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_NETWORK_SIMPLEX_H |
---|
20 | #define LEMON_NETWORK_SIMPLEX_H |
---|
21 | |
---|
22 | /// \ingroup min_cost_flow |
---|
23 | /// |
---|
24 | /// \file |
---|
25 | /// \brief Network Simplex algorithm for finding a minimum cost flow. |
---|
26 | |
---|
27 | #include <vector> |
---|
28 | #include <limits> |
---|
29 | #include <algorithm> |
---|
30 | |
---|
31 | #include <lemon/core.h> |
---|
32 | #include <lemon/math.h> |
---|
33 | |
---|
34 | namespace lemon { |
---|
35 | |
---|
36 | /// \addtogroup min_cost_flow |
---|
37 | /// @{ |
---|
38 | |
---|
39 | /// \brief Implementation of the primal Network Simplex algorithm |
---|
40 | /// for finding a \ref min_cost_flow "minimum cost flow". |
---|
41 | /// |
---|
42 | /// \ref NetworkSimplex implements the primal Network Simplex algorithm |
---|
43 | /// for finding a \ref min_cost_flow "minimum cost flow". |
---|
44 | /// |
---|
45 | /// \tparam GR The digraph type the algorithm runs on. |
---|
46 | /// \tparam V The value type used in the algorithm. |
---|
47 | /// By default it is \c int. |
---|
48 | /// |
---|
49 | /// \warning \c V must be a signed integer type. |
---|
50 | /// |
---|
51 | /// \note %NetworkSimplex provides five different pivot rule |
---|
52 | /// implementations. For more information see \ref PivotRule. |
---|
53 | template <typename GR, typename V = int> |
---|
54 | class NetworkSimplex |
---|
55 | { |
---|
56 | public: |
---|
57 | |
---|
58 | /// The value type of the algorithm |
---|
59 | typedef V Value; |
---|
60 | /// The type of the flow map |
---|
61 | typedef typename GR::template ArcMap<Value> FlowMap; |
---|
62 | /// The type of the potential map |
---|
63 | typedef typename GR::template NodeMap<Value> PotentialMap; |
---|
64 | |
---|
65 | public: |
---|
66 | |
---|
67 | /// \brief Enum type for selecting the pivot rule. |
---|
68 | /// |
---|
69 | /// Enum type for selecting the pivot rule for the \ref run() |
---|
70 | /// function. |
---|
71 | /// |
---|
72 | /// \ref NetworkSimplex provides five different pivot rule |
---|
73 | /// implementations that significantly affect the running time |
---|
74 | /// of the algorithm. |
---|
75 | /// By default \ref BLOCK_SEARCH "Block Search" is used, which |
---|
76 | /// proved to be the most efficient and the most robust on various |
---|
77 | /// test inputs according to our benchmark tests. |
---|
78 | /// However another pivot rule can be selected using the \ref run() |
---|
79 | /// function with the proper parameter. |
---|
80 | enum PivotRule { |
---|
81 | |
---|
82 | /// The First Eligible pivot rule. |
---|
83 | /// The next eligible arc is selected in a wraparound fashion |
---|
84 | /// in every iteration. |
---|
85 | FIRST_ELIGIBLE, |
---|
86 | |
---|
87 | /// The Best Eligible pivot rule. |
---|
88 | /// The best eligible arc is selected in every iteration. |
---|
89 | BEST_ELIGIBLE, |
---|
90 | |
---|
91 | /// The Block Search pivot rule. |
---|
92 | /// A specified number of arcs are examined in every iteration |
---|
93 | /// in a wraparound fashion and the best eligible arc is selected |
---|
94 | /// from this block. |
---|
95 | BLOCK_SEARCH, |
---|
96 | |
---|
97 | /// The Candidate List pivot rule. |
---|
98 | /// In a major iteration a candidate list is built from eligible arcs |
---|
99 | /// in a wraparound fashion and in the following minor iterations |
---|
100 | /// the best eligible arc is selected from this list. |
---|
101 | CANDIDATE_LIST, |
---|
102 | |
---|
103 | /// The Altering Candidate List pivot rule. |
---|
104 | /// It is a modified version of the Candidate List method. |
---|
105 | /// It keeps only the several best eligible arcs from the former |
---|
106 | /// candidate list and extends this list in every iteration. |
---|
107 | ALTERING_LIST |
---|
108 | }; |
---|
109 | |
---|
110 | private: |
---|
111 | |
---|
112 | TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
---|
113 | |
---|
114 | typedef typename GR::template ArcMap<Value> ValueArcMap; |
---|
115 | typedef typename GR::template NodeMap<Value> ValueNodeMap; |
---|
116 | |
---|
117 | typedef std::vector<Arc> ArcVector; |
---|
118 | typedef std::vector<Node> NodeVector; |
---|
119 | typedef std::vector<int> IntVector; |
---|
120 | typedef std::vector<bool> BoolVector; |
---|
121 | typedef std::vector<Value> ValueVector; |
---|
122 | |
---|
123 | // State constants for arcs |
---|
124 | enum ArcStateEnum { |
---|
125 | STATE_UPPER = -1, |
---|
126 | STATE_TREE = 0, |
---|
127 | STATE_LOWER = 1 |
---|
128 | }; |
---|
129 | |
---|
130 | private: |
---|
131 | |
---|
132 | // Data related to the underlying digraph |
---|
133 | const GR &_graph; |
---|
134 | int _node_num; |
---|
135 | int _arc_num; |
---|
136 | |
---|
137 | // Parameters of the problem |
---|
138 | ValueArcMap *_plower; |
---|
139 | ValueArcMap *_pupper; |
---|
140 | ValueArcMap *_pcost; |
---|
141 | ValueNodeMap *_psupply; |
---|
142 | bool _pstsup; |
---|
143 | Node _psource, _ptarget; |
---|
144 | Value _pstflow; |
---|
145 | |
---|
146 | // Result maps |
---|
147 | FlowMap *_flow_map; |
---|
148 | PotentialMap *_potential_map; |
---|
149 | bool _local_flow; |
---|
150 | bool _local_potential; |
---|
151 | |
---|
152 | // Data structures for storing the digraph |
---|
153 | IntNodeMap _node_id; |
---|
154 | ArcVector _arc_ref; |
---|
155 | IntVector _source; |
---|
156 | IntVector _target; |
---|
157 | |
---|
158 | // Node and arc data |
---|
159 | ValueVector _cap; |
---|
160 | ValueVector _cost; |
---|
161 | ValueVector _supply; |
---|
162 | ValueVector _flow; |
---|
163 | ValueVector _pi; |
---|
164 | |
---|
165 | // Data for storing the spanning tree structure |
---|
166 | IntVector _parent; |
---|
167 | IntVector _pred; |
---|
168 | IntVector _thread; |
---|
169 | IntVector _rev_thread; |
---|
170 | IntVector _succ_num; |
---|
171 | IntVector _last_succ; |
---|
172 | IntVector _dirty_revs; |
---|
173 | BoolVector _forward; |
---|
174 | IntVector _state; |
---|
175 | int _root; |
---|
176 | |
---|
177 | // Temporary data used in the current pivot iteration |
---|
178 | int in_arc, join, u_in, v_in, u_out, v_out; |
