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 | #include <lemon/maps.h> |
---|
34 | #include <lemon/circulation.h> |
---|
35 | #include <lemon/adaptors.h> |
---|
36 | |
---|
37 | namespace lemon { |
---|
38 | |
---|
39 | /// \addtogroup min_cost_flow |
---|
40 | /// @{ |
---|
41 | |
---|
42 | /// \brief Implementation of the primal Network Simplex algorithm |
---|
43 | /// for finding a \ref min_cost_flow "minimum cost flow". |
---|
44 | /// |
---|
45 | /// \ref NetworkSimplex implements the primal Network Simplex algorithm |
---|
46 | /// for finding a \ref min_cost_flow "minimum cost flow". |
---|
47 | /// This algorithm is a specialized version of the linear programming |
---|
48 | /// simplex method directly for the minimum cost flow problem. |
---|
49 | /// It is one of the most efficient solution methods. |
---|
50 | /// |
---|
51 | /// In general this class is the fastest implementation available |
---|
52 | /// in LEMON for the minimum cost flow problem. |
---|
53 | /// Moreover it supports both direction of the supply/demand inequality |
---|
54 | /// constraints. For more information see \ref ProblemType. |
---|
55 | /// |
---|
56 | /// \tparam GR The digraph type the algorithm runs on. |
---|
57 | /// \tparam F The value type used for flow amounts, capacity bounds |
---|
58 | /// and supply values in the algorithm. By default it is \c int. |
---|
59 | /// \tparam C The value type used for costs and potentials in the |
---|
60 | /// algorithm. By default it is the same as \c F. |
---|
61 | /// |
---|
62 | /// \warning Both value types must be signed and all input data must |
---|
63 | /// be integer. |
---|
64 | /// |
---|
65 | /// \note %NetworkSimplex provides five different pivot rule |
---|
66 | /// implementations, from which the most efficient one is used |
---|
67 | /// by default. For more information see \ref PivotRule. |
---|
68 | template <typename GR, typename F = int, typename C = F> |
---|
69 | class NetworkSimplex |
---|
70 | { |
---|
71 | public: |
---|
72 | |
---|
73 | /// The flow type of the algorithm |
---|
74 | typedef F Flow; |
---|
75 | /// The cost type of the algorithm |
---|
76 | typedef C Cost; |
---|
77 | #ifdef DOXYGEN |
---|
78 | /// The type of the flow map |
---|
79 | typedef GR::ArcMap<Flow> FlowMap; |
---|
80 | /// The type of the potential map |
---|
81 | typedef GR::NodeMap<Cost> PotentialMap; |
---|
82 | #else |
---|
83 | /// The type of the flow map |
---|
84 | typedef typename GR::template ArcMap<Flow> FlowMap; |
---|
85 | /// The type of the potential map |
---|
86 | typedef typename GR::template NodeMap<Cost> PotentialMap; |
---|
87 | #endif |
---|
88 | |
---|
89 | public: |
---|
90 | |
---|
91 | /// \brief Enum type for selecting the pivot rule. |
---|
92 | /// |
---|
93 | /// Enum type for selecting the pivot rule for the \ref run() |
---|
94 | /// function. |
---|
95 | /// |
---|
96 | /// \ref NetworkSimplex provides five different pivot rule |
---|
97 | /// implementations that significantly affect the running time |
---|
98 | /// of the algorithm. |
---|
99 | /// By default \ref BLOCK_SEARCH "Block Search" is used, which |
---|
100 | /// proved to be the most efficient and the most robust on various |
---|
101 | /// test inputs according to our benchmark tests. |
---|
102 | /// However another pivot rule can be selected using the \ref run() |
---|
103 | /// function with the proper parameter. |
---|
104 | enum PivotRule { |
---|
105 | |
---|
