)[se]; |
---|
572 | for (n = u; n != v; n = pred_node[n]) { |
---|
573 | d = _graph.target(pred_arc[n]) == n ? |
---|
574 | _capacity[pred_arc[n]] - (*_flow)[pred_arc[n]] : |
---|
575 | (*_flow)[pred_arc[n]]; |
---|
576 | if (d <= delta) { |
---|
577 | delta = d; |
---|
578 | w = pred_node[n]; |
---|
579 | } |
---|
580 | } |
---|
581 | |
---|
582 | /* |
---|
583 | std::cout << "CYCLE FOUND: "; |
---|
584 | if (sf) |
---|
585 | std::cout << _cost[se] + pi[_graph.source(se)] - pi[_graph.target(se)]; |
---|
586 | else |
---|
587 | std::cout << _graph.id(se) << ":" << -(_cost[se] + pi[_graph.source(se)] - pi[_graph.target(se)]); |
---|
588 | for (n = u; n != v; n = pred_node[n]) { |
---|
589 | if (_graph.target(pred_arc[n]) == n) |
---|
590 | std::cout << " " << _cost[pred_arc[n]] + pi[_graph.source(pred_arc[n])] - pi[_graph.target(pred_arc[n])]; |
---|
591 | else |
---|
592 | std::cout << " " << -(_cost[pred_arc[n]] + pi[_graph.source(pred_arc[n])] - pi[_graph.target(pred_arc[n])]); |
---|
593 | } |
---|
594 | std::cout << "\n"; |
---|
595 | */ |
---|
596 | // Augment along the cycle |
---|
597 | (*_flow)[se] = sf ? (*_flow)[se] + delta : |
---|
598 | (*_flow)[se] - delta; |
---|
599 | for (n = u; n != v; n = pred_node[n]) { |
---|
600 | if (_graph.target(pred_arc[n]) == n) |
---|
601 | (*_flow)[pred_arc[n]] += delta; |
---|
602 | else |
---|
603 | (*_flow)[pred_arc[n]] -= delta; |
---|
604 | } |
---|
605 | for (n = u; stack_head > 0 && n != w; n = pred_node[n]) { |
---|
606 | --stack_head; |
---|
607 | reached[n] = false; |
---|
608 | } |
---|
609 | u = w; |
---|
610 | } |
---|
611 | v = u; |
---|
612 | |
---|
613 | // Find the next admissible residual outgoing arc |
---|
614 | double p = pi[v]; |
---|
615 | Arc e = stack[stack_head].first; |
---|
616 | if (!stack[stack_head].second) { |
---|
617 | _graph.nextIn(e); |
---|
618 | goto in_arc_3; |
---|
619 | } |
---|
620 | _graph.nextOut(e); |
---|
621 | while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 || |
---|
622 | !tol.negative(_cost[e] + p - pi[_graph.target(e)])) ) |
---|
623 | _graph.nextOut(e); |
---|
624 | if (e != INVALID) { |
---|
625 | stack[stack_head] = pair(e, true); |
---|
626 | goto next_step_3; |
---|
627 | } |
---|
628 | _graph.firstIn(e, v); |
---|
629 | in_arc_3: |
---|
630 | while ( e != INVALID && ((*_flow)[e] == 0 || |
---|
631 | !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) ) |
---|
632 | _graph.nextIn(e); |
---|
633 | stack[stack_head] = pair(e, false); |
---|
634 | next_step_3: ; |
---|
635 | } |
---|
636 | |
---|
637 | while (stack_head >= 0 && stack[stack_head].first == INVALID) { |
---|
638 | processed[v] = true; |
---|
639 | proc_vector[++proc_head] = v; |
---|
640 | if (--stack_head >= 0) { |
---|
641 | v = stack[stack_head].second ? |
---|
642 | _graph.source(stack[stack_head].first) : |
---|
643 | _graph.target(stack[stack_head].first); |
---|
644 | // Find the next admissible residual outgoing arc |
---|
645 | double p = pi[v]; |