---|
179 | int first, second, right, last; |
---|
180 | int stem, par_stem, new_stem; |
---|
181 | Value delta; |
---|
182 | |
---|
183 | private: |
---|
184 | |
---|
185 | // Implementation of the First Eligible pivot rule |
---|
186 | class FirstEligiblePivotRule |
---|
187 | { |
---|
188 | private: |
---|
189 | |
---|
190 | // References to the NetworkSimplex class |
---|
191 | const IntVector &_source; |
---|
192 | const IntVector &_target; |
---|
193 | const ValueVector &_cost; |
---|
194 | const IntVector &_state; |
---|
195 | const ValueVector &_pi; |
---|
196 | int &_in_arc; |
---|
197 | int _arc_num; |
---|
198 | |
---|
199 | // Pivot rule data |
---|
200 | int _next_arc; |
---|
201 | |
---|
202 | public: |
---|
203 | |
---|
204 | // Constructor |
---|
205 | FirstEligiblePivotRule(NetworkSimplex &ns) : |
---|
206 | _source(ns._source), _target(ns._target), |
---|
207 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
---|
208 | _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0) |
---|
209 | {} |
---|
210 | |
---|
211 | // Find next entering arc |
---|
212 | bool findEnteringArc() { |
---|
213 | Value c; |
---|
214 | for (int e = _next_arc; e < _arc_num; ++e) { |
---|
215 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
216 | if (c < 0) { |
---|
217 | _in_arc = e; |
---|
218 | _next_arc = e + 1; |
---|
219 | return true; |
---|
220 | } |
---|
221 | } |
---|
222 | for (int e = 0; e < _next_arc; ++e) { |
---|
223 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
224 | if (c < 0) { |
---|
225 | _in_arc = e; |
---|
226 | _next_arc = e + 1; |
---|
227 | return true; |
---|
228 | } |
---|
229 | } |
---|
230 | return false; |
---|
231 | } |
---|
232 | |
---|
233 | }; //class FirstEligiblePivotRule |
---|
234 | |
---|
235 | |
---|
236 | // Implementation of the Best Eligible pivot rule |
---|
237 | class BestEligiblePivotRule |
---|
238 | { |
---|
239 | private: |
---|
240 | |
---|
241 | // References to the NetworkSimplex class |
---|
242 | const IntVector &_source; |
---|
243 | const IntVector &_target; |
---|
244 | const ValueVector &_cost; |
---|
245 | const IntVector &_state; |
---|
246 | const ValueVector &_pi; |
---|
247 | int &_in_arc; |
---|
248 | int _arc_num; |
---|
249 | |
---|
250 | public: |
---|
251 | |
---|
252 | // Constructor |
---|
253 | BestEligiblePivotRule(NetworkSimplex &ns) : |
---|
254 | _source(ns._source), _target(ns._target), |
---|
255 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
---|
256 | _in_arc(ns.in_arc), _arc_num(ns._arc_num) |
---|
257 | {} |
---|
258 | |
---|
259 | // Find next entering arc |
---|
260 | bool findEnteringArc() { |
---|
261 | Value c, min = 0; |
---|
262 | for (int e = 0; e < _arc_num; ++e) { |
---|
263 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
264 | if (c < min) { |
---|
265 | min = c; |
---|
266 | _in_arc = e; |
---|
267 | } |
---|
268 | } |
---|
269 | return min < 0; |
---|
270 | } |
---|
271 | |
---|
272 | }; //class BestEligiblePivotRule |
---|
273 | |
---|
274 | |
---|
275 | // Implementation of the Block Search pivot rule |
---|
276 | class BlockSearchPivotRule |
---|
277 | { |
---|
278 | private: |
---|
279 | |
---|
280 | // References to the NetworkSimplex class |
---|
281 | const IntVector &_source; |
---|
282 | const IntVector &_target; |
---|
283 | const ValueVector &_cost; |
---|
284 | const IntVector &_state; |
---|
285 | const ValueVector &_pi; |
---|
286 | int &_in_arc; |
---|
287 | int _arc_num; |
---|
288 | |
---|
289 | // Pivot rule data |
---|
290 | int _block_size; |
---|
291 | int _next_arc; |
---|
292 | |
---|
293 | public: |
---|
294 | |
---|
295 | // Constructor |
---|
296 | BlockSearchPivotRule(NetworkSimplex &ns) : |
---|
297 | _source(ns._source), _target(ns._target), |
---|
298 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
---|
299 | _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0) |
---|
300 | { |
---|
301 | // The main parameters of the pivot rule |
---|
302 | const double BLOCK_SIZE_FACTOR = 2.0; |
---|
303 | const int MIN_BLOCK_SIZE = 10; |
---|
304 | |
---|
305 | _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_arc_num)), |
---|
306 | MIN_BLOCK_SIZE ); |
---|
307 | } |
---|
308 | |
---|
309 | // Find next entering arc |
---|
310 | bool findEnteringArc() { |
---|
311 | Value c, min = 0; |
---|
312 | int cnt = _block_size; |
---|
313 | int e, min_arc = _next_arc; |
---|
314 | for (e = _next_arc; e < _arc_num; ++e) { |
---|
315 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
316 | if (c < min) { |
---|
317 | min = c; |
---|
318 | min_arc = e; |
---|
319 | } |
---|
320 | if (--cnt == 0) { |
---|
321 | if (min < 0) break; |
---|
322 | cnt = _block_size; |
---|
323 | } |
---|
324 | } |
---|
325 | if (min == 0 || cnt > 0) { |
---|
326 | for (e = 0; e < _next_arc; ++e) { |
---|
327 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
328 | if (c < min) { |
---|
329 | min = c; |
---|
330 | min_arc = e; |
---|
331 | } |
---|
332 | if (--cnt == 0) { |
---|
333 | if (min < 0) break; |
---|
334 | cnt = _block_size; |
---|
335 | } |
---|
336 | } |
---|
337 | } |
---|
338 | if (min >= 0) return false; |
---|
339 | _in_arc = min_arc; |
---|
340 | _next_arc = e; |
---|
341 | return true; |
---|
342 | } |
---|
343 | |
---|
344 | }; //class BlockSearchPivotRule |
---|
345 | |
---|
346 | |
---|
347 | // Implementation of the Candidate List pivot rule |
---|
348 | class CandidateListPivotRule |
---|
349 | { |
---|
350 | private: |
---|
351 | |
---|
352 | // References to the NetworkSimplex class |
---|
353 | const IntVector &_source; |
---|
354 | const IntVector &_target; |
---|
355 | const ValueVector &_cost; |
---|
356 | const IntVector &_state; |
---|
357 | const ValueVector &_pi; |
---|
358 | int &_in_arc; |
---|
359 | int _arc_num; |
---|
360 | |
---|
361 | // Pivot rule data |
---|
362 | IntVector _candidates; |
---|
363 | int _list_length, _minor_limit; |
---|
364 | int _curr_length, _minor_count; |
---|
365 | int _next_arc; |
---|
366 | |
---|
367 | public: |
---|
368 | |
---|
369 | /// Constructor |
---|
370 | CandidateListPivotRule(NetworkSimplex &ns) : |
---|
371 | _source(ns._source), _target(ns._target), |
---|