106 | /// The First Eligible pivot rule. |
---|
107 | /// The next eligible arc is selected in a wraparound fashion |
---|
108 | /// in every iteration. |
---|
109 | FIRST_ELIGIBLE, |
---|
110 | |
---|
111 | /// The Best Eligible pivot rule. |
---|
112 | /// The best eligible arc is selected in every iteration. |
---|
113 | BEST_ELIGIBLE, |
---|
114 | |
---|
115 | /// The Block Search pivot rule. |
---|
116 | /// A specified number of arcs are examined in every iteration |
---|
117 | /// in a wraparound fashion and the best eligible arc is selected |
---|
118 | /// from this block. |
---|
119 | BLOCK_SEARCH, |
---|
120 | |
---|
121 | /// The Candidate List pivot rule. |
---|
122 | /// In a major iteration a candidate list is built from eligible arcs |
---|
123 | /// in a wraparound fashion and in the following minor iterations |
---|
124 | /// the best eligible arc is selected from this list. |
---|
125 | CANDIDATE_LIST, |
---|
126 | |
---|
127 | /// The Altering Candidate List pivot rule. |
---|
128 | /// It is a modified version of the Candidate List method. |
---|
129 | /// It keeps only the several best eligible arcs from the former |
---|
130 | /// candidate list and extends this list in every iteration. |
---|
131 | ALTERING_LIST |
---|
132 | }; |
---|
133 | |
---|
134 | /// \brief Enum type for selecting the problem type. |
---|
135 | /// |
---|
136 | /// Enum type for selecting the problem type, i.e. the direction of |
---|
137 | /// the inequalities in the supply/demand constraints of the |
---|
138 | /// \ref min_cost_flow "minimum cost flow problem". |
---|
139 | /// |
---|
140 | /// The default problem type is \c GEQ, since this form is supported |
---|
141 | /// by other minimum cost flow algorithms and the \ref Circulation |
---|
142 | /// algorithm as well. |
---|
143 | /// The \c LEQ problem type can be selected using the \ref problemType() |
---|
144 | /// function. |
---|
145 | /// |
---|
146 | /// Note that the equality form is a special case of both problem type. |
---|
147 | enum ProblemType { |
---|
148 | |
---|
149 | /// This option means that there are "<em>greater or equal</em>" |
---|
150 | /// constraints in the defintion, i.e. the exact formulation of the |
---|
151 | /// problem is the following. |
---|
152 | /** |
---|
153 | \f[ \min\sum_{uv\in A} f(uv) \cdot cost(uv) \f] |
---|
154 | \f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \geq |
---|
155 | sup(u) \quad \forall u\in V \f] |
---|
156 | \f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f] |
---|
157 | */ |
---|
158 | /// It means that the total demand must be greater or equal to the |
---|
159 | /// total supply (i.e. \f$\sum_{u\in V} sup(u)\f$ must be zero or |
---|
160 | /// negative) and all the supplies have to be carried out from |
---|
161 | /// the supply nodes, but there could be demands that are not |
---|
162 | /// satisfied. |
---|
163 | GEQ, |
---|
164 | /// It is just an alias for the \c GEQ option. |
---|
165 | CARRY_SUPPLIES = GEQ, |
---|
166 | |
---|
167 | /// This option means that there are "<em>less or equal</em>" |
---|
168 | /// constraints in the defintion, i.e. the exact formulation of the |
---|
169 | /// problem is the following. |
---|
170 | /** |
---|
171 | \f[ \min\sum_{uv\in A} f(uv) \cdot cost(uv) \f] |
---|
172 | \f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \leq |
---|
173 | sup(u) \quad \forall u\in V \f] |
---|
174 | \f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f] |