---|
646 | Arc e = stack[stack_head].first; |
---|
647 | if (!stack[stack_head].second) { |
---|
648 | _graph.nextIn(e); |
---|
649 | goto in_arc_4; |
---|
650 | } |
---|
651 | _graph.nextOut(e); |
---|
652 | while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 || |
---|
653 | !tol.negative(_cost[e] + p - pi[_graph.target(e)])) ) |
---|
654 | _graph.nextOut(e); |
---|
655 | if (e != INVALID) { |
---|
656 | stack[stack_head] = pair(e, true); |
---|
657 | goto next_step_4; |
---|
658 | } |
---|
659 | _graph.firstIn(e, v); |
---|
660 | in_arc_4: |
---|
661 | while ( e != INVALID && ((*_flow)[e] == 0 || |
---|
662 | !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) ) |
---|
663 | _graph.nextIn(e); |
---|
664 | stack[stack_head] = pair(e, false); |
---|
665 | next_step_4: ; |
---|
666 | } |
---|
667 | } |
---|
668 | } |
---|
669 | } |
---|
670 | t1.stop(); |
---|
671 | |
---|
672 | // Tighten potentials and epsilon |
---|
673 | if (--iter > 0) { |
---|
674 | // Compute levels |
---|
675 | t2.start(); |
---|
676 | for (int i = proc_head; i >= 0; --i) { |
---|
677 | Node v = proc_vector[i]; |
---|
678 | double p = pi[v]; |
---|
679 | int l = 0; |
---|
680 | for (InArcIt e(_graph, v); e != INVALID; ++e) { |
---|
681 | Node u = _graph.source(e); |
---|
682 | if ( _capacity[e] - (*_flow)[e] > 0 && |
---|
683 | tol.negative(_cost[e] + pi[u] - p) && |
---|
684 | level[u] + 1 > l ) l = level[u] + 1; |
---|
685 | } |
---|
686 | for (OutArcIt e(_graph, v); e != INVALID; ++e) { |
---|
687 | Node u = _graph.target(e); |
---|
688 | if ( (*_flow)[e] > 0 && |
---|
689 | tol.negative(-_cost[e] + pi[u] - p) && |
---|
690 | level[u] + 1 > l ) l = level[u] + 1; |
---|
691 | } |
---|
692 | level[v] = l; |
---|
693 | } |
---|
694 | |
---|
695 | // Modify potentials |
---|
696 | double p, q = -1; |
---|
697 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
698 | Node u = _graph.source(e); |
---|
699 | Node v = _graph.target(e); |
---|
700 | if (_capacity[e] - (*_flow)[e] > 0 && level[u] - level[v] > 0) { |
---|
701 | p = (_cost[e] + pi[u] - pi[v] + epsilon) / |
---|
702 | (level[u] - level[v] + 1); |
---|
703 | if (q < 0 || p < q) q = p; |
---|
704 | } |
---|
705 | else if ((*_flow)[e] > 0 && level[v] - level[u] > 0) { |
---|
706 | p = (-_cost[e] - pi[u] + pi[v] + epsilon) / |
---|
707 | (level[v] - level[u] + 1); |
---|
708 | if (q < 0 || p < q) q = p; |
---|
709 | } |
---|
710 | } |
---|
711 | for (NodeIt v(_graph); v != INVALID; ++v) { |
---|
712 | pi[v] -= q * level[v]; |
---|
713 | } |
---|
714 | |
---|
715 | // Modify epsilon |
---|
716 | epsilon = 0; |
---|
717 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
718 | double curr = _cost[e] + pi[_graph.source(e)] |
---|
719 | - pi[_graph.target(e)]; |
---|
720 | if (_capacity[e] - (*_flow)[e] > 0 && curr < -epsilon) |
---|
721 | epsilon = -curr; |
---|
722 | else if ((*_flow)[e] > 0 && curr > epsilon) |
---|
723 | epsilon = curr; |
---|
724 | } |
---|
725 | t2.stop(); |
---|