372 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
---|
373 | _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0) |
---|
374 | { |
---|
375 | // The main parameters of the pivot rule |
---|
376 | const double LIST_LENGTH_FACTOR = 1.0; |
---|
377 | const int MIN_LIST_LENGTH = 10; |
---|
378 | const double MINOR_LIMIT_FACTOR = 0.1; |
---|
379 | const int MIN_MINOR_LIMIT = 3; |
---|
380 | |
---|
381 | _list_length = std::max( int(LIST_LENGTH_FACTOR * sqrt(_arc_num)), |
---|
382 | MIN_LIST_LENGTH ); |
---|
383 | _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length), |
---|
384 | MIN_MINOR_LIMIT ); |
---|
385 | _curr_length = _minor_count = 0; |
---|
386 | _candidates.resize(_list_length); |
---|
387 | } |
---|
388 | |
---|
389 | /// Find next entering arc |
---|
390 | bool findEnteringArc() { |
---|
391 | Value min, c; |
---|
392 | int e, min_arc = _next_arc; |
---|
393 | if (_curr_length > 0 && _minor_count < _minor_limit) { |
---|
394 | // Minor iteration: select the best eligible arc from the |
---|
395 | // current candidate list |
---|
396 | ++_minor_count; |
---|
397 | min = 0; |
---|
398 | for (int i = 0; i < _curr_length; ++i) { |
---|
399 | e = _candidates[i]; |
---|
400 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
401 | if (c < min) { |
---|
402 | min = c; |
---|
403 | min_arc = e; |
---|
404 | } |
---|
405 | if (c >= 0) { |
---|
406 | _candidates[i--] = _candidates[--_curr_length]; |
---|
407 | } |
---|
408 | } |
---|
409 | if (min < 0) { |
---|
410 | _in_arc = min_arc; |
---|
411 | return true; |
---|
412 | } |
---|
413 | } |
---|
414 | |
---|
415 | // Major iteration: build a new candidate list |
---|
416 | min = 0; |
---|
417 | _curr_length = 0; |
---|
418 | for (e = _next_arc; e < _arc_num; ++e) { |
---|
419 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
420 | if (c < 0) { |
---|
421 | _candidates[_curr_length++] = e; |
---|
422 | if (c < min) { |
---|
423 | min = c; |
---|
424 | min_arc = e; |
---|
425 | } |
---|
426 | if (_curr_length == _list_length) break; |
---|
427 | } |
---|
428 | } |
---|
429 | if (_curr_length < _list_length) { |
---|
430 | for (e = 0; e < _next_arc; ++e) { |
---|
431 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
432 | if (c < 0) { |
---|
433 | _candidates[_curr_length++] = e; |
---|
434 | if (c < min) { |
---|
435 | min = c; |
---|
436 | min_arc = e; |
---|
437 | } |
---|
438 | if (_curr_length == _list_length) break; |
---|
439 | } |
---|
440 | } |
---|
441 | } |
---|
442 | if (_curr_length == 0) return false; |
---|
443 | _minor_count = 1; |
---|
444 | _in_arc = min_arc; |
---|
445 | _next_arc = e; |
---|
446 | return true; |
---|
447 | } |
---|
448 | |
---|
449 | }; //class CandidateListPivotRule |
---|
450 | |
---|
451 | |
---|
452 | // Implementation of the Altering Candidate List pivot rule |
---|
453 | class AlteringListPivotRule |
---|
454 | { |
---|
455 | private: |
---|
456 | |
---|
457 | // References to the NetworkSimplex class |
---|
458 | const IntVector &_source; |
---|
459 | const IntVector &_target; |
---|
460 | const ValueVector &_cost; |
---|
461 | const IntVector &_state; |
---|
462 | const ValueVector &_pi; |
---|
463 | int &_in_arc; |
---|
464 | int _arc_num; |
---|
465 | |
---|
466 | // Pivot rule data |
---|
467 | int _block_size, _head_length, _curr_length; |
---|
468 | int _next_arc; |
---|
469 | IntVector _candidates; |
---|
470 | ValueVector _cand_cost; |
---|
471 | |
---|
472 | // Functor class to compare arcs during sort of the candidate list |
---|
473 | class SortFunc |
---|
474 | { |
---|
475 | private: |
---|
476 | const ValueVector &_map; |
---|
477 | public: |
---|
478 | SortFunc(const ValueVector &map) : _map(map) {} |
---|
479 | bool operator()(int left, int right) { |
---|
480 | return _map[left] > _map[right]; |
---|
481 | } |
---|
482 | }; |
---|
483 | |
---|
484 | SortFunc _sort_func; |
---|
485 | |
---|
486 | public: |
---|
487 | |
---|
488 | // Constructor |
---|
489 | AlteringListPivotRule(NetworkSimplex &ns) : |
---|
490 | _source(ns._source), _target(ns._target), |
---|
491 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
---|
492 | _in_arc(ns.in_arc), _arc_num(ns._arc_num), |
---|
493 | _next_arc(0), _cand_cost(ns._arc_num), _sort_func(_cand_cost) |
---|
494 | { |
---|
495 | // The main parameters of the pivot rule |
---|
496 | const double BLOCK_SIZE_FACTOR = 1.5; |
---|
497 | const int MIN_BLOCK_SIZE = 10; |
---|
498 | const double HEAD_LENGTH_FACTOR = 0.1; |
---|
499 | const int MIN_HEAD_LENGTH = 3; |
---|
500 | |
---|
501 | _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_arc_num)), |
---|
502 | MIN_BLOCK_SIZE ); |
---|
503 | _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size), |
---|
504 | MIN_HEAD_LENGTH ); |
---|
505 | _candidates.resize(_head_length + _block_size); |
---|
506 | _curr_length = 0; |
---|
507 | } |
---|
508 | |
---|
509 | // Find next entering arc |
---|
510 | bool findEnteringArc() { |
---|
511 | // Check the current candidate list |
---|
512 | int e; |
---|
513 | for (int i = 0; i < _curr_length; ++i) { |
---|
514 | e = _candidates[i]; |
---|
515 | _cand_cost[e] = _state[e] * |
---|
516 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
517 | if (_cand_cost[e] >= 0) { |
---|
518 | _candidates[i--] = _candidates[--_curr_length]; |
---|
519 | } |
---|
520 | } |
---|
521 | |
---|
522 | // Extend the list |
---|
523 | int cnt = _block_size; |
---|
524 | int last_arc = 0; |
---|
525 | int limit = _head_length; |
---|
526 | |
---|
527 | for (int e = _next_arc; e < _arc_num; ++e) { |
---|
528 | _cand_cost[e] = _state[e] * |
---|
529 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
530 | if (_cand_cost[e] < 0) { |
---|
531 | _candidates[_curr_length++] = e; |
---|
532 | last_arc = e; |
---|
533 | } |
---|
534 | if (--cnt == 0) { |
---|
535 | if (_curr_length > limit) break; |
---|
536 | limit = 0; |
---|
537 | cnt = _block_size; |
---|
538 | } |
---|
539 | } |
---|
540 | if (_curr_length <= limit) { |
---|
541 | for (int e = 0; e < _next_arc; ++e) { |
---|
542 | _cand_cost[e] = _state[e] * |
---|
543 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
544 | if (_cand_cost[e] < 0) { |
---|
545 | _candidates[_curr_length++] = e; |