---|
175 | */ |
---|
176 | /// It means that the total demand must be less or equal to the |
---|
177 | /// total supply (i.e. \f$\sum_{u\in V} sup(u)\f$ must be zero or |
---|
178 | /// positive) and all the demands have to be satisfied, but there |
---|
179 | /// could be supplies that are not carried out from the supply |
---|
180 | /// nodes. |
---|
181 | LEQ, |
---|
182 | /// It is just an alias for the \c LEQ option. |
---|
183 | SATISFY_DEMANDS = LEQ |
---|
184 | }; |
---|
185 | |
---|
186 | private: |
---|
187 | |
---|
188 | TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
---|
189 | |
---|
190 | typedef typename GR::template ArcMap<Flow> FlowArcMap; |
---|
191 | typedef typename GR::template ArcMap<Cost> CostArcMap; |
---|
192 | typedef typename GR::template NodeMap<Flow> FlowNodeMap; |
---|
193 | |
---|
194 | typedef std::vector<Arc> ArcVector; |
---|
195 | typedef std::vector<Node> NodeVector; |
---|
196 | typedef std::vector<int> IntVector; |
---|
197 | typedef std::vector<bool> BoolVector; |
---|
198 | typedef std::vector<Flow> FlowVector; |
---|
199 | typedef std::vector<Cost> CostVector; |
---|
200 | |
---|
201 | // State constants for arcs |
---|
202 | enum ArcStateEnum { |
---|
203 | STATE_UPPER = -1, |
---|
204 | STATE_TREE = 0, |
---|
205 | STATE_LOWER = 1 |
---|
206 | }; |
---|
207 | |
---|
208 | private: |
---|
209 | |
---|
210 | // Data related to the underlying digraph |
---|
211 | const GR &_graph; |
---|
212 | int _node_num; |
---|
213 | int _arc_num; |
---|
214 | |
---|
215 | // Parameters of the problem |
---|
216 | FlowArcMap *_plower; |
---|
217 | FlowArcMap *_pupper; |
---|
218 | CostArcMap *_pcost; |
---|
219 | FlowNodeMap *_psupply; |
---|
220 | bool _pstsup; |
---|
221 | Node _psource, _ptarget; |
---|
222 | Flow _pstflow; |
---|
223 | ProblemType _ptype; |
---|
224 | |
---|
225 | // Result maps |
---|
226 | FlowMap *_flow_map; |
---|
227 | PotentialMap *_potential_map; |
---|
228 | bool _local_flow; |
---|
229 | bool _local_potential; |
---|
230 | |
---|
231 | // Data structures for storing the digraph |
---|
232 | IntNodeMap _node_id; |
---|
233 | ArcVector _arc_ref; |
---|
234 | IntVector _source; |
---|
235 | IntVector _target; |
---|
236 | |
---|
237 | // Node and arc data |
---|
238 | FlowVector _cap; |
---|
239 | CostVector _cost; |
---|
240 | FlowVector _supply; |
---|
241 | FlowVector _flow; |
---|
242 | CostVector _pi; |
---|
243 | |
---|
244 | // Data for storing the spanning tree structure |
---|
245 | IntVector _parent; |
---|
246 | IntVector _pred; |
---|
247 | IntVector _thread; |
---|
248 | IntVector _rev_thread; |
---|
249 | IntVector _succ_num; |
---|
250 | IntVector _last_succ; |
---|
251 | IntVector _dirty_revs; |
---|
252 | BoolVector _forward; |
---|
253 | IntVector _state; |
---|
254 | int _root; |
---|
255 | |
---|
256 | // Temporary data used in the current pivot iteration |
---|
257 | int in_arc, join, u_in, v_in, u_out, v_out; |
---|
258 | int first, second, right, last; |
---|
259 | int stem, par_stem, new_stem; |
---|
260 | Flow delta; |
---|
261 | |
---|
262 | private: |
---|
263 | |
---|
264 | // Implementation of the First Eligible pivot rule |
---|
265 | class FirstEligiblePivotRule |
---|
266 | { |
---|
267 | private: |
---|
268 | |
---|
269 | // References to the NetworkSimplex class |
---|
270 | const IntVector &_source; |
---|
271 | const IntVector &_target; |
---|
272 | const CostVector &_cost; |
---|
273 | const IntVector &_state; |