726 | } else { |
---|
727 | // Set epsilon to the minimum cycle mean |
---|
728 | t3.start(); |
---|
729 | |
---|
730 | /**/ |
---|
731 | StaticDigraph static_graph; |
---|
732 | typename ResDigraph::template NodeMap<typename StaticDigraph::Node> node_ref(*_res_graph); |
---|
733 | typename ResDigraph::template ArcMap<typename StaticDigraph::Arc> arc_ref(*_res_graph); |
---|
734 | static_graph.build(*_res_graph, node_ref, arc_ref); |
---|
735 | typename StaticDigraph::template NodeMap<double> static_pi(static_graph); |
---|
736 | typename StaticDigraph::template ArcMap<double> static_cost(static_graph); |
---|
737 | |
---|
738 | for (typename ResDigraph::ArcIt e(*_res_graph); e != INVALID; ++e) |
---|
739 | static_cost[arc_ref[e]] = _res_cost[e]; |
---|
740 | |
---|
741 | Howard<StaticDigraph, typename StaticDigraph::template ArcMap<double> > |
---|
742 | mmc(static_graph, static_cost); |
---|
743 | mmc.findMinMean(); |
---|
744 | epsilon = -mmc.cycleMean(); |
---|
745 | /**/ |
---|
746 | |
---|
747 | /* |
---|
748 | Howard<ResDigraph, ResidualCostMap> mmc(*_res_graph, _res_cost); |
---|
749 | mmc.findMinMean(); |
---|
750 | epsilon = -mmc.cycleMean(); |
---|
751 | */ |
---|
752 | |
---|
753 | // Compute feasible potentials for the current epsilon |
---|
754 | for (typename StaticDigraph::ArcIt e(static_graph); e != INVALID; ++e) |
---|
755 | static_cost[e] += epsilon; |
---|
756 | typename BellmanFord<StaticDigraph, typename StaticDigraph::template ArcMap<double> >:: |
---|
757 | template SetDistMap<typename StaticDigraph::template NodeMap<double> >:: |
---|
758 | template SetOperationTraits<BFOperationTraits>::Create |
---|
759 | bf(static_graph, static_cost); |
---|
760 | bf.distMap(static_pi).init(0); |
---|
761 | bf.start(); |
---|
762 | for (NodeIt n(_graph); n != INVALID; ++n) |
---|
763 | pi[n] = static_pi[node_ref[n]]; |
---|
764 | |
---|
765 | /* |
---|
766 | for (typename ResDigraph::ArcIt e(*_res_graph); e != INVALID; ++e) |
---|
767 | shift_cost[e] = _res_cost[e] + epsilon; |
---|
768 | typename BellmanFord<ResDigraph, ResShiftCostMap>:: |
---|
769 | template SetDistMap<FloatPotentialMap>:: |
---|
770 | template SetOperationTraits<BFOperationTraits>::Create |
---|
771 | bf(*_res_graph, shift_cost); |
---|
772 | bf.distMap(pi).init(0); |
---|
773 | bf.start(); |
---|
774 | */ |
---|
775 | |
---|
776 | iter = limit; |
---|
777 | t3.stop(); |
---|
778 | } |
---|
779 | } |
---|
780 | |
---|
781 | // std::cout << t1.realTime() << " " << t2.realTime() << " " << t3.realTime() << "\n"; |
---|
782 | |
---|
783 | // Handle non-zero lower bounds |
---|
784 | if (_lower) { |
---|
785 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
786 | (*_flow)[e] += (*_lower)[e]; |
---|
787 | } |
---|
788 | return true; |
---|
789 | } |
---|
790 | |
---|
791 | }; //class CancelAndTighten |
---|
792 | |
---|
793 | ///@} |
---|
794 | |
---|
795 | } //namespace lemon |
---|
796 | |
---|
797 | #endif //LEMON_CANCEL_AND_TIGHTEN_H |
---|