---|
546 | last_arc = e; |
---|
547 | } |
---|
548 | if (--cnt == 0) { |
---|
549 | if (_curr_length > limit) break; |
---|
550 | limit = 0; |
---|
551 | cnt = _block_size; |
---|
552 | } |
---|
553 | } |
---|
554 | } |
---|
555 | if (_curr_length == 0) return false; |
---|
556 | _next_arc = last_arc + 1; |
---|
557 | |
---|
558 | // Make heap of the candidate list (approximating a partial sort) |
---|
559 | make_heap( _candidates.begin(), _candidates.begin() + _curr_length, |
---|
560 | _sort_func ); |
---|
561 | |
---|
562 | // Pop the first element of the heap |
---|
563 | _in_arc = _candidates[0]; |
---|
564 | pop_heap( _candidates.begin(), _candidates.begin() + _curr_length, |
---|
565 | _sort_func ); |
---|
566 | _curr_length = std::min(_head_length, _curr_length - 1); |
---|
567 | return true; |
---|
568 | } |
---|
569 | |
---|
570 | }; //class AlteringListPivotRule |
---|
571 | |
---|
572 | public: |
---|
573 | |
---|
574 | /// \brief Constructor. |
---|
575 | /// |
---|
576 | /// Constructor. |
---|
577 | /// |
---|
578 | /// \param graph The digraph the algorithm runs on. |
---|
579 | NetworkSimplex(const GR& graph) : |
---|
580 | _graph(graph), |
---|
581 | _plower(NULL), _pupper(NULL), _pcost(NULL), |
---|
582 | _psupply(NULL), _pstsup(false), |
---|
583 | _flow_map(NULL), _potential_map(NULL), |
---|
584 | _local_flow(false), _local_potential(false), |
---|
585 | _node_id(graph) |
---|
586 | { |
---|
587 | LEMON_ASSERT(std::numeric_limits<Value>::is_integer && |
---|
588 | std::numeric_limits<Value>::is_signed, |
---|
589 | "The value type of NetworkSimplex must be a signed integer"); |
---|
590 | } |
---|
591 | |
---|
592 | /// Destructor. |
---|
593 | ~NetworkSimplex() { |
---|
594 | if (_local_flow) delete _flow_map; |
---|
595 | if (_local_potential) delete _potential_map; |
---|
596 | } |
---|
597 | |
---|
598 | /// \brief Set the lower bounds on the arcs. |
---|
599 | /// |
---|
600 | /// This function sets the lower bounds on the arcs. |
---|
601 | /// If neither this function nor \ref boundMaps() is used before |
---|
602 | /// calling \ref run(), the lower bounds will be set to zero |
---|
603 | /// on all arcs. |
---|
604 | /// |
---|
605 | /// \param map An arc map storing the lower bounds. |
---|
606 | /// Its \c Value type must be convertible to the \c Value type |
---|
607 | /// of the algorithm. |
---|
608 | /// |
---|
609 | /// \return <tt>(*this)</tt> |
---|
610 | template <typename LOWER> |
---|
611 | NetworkSimplex& lowerMap(const LOWER& map) { |
---|
612 | delete _plower; |
---|
613 | _plower = new ValueArcMap(_graph); |
---|
614 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
615 | (*_plower)[a] = map[a]; |
---|
616 | } |
---|
617 | return *this; |
---|
618 | } |
---|
619 | |
---|
620 | /// \brief Set the upper bounds (capacities) on the arcs. |
---|
621 | /// |
---|
622 | /// This function sets the upper bounds (capacities) on the arcs. |
---|
623 | /// If none of the functions \ref upperMap(), \ref capacityMap() |
---|
624 | /// and \ref boundMaps() is used before calling \ref run(), |
---|
625 | /// the upper bounds (capacities) will be set to |
---|
626 | /// \c std::numeric_limits<Value>::max() on all arcs. |
---|
627 | /// |
---|
628 | /// \param map An arc map storing the upper bounds. |
---|
629 | /// Its \c Value type must be convertible to the \c Value type |
---|
630 | /// of the algorithm. |
---|
631 | /// |
---|
632 | /// \return <tt>(*this)</tt> |
---|
633 | template<typename UPPER> |
---|
634 | NetworkSimplex& upperMap(const UPPER& map) { |
---|
635 | delete _pupper; |
---|
636 | _pupper = new ValueArcMap(_graph); |
---|
637 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
638 | (*_pupper)[a] = map[a]; |
---|
639 | } |
---|
640 | return *this; |
---|
641 | } |
---|
642 | |
---|
643 | /// \brief Set the upper bounds (capacities) on the arcs. |
---|
644 | /// |
---|
645 | /// This function sets the upper bounds (capacities) on the arcs. |
---|
646 | /// It is just an alias for \ref upperMap(). |
---|
647 | /// |
---|
648 | /// \return <tt>(*this)</tt> |
---|
649 | template<typename CAP> |
---|
650 | NetworkSimplex& capacityMap(const CAP& map) { |
---|
651 | return upperMap(map); |
---|
652 | } |
---|
653 | |
---|
654 | /// \brief Set the lower and upper bounds on the arcs. |
---|
655 | /// |
---|
656 | /// This function sets the lower and upper bounds on the arcs. |
---|
657 | /// If neither this function nor \ref lowerMap() is used before |
---|
658 | /// calling \ref run(), the lower bounds will be set to zero |
---|
659 | /// on all arcs. |
---|
660 | /// If none of the functions \ref upperMap(), \ref capacityMap() |
---|
661 | /// and \ref boundMaps() is used before calling \ref run(), |
---|
662 | /// the upper bounds (capacities) will be set to |
---|
663 | /// \c std::numeric_limits<Value>::max() on all arcs. |
---|
664 | /// |
---|
665 | /// \param lower An arc map storing the lower bounds. |
---|
666 | /// \param upper An arc map storing the upper bounds. |
---|
667 | /// |
---|
668 | /// The \c Value type of the maps must be convertible to the |
---|
669 | /// \c Value type of the algorithm. |
---|
670 | /// |
---|
671 | /// \note This function is just a shortcut of calling \ref lowerMap() |
---|
672 | /// and \ref upperMap() separately. |
---|
673 | /// |
---|
674 | /// \return <tt>(*this)</tt> |
---|
675 | template <typename LOWER, typename UPPER> |
---|
676 | NetworkSimplex& boundMaps(const LOWER& lower, const UPPER& upper) { |
---|
677 | return lowerMap(lower).upperMap(upper); |
---|
678 | } |
---|
679 | |
---|
680 | /// \brief Set the costs of the arcs. |
---|
681 | /// |
---|
682 | /// This function sets the costs of the arcs. |
---|
683 | /// If it is not used before calling \ref run(), the costs |
---|
684 | /// will be set to \c 1 on all arcs. |
---|
685 | /// |
---|
686 | /// \param map An arc map storing the costs. |
---|
687 | /// Its \c Value type must be convertible to the \c Value type |
---|
688 | /// of the algorithm. |
---|
689 | /// |
---|
690 | /// \return <tt>(*this)</tt> |
---|
691 | template<typename COST> |
---|
692 | NetworkSimplex& costMap(const COST& map) { |