---|
274 | const CostVector &_pi; |
---|
275 | int &_in_arc; |
---|
276 | int _arc_num; |
---|
277 | |
---|
278 | // Pivot rule data |
---|
279 | int _next_arc; |
---|
280 | |
---|
281 | public: |
---|
282 | |
---|
283 | // Constructor |
---|
284 | FirstEligiblePivotRule(NetworkSimplex &ns) : |
---|
285 | _source(ns._source), _target(ns._target), |
---|
286 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
---|
287 | _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0) |
---|
288 | {} |
---|
289 | |
---|
290 | // Find next entering arc |
---|
291 | bool findEnteringArc() { |
---|
292 | Cost c; |
---|
293 | for (int e = _next_arc; e < _arc_num; ++e) { |
---|
294 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
295 | if (c < 0) { |
---|
296 | _in_arc = e; |
---|
297 | _next_arc = e + 1; |
---|
298 | return true; |
---|
299 | } |
---|
300 | } |
---|
301 | for (int e = 0; e < _next_arc; ++e) { |
---|
302 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
303 | if (c < 0) { |
---|
304 | _in_arc = e; |
---|
305 | _next_arc = e + 1; |
---|
306 | return true; |
---|
307 | } |
---|
308 | } |
---|
309 | return false; |
---|
310 | } |
---|
311 | |
---|
312 | }; //class FirstEligiblePivotRule |
---|
313 | |
---|
314 | |
---|
315 | // Implementation of the Best Eligible pivot rule |
---|
316 | class BestEligiblePivotRule |
---|
317 | { |
---|
318 | private: |
---|
319 | |
---|
320 | // References to the NetworkSimplex class |
---|
321 | const IntVector &_source; |
---|
322 | const IntVector &_target; |
---|
323 | const CostVector &_cost; |
---|
324 | const IntVector &_state; |
---|
325 | const CostVector &_pi; |
---|
326 | int &_in_arc; |
---|
327 | int _arc_num; |
---|
328 | |
---|
329 | public: |
---|
330 | |
---|
331 | // Constructor |
---|
332 | BestEligiblePivotRule(NetworkSimplex &ns) : |
---|
333 | _source(ns._source), _target(ns._target), |
---|
334 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
---|
335 | _in_arc(ns.in_arc), _arc_num(ns._arc_num) |
---|
336 | {} |
---|
337 | |
---|
338 | // Find next entering arc |
---|
339 | bool findEnteringArc() { |
---|
340 | Cost c, min = 0; |
---|
341 | for (int e = 0; e < _arc_num; ++e) { |
---|
342 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
343 | if (c < min) { |
---|
344 | min = c; |
---|
345 | _in_arc = e; |
---|
346 | } |
---|
347 | } |
---|
348 | return min < 0; |
---|
349 | } |
---|
350 | |
---|
351 | }; //class BestEligiblePivotRule |
---|
352 | |
---|
353 | |
---|
354 | // Implementation of the Block Search pivot rule |
---|
355 | class BlockSearchPivotRule |
---|
356 | { |
---|
357 | private: |
---|
358 | |
---|
359 | // References to the NetworkSimplex class |
---|
360 | const IntVector &_source; |
---|
361 | const IntVector &_target; |
---|
362 | const CostVector &_cost; |
---|
363 | const IntVector &_state; |
---|
364 | const CostVector &_pi; |
---|
365 | int &_in_arc; |
---|
366 | int _arc_num; |
---|
367 | |
---|
368 | // Pivot rule data |
---|
369 | int _block_size; |
---|
370 | int _next_arc; |
---|
371 | |
---|
372 | public: |
---|
373 | |
---|
374 | // Constructor |
---|
375 | BlockSearchPivotRule(NetworkSimplex &ns) : |
---|
376 | _source(ns._source), _target(ns._target), |
---|
377 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
---|
378 | _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0) |
---|
379 | { |
---|
380 | // The main parameters of the pivot rule |
---|
381 | const double BLOCK_SIZE_FACTOR = 2.0; |