---|
693 | delete _pcost; |
---|
694 | _pcost = new ValueArcMap(_graph); |
---|
695 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
696 | (*_pcost)[a] = map[a]; |
---|
697 | } |
---|
698 | return *this; |
---|
699 | } |
---|
700 | |
---|
701 | /// \brief Set the supply values of the nodes. |
---|
702 | /// |
---|
703 | /// This function sets the supply values of the nodes. |
---|
704 | /// If neither this function nor \ref stSupply() is used before |
---|
705 | /// calling \ref run(), the supply of each node will be set to zero. |
---|
706 | /// (It makes sense only if non-zero lower bounds are given.) |
---|
707 | /// |
---|
708 | /// \param map A node map storing the supply values. |
---|
709 | /// Its \c Value type must be convertible to the \c Value type |
---|
710 | /// of the algorithm. |
---|
711 | /// |
---|
712 | /// \return <tt>(*this)</tt> |
---|
713 | template<typename SUP> |
---|
714 | NetworkSimplex& supplyMap(const SUP& map) { |
---|
715 | delete _psupply; |
---|
716 | _pstsup = false; |
---|
717 | _psupply = new ValueNodeMap(_graph); |
---|
718 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
719 | (*_psupply)[n] = map[n]; |
---|
720 | } |
---|
721 | return *this; |
---|
722 | } |
---|
723 | |
---|
724 | /// \brief Set single source and target nodes and a supply value. |
---|
725 | /// |
---|
726 | /// This function sets a single source node and a single target node |
---|
727 | /// and the required flow value. |
---|
728 | /// If neither this function nor \ref supplyMap() is used before |
---|
729 | /// calling \ref run(), the supply of each node will be set to zero. |
---|
730 | /// (It makes sense only if non-zero lower bounds are given.) |
---|
731 | /// |
---|
732 | /// \param s The source node. |
---|
733 | /// \param t The target node. |
---|
734 | /// \param k The required amount of flow from node \c s to node \c t |
---|
735 | /// (i.e. the supply of \c s and the demand of \c t). |
---|
736 | /// |
---|
737 | /// \return <tt>(*this)</tt> |
---|
738 | NetworkSimplex& stSupply(const Node& s, const Node& t, Value k) { |
---|
739 | delete _psupply; |
---|
740 | _psupply = NULL; |
---|
741 | _pstsup = true; |
---|
742 | _psource = s; |
---|
743 | _ptarget = t; |
---|
744 | _pstflow = k; |
---|
745 | return *this; |
---|
746 | } |
---|
747 | |
---|
748 | /// \brief Set the flow map. |
---|
749 | /// |
---|
750 | /// This function sets the flow map. |
---|
751 | /// If it is not used before calling \ref run(), an instance will |
---|
752 | /// be allocated automatically. The destructor deallocates this |
---|
753 | /// automatically allocated map, of course. |
---|
754 | /// |
---|
755 | /// \return <tt>(*this)</tt> |
---|
756 | NetworkSimplex& flowMap(FlowMap& map) { |
---|
757 | if (_local_flow) { |
---|
758 | delete _flow_map; |
---|
759 | _local_flow = false; |
---|
760 | } |
---|
761 | _flow_map = ↦ |
---|
762 | return *this; |
---|
763 | } |
---|
764 | |
---|
765 | /// \brief Set the potential map. |
---|
766 | /// |
---|
767 | /// This function sets the potential map, which is used for storing |
---|
768 | /// the dual solution. |
---|
769 | /// If it is not used before calling \ref run(), an instance will |
---|
770 | /// be allocated automatically. The destructor deallocates this |
---|
771 | /// automatically allocated map, of course. |
---|
772 | /// |
---|
773 | /// \return <tt>(*this)</tt> |
---|
774 | NetworkSimplex& potentialMap(PotentialMap& map) { |
---|
775 | if (_local_potential) { |
---|
776 | delete _potential_map; |
---|
777 | _local_potential = false; |
---|
778 | } |
---|
779 | _potential_map = ↦ |
---|
780 | return *this; |
---|
781 | } |
---|
782 | |
---|
783 | /// \name Execution Control |
---|
784 | /// The algorithm can be executed using \ref run(). |
---|
785 | |
---|
786 | /// @{ |
---|
787 | |
---|
788 | /// \brief Run the algorithm. |
---|
789 | /// |
---|
790 | /// This function runs the algorithm. |
---|
791 | /// The paramters can be specified using \ref lowerMap(), |
---|
792 | /// \ref upperMap(), \ref capacityMap(), \ref boundMaps(), |
---|
793 | /// \ref costMap(), \ref supplyMap() and \ref stSupply() |
---|
794 | /// functions. For example, |
---|
795 | /// \code |
---|
796 | /// NetworkSimplex<ListDigraph> ns(graph); |
---|
797 | /// ns.boundMaps(lower, upper).costMap(cost) |
---|
798 | /// .supplyMap(sup).run(); |
---|
799 | /// \endcode |
---|
800 | /// |
---|
801 | /// \param pivot_rule The pivot rule that will be used during the |
---|
802 | /// algorithm. For more information see \ref PivotRule. |
---|
803 | /// |
---|
804 | /// \return \c true if a feasible flow can be found. |
---|
805 | bool run(PivotRule pivot_rule = BLOCK_SEARCH) { |
---|
806 | return init() && start(pivot_rule); |
---|
807 | } |
---|
808 | |
---|
809 | /// @} |
---|
810 | |
---|
811 | /// \name Query Functions |
---|
812 | /// The results of the algorithm can be obtained using these |
---|
813 | /// functions.\n |
---|
814 | /// The \ref run() function must be called before using them. |
---|
815 | |
---|
816 | /// @{ |
---|
817 | |
---|
818 | /// \brief Return the total cost of the found flow. |
---|
819 | /// |
---|
820 | /// This function returns the total cost of the found flow. |
---|
821 | /// The complexity of the function is \f$ O(e) \f$. |
---|
822 | /// |
---|
823 | /// \note The return type of the function can be specified as a |
---|
824 | /// template parameter. For example, |
---|
825 | /// \code |
---|
826 | /// ns.totalCost<double>(); |
---|
827 | /// \endcode |
---|
828 | /// It is useful if the total cost cannot be stored in the \c Value |
---|
829 | /// type of the algorithm, which is the default return type of the |
---|
830 | /// function. |
---|
831 | /// |
---|
832 | /// \pre \ref run() must be called before using this function. |
---|
833 | template <typename Num> |
---|
834 | Num totalCost() const { |
---|
835 | Num c = 0; |
---|
836 | if (_pcost) { |
---|
837 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
838 | c += (*_flow_map)[e] * (*_pcost)[e]; |
---|
839 | } else { |
---|
840 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
841 | c += (*_flow_map)[e]; |
---|
842 | } |
---|