---|
382 | const int MIN_BLOCK_SIZE = 10; |
---|
383 | |
---|
384 | _block_size = std::max( int(BLOCK_SIZE_FACTOR * |
---|
385 | std::sqrt(double(_arc_num))), |
---|
386 | MIN_BLOCK_SIZE ); |
---|
387 | } |
---|
388 | |
---|
389 | // Find next entering arc |
---|
390 | bool findEnteringArc() { |
---|
391 | Cost c, min = 0; |
---|
392 | int cnt = _block_size; |
---|
393 | int e, min_arc = _next_arc; |
---|
394 | for (e = _next_arc; e < _arc_num; ++e) { |
---|
395 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
396 | if (c < min) { |
---|
397 | min = c; |
---|
398 | min_arc = e; |
---|
399 | } |
---|
400 | if (--cnt == 0) { |
---|
401 | if (min < 0) break; |
---|
402 | cnt = _block_size; |
---|
403 | } |
---|
404 | } |
---|
405 | if (min == 0 || cnt > 0) { |
---|
406 | for (e = 0; e < _next_arc; ++e) { |
---|
407 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
408 | if (c < min) { |
---|
409 | min = c; |
---|
410 | min_arc = e; |
---|
411 | } |
---|
412 | if (--cnt == 0) { |
---|
413 | if (min < 0) break; |
---|
414 | cnt = _block_size; |
---|
415 | } |
---|
416 | } |
---|
417 | } |
---|
418 | if (min >= 0) return false; |
---|
419 | _in_arc = min_arc; |
---|
420 | _next_arc = e; |
---|
421 | return true; |
---|
422 | } |
---|
423 | |
---|
424 | }; //class BlockSearchPivotRule |
---|
425 | |
---|
426 | |
---|
427 | // Implementation of the Candidate List pivot rule |
---|
428 | class CandidateListPivotRule |
---|
429 | { |
---|
430 | private: |
---|
431 | |
---|
432 | // References to the NetworkSimplex class |
---|
433 | const IntVector &_source; |
---|
434 | const IntVector &_target; |
---|
435 | const CostVector &_cost; |
---|
436 | const IntVector &_state; |
---|
437 | const CostVector &_pi; |
---|
438 | int &_in_arc; |
---|
439 | int _arc_num; |
---|
440 | |
---|
441 | // Pivot rule data |
---|
442 | IntVector _candidates; |
---|
443 | int _list_length, _minor_limit; |
---|
444 | int _curr_length, _minor_count; |
---|
445 | int _next_arc; |
---|
446 | |
---|
447 | public: |
---|
448 | |
---|
449 | /// Constructor |
---|
450 | CandidateListPivotRule(NetworkSimplex &ns) : |
---|
451 | _source(ns._source), _target(ns._target), |
---|
452 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
---|
453 | _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0) |
---|
454 | { |
---|
455 | // The main parameters of the pivot rule |
---|
456 | const double LIST_LENGTH_FACTOR = 1.0; |
---|
457 | const int MIN_LIST_LENGTH = 10; |
---|
458 | const double MINOR_LIMIT_FACTOR = 0.1; |
---|
459 | const int MIN_MINOR_LIMIT = 3; |
---|
460 | |
---|
461 | _list_length = std::max( int(LIST_LENGTH_FACTOR * |
---|
462 | std::sqrt(double(_arc_num))), |
---|
463 | MIN_LIST_LENGTH ); |
---|
464 | _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length), |
---|
465 | MIN_MINOR_LIMIT ); |
---|
466 | _curr_length = _minor_count = 0; |
---|
467 | _candidates.resize(_list_length); |
---|
468 | } |
---|
469 | |
---|
470 | /// Find next entering arc |
---|
471 | bool findEnteringArc() { |
---|
472 | Cost min, c; |
---|
473 | int e, min_arc = _next_arc; |
---|
474 | if (_curr_length > 0 && _minor_count < _minor_limit) { |
---|
475 | // Minor iteration: select the best eligible arc from the |
---|
476 | // current candidate list |
---|
477 | ++_minor_count; |
---|
478 | min = 0; |
---|
479 | for (int i = 0; i < _curr_length; ++i) { |
---|
480 | e = _candidates[i]; |
---|
481 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
482 | if (c < min) { |
---|
483 | min = c; |
---|
484 | min_arc = e; |
---|
485 | } |
---|
486 | if (c >= 0) { |
---|
487 | _candidates[i--] = _candidates[--_curr_length]; |
---|
488 | } |
---|
489 | } |
---|
490 | if (min < 0) { |
---|
491 | _in_arc = min_arc; |
---|
492 | return true; |
---|
493 | } |
---|
494 | } |
---|
495 | |
---|
496 | // Major iteration: build a new candidate list |
---|
497 | min = 0; |
---|
498 | _curr_length = 0; |
---|
499 | for (e = _next_arc; e < _arc_num; ++e) { |
---|
500 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
501 | if (c < 0) { |
---|
502 | _candidates[_curr_length++] = e; |
---|
503 | if (c < min) { |
---|
504 | min = c; |
---|
505 | min_arc = e; |
---|
506 | } |
---|
507 | if (_curr_length == _list_length) break; |
---|
508 | } |
---|
509 | } |
---|
510 | if (_curr_length < _list_length) { |
---|
511 | for (e = 0; e < _next_arc; ++e) { |
---|
512 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
513 | if (c < 0) { |
---|
514 | _candidates[_curr_length++] = e; |
---|
515 | if (c < min) { |
---|
516 | min = c; |
---|
517 | min_arc = e; |
---|
518 | } |
---|
519 | if (_curr_length == _list_length) break; |
---|
520 | } |
---|
521 | } |
---|
522 | } |
---|
523 | if (_curr_length == 0) return false; |
---|
524 | _minor_count = 1; |
---|
525 | _in_arc = min_arc; |
---|
526 | _next_arc = e; |
---|
527 | return true; |
---|
528 | } |
---|
529 | |
---|
530 | }; //class CandidateListPivotRule |
---|
531 | |
---|
532 | |
---|
533 | // Implementation of the Altering Candidate List pivot rule |
---|
534 | class AlteringListPivotRule |
---|
535 | { |
---|
536 | private: |
---|
537 | |
---|
538 | // References to the NetworkSimplex class |
---|
539 | const IntVector &_source; |
---|
540 | const IntVector &_target; |
---|
541 | const CostVector &_cost; |
---|
542 | const IntVector &_state; |
---|
543 | const CostVector &_pi; |
---|
544 | int &_in_arc; |
---|
545 | int _arc_num; |
---|
546 | |
---|
547 | // Pivot rule data |
---|
548 | int _block_size, _head_length, _curr_length; |
---|
549 | int _next_arc; |
---|
550 | IntVector _candidates; |
---|
551 | CostVector _cand_cost; |
---|
552 | |
---|
553 | // Functor class to compare arcs during sort of the candidate list |
---|
554 | class SortFunc |
---|
555 | { |
---|
556 | private: |
---|
557 | const CostVector &_map; |
---|
558 | public: |
---|
559 | SortFunc(const CostVector &map) : _map(map) {} |
---|
560 | bool operator()(int left, int right) { |
---|
561 | return _map[left] > _map[right]; |
---|
562 | } |
---|
563 | }; |
---|
564 | |
---|
565 | SortFunc _sort_func; |
---|
566 | |
---|
567 | public: |
---|
568 | |
---|
569 | // Constructor |
---|
570 | AlteringListPivotRule(NetworkSimplex &ns) : |
---|
571 | _source(ns._source), _target(ns._target), |
---|
572 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
---|
573 | _in_arc(ns.in_arc), _arc_num(ns._arc_num), |
---|
574 | _next_arc(0), _cand_cost(ns._arc_num), _sort_func(_cand_cost) |
---|
575 | { |
---|
576 | // The main parameters of the pivot rule |
---|
577 | const double BLOCK_SIZE_FACTOR = 1.5; |
---|
578 | const int MIN_BLOCK_SIZE = 10; |
---|
579 | const double HEAD_LENGTH_FACTOR = 0.1; |
---|
580 | const int MIN_HEAD_LENGTH = 3; |
---|
581 | |
---|
582 | _block_size = std::max( int(BLOCK_SIZE_FACTOR * |
---|
583 | std::sqrt(double(_arc_num))), |
---|
584 | MIN_BLOCK_SIZE ); |
---|
585 | _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size), |