843 | return c; |
---|
844 | } |
---|
845 | |
---|
846 | #ifndef DOXYGEN |
---|
847 | Value totalCost() const { |
---|
848 | return totalCost<Value>(); |
---|
849 | } |
---|
850 | #endif |
---|
851 | |
---|
852 | /// \brief Return the flow on the given arc. |
---|
853 | /// |
---|
854 | /// This function returns the flow on the given arc. |
---|
855 | /// |
---|
856 | /// \pre \ref run() must be called before using this function. |
---|
857 | Value flow(const Arc& a) const { |
---|
858 | return (*_flow_map)[a]; |
---|
859 | } |
---|
860 | |
---|
861 | /// \brief Return a const reference to the flow map. |
---|
862 | /// |
---|
863 | /// This function returns a const reference to an arc map storing |
---|
864 | /// the found flow. |
---|
865 | /// |
---|
866 | /// \pre \ref run() must be called before using this function. |
---|
867 | const FlowMap& flowMap() const { |
---|
868 | return *_flow_map; |
---|
869 | } |
---|
870 | |
---|
871 | /// \brief Return the potential (dual value) of the given node. |
---|
872 | /// |
---|
873 | /// This function returns the potential (dual value) of the |
---|
874 | /// given node. |
---|
875 | /// |
---|
876 | /// \pre \ref run() must be called before using this function. |
---|
877 | Value potential(const Node& n) const { |
---|
878 | return (*_potential_map)[n]; |
---|
879 | } |
---|
880 | |
---|
881 | /// \brief Return a const reference to the potential map |
---|
882 | /// (the dual solution). |
---|
883 | /// |
---|
884 | /// This function returns a const reference to a node map storing |
---|
885 | /// the found potentials, which form the dual solution of the |
---|
886 | /// \ref min_cost_flow "minimum cost flow" problem. |
---|
887 | /// |
---|
888 | /// \pre \ref run() must be called before using this function. |
---|
889 | const PotentialMap& potentialMap() const { |
---|
890 | return *_potential_map; |
---|
891 | } |
---|
892 | |
---|
893 | /// @} |
---|
894 | |
---|
895 | private: |
---|
896 | |
---|
897 | // Initialize internal data structures |
---|
898 | bool init() { |
---|
899 | // Initialize result maps |
---|
900 | if (!_flow_map) { |
---|
901 | _flow_map = new FlowMap(_graph); |
---|
902 | _local_flow = true; |
---|
903 | } |
---|
904 | if (!_potential_map) { |
---|
905 | _potential_map = new PotentialMap(_graph); |
---|
906 | _local_potential = true; |
---|
907 | } |
---|
908 | |
---|
909 | // Initialize vectors |
---|
910 | _node_num = countNodes(_graph); |
---|
911 | _arc_num = countArcs(_graph); |
---|
912 | int all_node_num = _node_num + 1; |
---|
913 | int all_arc_num = _arc_num + _node_num; |
---|
914 | if (_node_num == 0) return false; |
---|
915 | |
---|
916 | _arc_ref.resize(_arc_num); |
---|
917 | _source.resize(all_arc_num); |
---|
918 | _target.resize(all_arc_num); |
---|
919 | |
---|
920 | _cap.resize(all_arc_num); |
---|
921 | _cost.resize(all_arc_num); |
---|
922 | _supply.resize(all_node_num); |
---|
923 | _flow.resize(all_arc_num, 0); |
---|
924 | _pi.resize(all_node_num, 0); |
---|
925 | |
---|
926 | _parent.resize(all_node_num); |
---|
927 | _pred.resize(all_node_num); |
---|
928 | _forward.resize(all_node_num); |
---|
929 | _thread.resize(all_node_num); |
---|
930 | _rev_thread.resize(all_node_num); |
---|
931 | _succ_num.resize(all_node_num); |
---|
932 | _last_succ.resize(all_node_num); |
---|
933 | _state.resize(all_arc_num, STATE_LOWER); |
---|
934 | |
---|
935 | // Initialize node related data |
---|
936 | bool valid_supply = true; |
---|
937 | if (!_pstsup && !_psupply) { |
---|
938 | _pstsup = true; |
---|
939 | _psource = _ptarget = NodeIt(_graph); |
---|
940 | _pstflow = 0; |
---|
941 | } |
---|
942 | if (_psupply) { |
---|
943 | Value sum = 0; |
---|
944 | int i = 0; |
---|
945 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
---|
946 | _node_id[n] = i; |
---|
947 | _supply[i] = (*_psupply)[n]; |
---|
948 | sum += _supply[i]; |
---|
949 | } |
---|
950 | valid_supply = (sum == 0); |
---|
951 | } else { |
---|
952 | int i = 0; |
---|
953 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
---|
954 | _node_id[n] = i; |
---|
955 | _supply[i] = 0; |
---|
956 | } |
---|
957 | _supply[_node_id[_psource]] = _pstflow; |
---|
958 | _supply[_node_id[_ptarget]] = -_pstflow; |
---|
959 | } |
---|
960 | if (!valid_supply) return false; |
---|
961 | |
---|
962 | // Set data for the artificial root node |
---|
963 | _root = _node_num; |
---|
964 | _parent[_root] = -1; |
---|
965 | _pred[_root] = -1; |
---|
966 | _thread[_root] = 0; |
---|
967 | _rev_thread[0] = _root; |
---|
968 | _succ_num[_root] = all_node_num; |
---|
969 | _last_succ[_root] = _root - 1; |
---|
970 | _supply[_root] = 0; |
---|
971 | _pi[_root] = 0; |
---|
972 | |
---|
973 | // Store the arcs in a mixed order |
---|
974 | int k = std::max(int(sqrt(_arc_num)), 10); |
---|
975 | int i = 0; |
---|
976 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
977 | _arc_ref[i] = e; |
---|
978 | if ((i += k) >= _arc_num) i = (i % k) + 1; |
---|
979 | } |
---|
980 | |
---|
981 | // Initialize arc maps |
---|
982 | if (_pupper && _pcost) { |
---|
983 | for (int i = 0; i != _arc_num; ++i) { |
---|
984 | Arc e = _arc_ref[i]; |
---|
985 | _source[i] = _node_id[_graph.source(e)]; |
---|
986 | _target[i] = _node_id[_graph.target(e)]; |
---|
987 | _cap[i] = (*_pupper)[e]; |
---|
988 | _cost[i] = (*_pcost)[e]; |
---|
989 | } |
---|
990 | } else { |
---|
991 | for (int i = 0; i != _arc_num; ++i) { |
---|
992 | Arc e = _arc_ref[i]; |
---|
993 | _source[i] = _node_id[_graph.source(e)]; |
---|
994 | _target[i] = _node_id[_graph.target(e)]; |
---|
995 | } |
---|
996 | if (_pupper) { |
---|
997 | for (int i = 0; i != _arc_num; ++i) |
---|
998 | _cap[i] = (*_pupper)[_arc_ref[i]]; |
---|
999 | } else { |
---|
1000 | Value val = std::numeric_limits<Value>::max(); |
---|
1001 | for (int i = 0; i != _arc_num; ++i) |
---|
1002 | _cap[i] = val; |
---|
1003 | } |
---|
1004 | if (_pcost) { |
---|
1005 | for (int i = 0; i != _arc_num; ++i) |
---|
1006 | _cost[i] = (*_pcost)[_arc_ref[i]]; |
---|
1007 | } else { |
---|
1008 | for (int i = 0; i != _arc_num; ++i) |
---|
1009 | _cost[i] = 1; |
---|
1010 | } |
---|
1011 | } |
---|
1012 | |
---|