---|
586 | MIN_HEAD_LENGTH ); |
---|
587 | _candidates.resize(_head_length + _block_size); |
---|
588 | _curr_length = 0; |
---|
589 | } |
---|
590 | |
---|
591 | // Find next entering arc |
---|
592 | bool findEnteringArc() { |
---|
593 | // Check the current candidate list |
---|
594 | int e; |
---|
595 | for (int i = 0; i < _curr_length; ++i) { |
---|
596 | e = _candidates[i]; |
---|
597 | _cand_cost[e] = _state[e] * |
---|
598 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
599 | if (_cand_cost[e] >= 0) { |
---|
600 | _candidates[i--] = _candidates[--_curr_length]; |
---|
601 | } |
---|
602 | } |
---|
603 | |
---|
604 | // Extend the list |
---|
605 | int cnt = _block_size; |
---|
606 | int last_arc = 0; |
---|
607 | int limit = _head_length; |
---|
608 | |
---|
609 | for (int e = _next_arc; e < _arc_num; ++e) { |
---|
610 | _cand_cost[e] = _state[e] * |
---|
611 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
612 | if (_cand_cost[e] < 0) { |
---|
613 | _candidates[_curr_length++] = e; |
---|
614 | last_arc = e; |
---|
615 | } |
---|
616 | if (--cnt == 0) { |
---|
617 | if (_curr_length > limit) break; |
---|
618 | limit = 0; |
---|
619 | cnt = _block_size; |
---|
620 | } |
---|
621 | } |
---|
622 | if (_curr_length <= limit) { |
---|
623 | for (int e = 0; e < _next_arc; ++e) { |
---|
624 | _cand_cost[e] = _state[e] * |
---|
625 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
---|
626 | if (_cand_cost[e] < 0) { |
---|
627 | _candidates[_curr_length++] = e; |
---|
628 | last_arc = e; |
---|
629 | } |
---|
630 | if (--cnt == 0) { |
---|
631 | if (_curr_length > limit) break; |
---|
632 | limit = 0; |
---|
633 | cnt = _block_size; |
---|
634 | } |
---|
635 | } |
---|
636 | } |
---|
637 | if (_curr_length == 0) return false; |
---|
638 | _next_arc = last_arc + 1; |
---|
639 | |
---|
640 | // Make heap of the candidate list (approximating a partial sort) |
---|
641 | make_heap( _candidates.begin(), _candidates.begin() + _curr_length, |
---|
642 | _sort_func ); |
---|
643 | |
---|
644 | // Pop the first element of the heap |
---|
645 | _in_arc = _candidates[0]; |
---|
646 | pop_heap( _candidates.begin(), _candidates.begin() + _curr_length, |
---|
647 | _sort_func ); |
---|
648 | _curr_length = std::min(_head_length, _curr_length - 1); |
---|
649 | return true; |
---|
650 | } |
---|
651 | |
---|
652 | }; //class AlteringListPivotRule |
---|
653 | |
---|
654 | public: |
---|
655 | |
---|
656 | /// \brief Constructor. |
---|
657 | /// |
---|
658 | /// The constructor of the class. |
---|
659 | /// |
---|
660 | /// \param graph The digraph the algorithm runs on. |
---|
661 | NetworkSimplex(const GR& graph) : |
---|
662 | _graph(graph), |
---|
663 | _plower(NULL), _pupper(NULL), _pcost(NULL), |
---|
664 | _psupply(NULL), _pstsup(false), _ptype(GEQ), |
---|
665 | _flow_map(NULL), _potential_map(NULL), |
---|
666 | _local_flow(false), _local_potential(false), |
---|
667 | _node_id(graph) |
---|
668 | { |
---|
669 | LEMON_ASSERT(std::numeric_limits<Flow>::is_integer && |
---|
670 | std::numeric_limits<Flow>::is_signed, |
---|
671 | "The flow type of NetworkSimplex must be signed integer"); |
---|
672 | LEMON_ASSERT(std::numeric_limits<Cost>::is_integer && |
---|
673 | std::numeric_limits<Cost>::is_signed, |
---|
674 | "The cost type of NetworkSimplex must be signed integer"); |
---|
675 | } |
---|
676 | |
---|
677 | /// Destructor. |
---|
678 | ~NetworkSimplex() { |
---|
679 | if (_local_flow) delete _flow_map; |