1013 | // Remove non-zero lower bounds |
---|
1014 | if (_plower) { |
---|
1015 | for (int i = 0; i != _arc_num; ++i) { |
---|
1016 | Value c = (*_plower)[_arc_ref[i]]; |
---|
1017 | if (c != 0) { |
---|
1018 | _cap[i] -= c; |
---|
1019 | _supply[_source[i]] -= c; |
---|
1020 | _supply[_target[i]] += c; |
---|
1021 | } |
---|
1022 | } |
---|
1023 | } |
---|
1024 | |
---|
1025 | // Add artificial arcs and initialize the spanning tree data structure |
---|
1026 | Value max_cap = std::numeric_limits<Value>::max(); |
---|
1027 | Value max_cost = std::numeric_limits<Value>::max() / 4; |
---|
1028 | for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { |
---|
1029 | _thread[u] = u + 1; |
---|
1030 | _rev_thread[u + 1] = u; |
---|
1031 | _succ_num[u] = 1; |
---|
1032 | _last_succ[u] = u; |
---|
1033 | _parent[u] = _root; |
---|
1034 | _pred[u] = e; |
---|
1035 | if (_supply[u] >= 0) { |
---|
1036 | _flow[e] = _supply[u]; |
---|
1037 | _forward[u] = true; |
---|
1038 | _pi[u] = -max_cost; |
---|
1039 | } else { |
---|
1040 | _flow[e] = -_supply[u]; |
---|
1041 | _forward[u] = false; |
---|
1042 | _pi[u] = max_cost; |
---|
1043 | } |
---|
1044 | _cost[e] = max_cost; |
---|
1045 | _cap[e] = max_cap; |
---|
1046 | _state[e] = STATE_TREE; |
---|
1047 | } |
---|
1048 | |
---|
1049 | return true; |
---|
1050 | } |
---|
1051 | |
---|
1052 | // Find the join node |
---|
1053 | void findJoinNode() { |
---|
1054 | int u = _source[in_arc]; |
---|
1055 | int v = _target[in_arc]; |
---|
1056 | while (u != v) { |
---|
1057 | if (_succ_num[u] < _succ_num[v]) { |
---|
1058 | u = _parent[u]; |
---|
1059 | } else { |
---|
1060 | v = _parent[v]; |
---|
1061 | } |
---|
1062 | } |
---|
1063 | join = u; |
---|
1064 | } |
---|
1065 | |
---|
1066 | // Find the leaving arc of the cycle and returns true if the |
---|
1067 | // leaving arc is not the same as the entering arc |
---|
1068 | bool findLeavingArc() { |
---|
1069 | // Initialize first and second nodes according to the direction |
---|
1070 | // of the cycle |
---|
1071 | if (_state[in_arc] == STATE_LOWER) { |
---|
1072 | first = _source[in_arc]; |
---|
1073 | second = _target[in_arc]; |
---|
1074 | } else { |
---|
1075 | first = _target[in_arc]; |
---|
1076 | second = _source[in_arc]; |
---|
1077 | } |
---|
1078 | delta = _cap[in_arc]; |
---|
1079 | int result = 0; |
---|
1080 | Value d; |
---|
1081 | int e; |
---|
1082 | |
---|
1083 | // Search the cycle along the path form the first node to the root |
---|
1084 | for (int u = first; u != join; u = _parent[u]) { |
---|
1085 | e = _pred[u]; |
---|
1086 | d = _forward[u] ? _flow[e] : _cap[e] - _flow[e]; |
---|
1087 | if (d < delta) { |
---|
1088 | delta = d; |
---|
1089 | u_out = u; |
---|
1090 | result = 1; |
---|
1091 | } |
---|
1092 | } |
---|
1093 | // Search the cycle along the path form the second node to the root |
---|
1094 | for (int u = second; u != join; u = _parent[u]) { |
---|
1095 | e = _pred[u]; |
---|
1096 | d = _forward[u] ? _cap[e] - _flow[e] : _flow[e]; |
---|
1097 | if (d <= delta) { |
---|
1098 | delta = d; |
---|
1099 | u_out = u; |
---|
1100 | result = 2; |
---|
1101 | } |
---|
1102 | } |
---|
1103 | |
---|
1104 | if (result == 1) { |
---|
1105 | u_in = first; |
---|
1106 | v_in = second; |
---|
1107 | } else { |
---|
1108 | u_in = second; |
---|
1109 | v_in = first; |
---|
1110 | } |
---|
1111 | return result != 0; |
---|
1112 | } |
---|
1113 | |
---|
1114 | // Change _flow and _state vectors |
---|
1115 | void changeFlow(bool change) { |
---|
1116 | // Augment along the cycle |
---|
1117 | if (delta > 0) { |
---|
1118 | Value val = _state[in_arc] * delta; |
---|
1119 | _flow[in_arc] += val; |
---|
1120 | for (int u = _source[in_arc]; u != join; u = _parent[u]) { |
---|
1121 | _flow[_pred[u]] += _forward[u] ? -val : val; |
---|
1122 | } |
---|
1123 | for (int u = _target[in_arc]; u != join; u = _parent[u]) { |
---|
1124 | _flow[_pred[u]] += _forward[u] ? val : -val; |
---|
1125 | } |
---|
1126 | } |
---|
1127 | // Update the state of the entering and leaving arcs |
---|
1128 | if (change) { |
---|
1129 | _state[in_arc] = STATE_TREE; |
---|
1130 | _state[_pred[u_out]] = |
---|
1131 | (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER; |
---|
1132 | } else { |
---|
1133 | _state[in_arc] = -_state[in_arc]; |
---|
1134 | } |
---|
1135 | } |
---|
1136 | |
---|
1137 | // Update the tree structure |
---|
1138 | void updateTreeStructure() { |
---|
1139 | int u, w; |
---|
1140 | int old_rev_thread = _rev_thread[u_out]; |
---|
1141 | int old_succ_num = _succ_num[u_out]; |
---|
1142 | int old_last_succ = _last_succ[u_out]; |
---|
1143 | v_out = _parent[u_out]; |
---|
1144 | |
---|
1145 | u = _last_succ[u_in]; // the last successor of u_in |
---|
1146 | right = _thread[u]; // the node after it |
---|
1147 | |
---|
1148 | // Handle the case when old_rev_thread equals to v_in |
---|
1149 | // (it also means that join and v_out coincide) |
---|
1150 | if (old_rev_thread == v_in) { |
---|
1151 | last = _thread[_last_succ[u_out]]; |
---|
1152 | } else { |
---|
1153 | last = _thread[v_in]; |
---|
1154 | } |
---|
1155 | |
---|
1156 | // Update _thread and _parent along the stem nodes (i.e. the nodes |
---|
1157 | // between u_in and u_out, whose parent have to be changed) |
---|
1158 | _thread[v_in] = stem = u_in; |
---|
1159 | _dirty_revs.clear(); |
---|
1160 | _dirty_revs.push_back(v_in); |
---|
1161 | par_stem = v_in; |
---|
1162 | while (stem != u_out) { |
---|
1163 | // Insert the next stem node into the thread list |
---|
1164 | new_stem = _parent[stem]; |
---|
1165 | _thread[u] = new_stem; |
---|
1166 | _dirty_revs.push_back(u); |
---|
1167 | |
---|
1168 | // Remove the subtree of stem from the thread list |
---|
1169 | w = _rev_thread[stem]; |
---|
1170 | _thread[w] = right; |
---|
1171 | _rev_thread[right] = w; |
---|
1172 | |
---|
1173 | // Change the parent node and shift stem nodes |
---|
1174 | _parent[stem] = par_stem; |
---|
1175 | par_stem = stem; |
---|
1176 | stem = new_stem; |
---|
1177 | |
---|
1178 | // Update u and right |
---|
1179 | u = _last_succ[stem] == _last_succ[par_stem] ? |
---|
1180 | _rev_thread[par_stem] : _last_succ[stem]; |
---|
1181 | right = _thread[u]; |
---|
1182 | } |
---|
1183 | _parent[u_out] = par_stem; |
---|
1184 | _thread[u] = last; |
---|
1185 | _rev_thread[last] = u; |
---|
1186 | _last_succ[u_out] = u; |
---|
1187 | |
---|
1188 | // Remove the subtree of u_out from the thread list except for |
---|
1189 | // the case when old_rev_thread equals to v_in |
---|
1190 | // (it also means that join and v_out coincide) |
---|
1191 | if (old_rev_thread != v_in) { |
---|
1192 | _thread[old_rev_thread] = right; |
---|
1193 | _rev_thread[right] = old_rev_thread; |
---|
1194 | } |
---|
1195 | |
---|
1196 | // Update _rev_thread using the new _thread values |
---|
1197 | for (int i = 0; i < int(_dirty_revs.size()); ++i) { |
---|
1198 | u = _dirty_revs[i]; |
---|
1199 | _rev_thread[_thread[u]] = u; |
---|
1200 | } |
---|
1201 | |
---|
1202 | // Update _pred, _forward, _last_succ and _succ_num for the |
---|
1203 | // stem nodes from u_out to u_in |
---|
1204 | int tmp_sc = 0, tmp_ls = _last_succ[u_out]; |
---|
1205 | u = u_out; |
---|
1206 | while (u != u_in) { |
---|
1207 | w = _parent[u]; |
---|
1208 | _pred[u] = _pred[w]; |
---|
1209 | _forward[u] = !_forward[w]; |
---|
1210 | tmp_sc += _succ_num[u] - _succ_num[w]; |
---|
1211 | _succ_num[u] = tmp_sc; |
---|
1212 | _last_succ[w] = tmp_ls; |
---|
1213 | u = w; |
---|
1214 | } |
---|
1215 | _pred[u_in] = in_arc; |
---|
1216 | _forward[u_in] = (u_in == _source[in_arc]); |
---|
1217 | _succ_num[u_in] = old_succ_num; |
---|
1218 | |
---|
1219 | // Set limits for updating _last_succ form v_in and v_out |
---|
1220 | // towards the root |
---|
1221 | int up_limit_in = -1; |
---|
1222 | int up_limit_out = -1; |
---|
1223 | if (_last_succ[join] == v_in) { |
---|
1224 | up_limit_out = join; |
---|
1225 | } else { |
---|
1226 | up_limit_in = join; |
---|
1227 | } |
---|
1228 | |
---|
1229 | // Update _last_succ from v_in towards the root |
---|
1230 | for (u = v_in; u != up_limit_in && _last_succ[u] == v_in; |
---|
1231 | u = _parent[u]) { |
---|
1232 | _last_succ[u] = _last_succ[u_out]; |
---|
1233 | } |
---|
1234 | // Update _last_succ from v_out towards the root |
---|
1235 | if (join != old_rev_thread && v_in != old_rev_thread) { |
---|
1236 | for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; |
---|
1237 | u = _parent[u]) { |
---|
1238 | _last_succ[u] = old_rev_thread; |
---|
1239 | } |
---|
1240 | } else { |
---|
1241 | for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; |
---|
1242 | u = _parent[u]) { |
---|
1243 | _last_succ[u] = _last_succ[u_out]; |
---|
1244 | } |
---|
1245 | } |
---|
1246 | |
---|
1247 | // Update _succ_num from v_in to join |
---|
1248 | for (u = v_in; u != join; u = _parent[u]) { |
---|
1249 | _succ_num[u] += old_succ_num; |
---|
1250 | } |
---|
1251 | // Update _succ_num from v_out to join |
---|
1252 | for (u = v_out; u != join; u = _parent[u]) { |
---|
1253 | _succ_num[u] -= old_succ_num; |
---|
1254 | } |
---|
1255 | } |
---|
1256 | |
---|
1257 | // Update potentials |
---|
1258 | void updatePotential() { |
---|
1259 | Value sigma = _forward[u_in] ? |
---|
1260 | _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] : |
---|
1261 | _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]]; |
---|
1262 | if (_succ_num[u_in] > _node_num / 2) { |
---|
1263 | // Update in the upper subtree (which contains the root) |
---|
1264 | int before = _rev_thread[u_in]; |
---|
1265 | int after = _thread[_last_succ[u_in]]; |
---|
1266 | _thread[before] = after; |
---|
1267 | _pi[_root] -= sigma; |
---|
1268 | for (int u = _thread[_root]; u != _root; u = _thread[u]) { |
---|
1269 | _pi[u] -= sigma; |
---|
1270 | } |
---|
1271 | _thread[before] = u_in; |
---|
1272 | } else { |
---|
1273 | // Update in the lower subtree (which has been moved) |
---|
1274 | int end = _thread[_last_succ[u_in]]; |
---|
1275 | for (int u = u_in; u != end; u = _thread[u]) { |
---|
1276 | _pi[u] += sigma; |
---|
1277 | } |
---|
1278 | } |
---|
1279 | } |
---|
1280 | |
---|
1281 | // Execute the algorithm |
---|
1282 | bool start(PivotRule pivot_rule) { |
---|
1283 | // Select the pivot rule implementation |
---|
1284 | switch (pivot_rule) { |
---|
1285 | case FIRST_ELIGIBLE: |
---|
1286 | return start<FirstEligiblePivotRule>(); |
---|
1287 | case BEST_ELIGIBLE: |
---|
1288 | return start<BestEligiblePivotRule>(); |
---|
1289 | case BLOCK_SEARCH: |
---|
1290 | return start<BlockSearchPivotRule>(); |
---|
1291 | case CANDIDATE_LIST: |
---|
1292 | return start<CandidateListPivotRule>(); |
---|
1293 | case ALTERING_LIST: |
---|
1294 | return start<AlteringListPivotRule>(); |
---|
1295 | } |
---|
1296 | return false; |
---|
1297 | } |
---|
1298 | |
---|
1299 | template <typename PivotRuleImpl> |
---|
1300 | bool start() { |
---|
1301 | PivotRuleImpl pivot(*this); |
---|
1302 | |
---|
1303 | // Execute the Network Simplex algorithm |
---|
1304 | while (pivot.findEnteringArc()) { |
---|
1305 | findJoinNode(); |
---|
1306 | bool change = findLeavingArc(); |
---|
1307 | changeFlow(change); |
---|
1308 | if (change) { |
---|
1309 | updateTreeStructure(); |
---|
1310 | updatePotential(); |
---|
1311 | } |
---|
1312 | } |
---|
1313 | |
---|
1314 | // Check if the flow amount equals zero on all the artificial arcs |
---|
1315 | for (int e = _arc_num; e != _arc_num + _node_num; ++e) { |
---|
1316 | if (_flow[e] > 0) return false; |
---|
1317 | } |
---|
1318 | |
---|
1319 | // Copy flow values to _flow_map |
---|
1320 | if (_plower) { |
---|
1321 | for (int i = 0; i != _arc_num; ++i) { |
---|
1322 | Arc e = _arc_ref[i]; |
---|
1323 | _flow_map->set(e, (*_plower)[e] + _flow[i]); |
---|
1324 | } |
---|
1325 | } else { |
---|
1326 | for (int i = 0; i != _arc_num; ++i) { |
---|
1327 | _flow_map->set(_arc_ref[i], _flow[i]); |
---|
1328 | } |
---|
1329 | } |
---|
1330 | // Copy potential values to _potential_map |
---|
1331 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
1332 | _potential_map->set(n, _pi[_node_id[n]]); |
---|
1333 | } |
---|
1334 | |
---|
1335 | return true; |
---|
1336 | } |
---|
1337 | |
---|
1338 | }; //class NetworkSimplex |
---|
1339 | |
---|
1340 | ///@} |
---|
1341 | |
---|
1342 | } //namespace lemon |
---|
1343 | |
---|
1344 | #endif //LEMON_NETWORK_SIMPLEX_H |
---|