---|
680 | if (_local_potential) delete _potential_map; |
---|
681 | } |
---|
682 | |
---|
683 | /// \name Parameters |
---|
684 | /// The parameters of the algorithm can be specified using these |
---|
685 | /// functions. |
---|
686 | |
---|
687 | /// @{ |
---|
688 | |
---|
689 | /// \brief Set the lower bounds on the arcs. |
---|
690 | /// |
---|
691 | /// This function sets the lower bounds on the arcs. |
---|
692 | /// If neither this function nor \ref boundMaps() is used before |
---|
693 | /// calling \ref run(), the lower bounds will be set to zero |
---|
694 | /// on all arcs. |
---|
695 | /// |
---|
696 | /// \param map An arc map storing the lower bounds. |
---|
697 | /// Its \c Value type must be convertible to the \c Flow type |
---|
698 | /// of the algorithm. |
---|
699 | /// |
---|
700 | /// \return <tt>(*this)</tt> |
---|
701 | template <typename LOWER> |
---|
702 | NetworkSimplex& lowerMap(const LOWER& map) { |
---|
703 | delete _plower; |
---|
704 | _plower = new FlowArcMap(_graph); |
---|
705 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
706 | (*_plower)[a] = map[a]; |
---|
707 | } |
---|
708 | return *this; |
---|
709 | } |
---|
710 | |
---|
711 | /// \brief Set the upper bounds (capacities) on the arcs. |
---|
712 | /// |
---|
713 | /// This function sets the upper bounds (capacities) on the arcs. |
---|
714 | /// If none of the functions \ref upperMap(), \ref capacityMap() |
---|
715 | /// and \ref boundMaps() is used before calling \ref run(), |
---|
716 | /// the upper bounds (capacities) will be set to |
---|
717 | /// \c std::numeric_limits<Flow>::max() on all arcs. |
---|
718 | /// |
---|
719 | /// \param map An arc map storing the upper bounds. |
---|
720 | /// Its \c Value type must be convertible to the \c Flow type |
---|
721 | /// of the algorithm. |
---|
722 | /// |
---|
723 | /// \return <tt>(*this)</tt> |
---|
724 | template<typename UPPER> |
---|
725 | NetworkSimplex& upperMap(const UPPER& map) { |
---|
726 | delete _pupper; |
---|
727 | _pupper = new FlowArcMap(_graph); |
---|
728 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
729 | (*_pupper)[a] = map[a]; |
---|
730 | } |
---|
731 | return *this; |
---|
732 | } |
---|
733 | |
---|
734 | /// \brief Set the upper bounds (capacities) on the arcs. |
---|
735 | /// |
---|
736 | /// This function sets the upper bounds (capacities) on the arcs. |
---|
737 | /// It is just an alias for \ref upperMap(). |
---|
738 | /// |
---|
739 | /// \return <tt>(*this)</tt> |
---|
740 | template<typename CAP> |
---|
741 | NetworkSimplex& capacityMap(const CAP& map) { |
---|
742 | return upperMap(map); |
---|
743 | } |
---|
744 | |
---|
745 | /// \brief Set the lower and upper bounds on the arcs. |
---|
746 | /// |
---|
747 | /// This function sets the lower and upper bounds on the arcs. |
---|
748 | /// If neither this function nor \ref lowerMap() is used before |
---|
749 | /// calling \ref run(), the lower bounds will be set to zero |
---|
750 | /// on all arcs. |
---|
751 | /// If none of the functions \ref upperMap(), \ref capacityMap() |
---|
752 | /// and \ref boundMaps() is used before calling \ref run(), |
---|
753 | /// the upper bounds (capacities) will be set to |
---|
754 | /// \c std::numeric_limits<Flow>::max() on all arcs. |
---|
755 | /// |
---|
756 | /// \param lower An arc map storing the lower bounds. |
---|
757 | /// \param upper An arc map storing the upper bounds. |
---|
758 | /// |
---|
759 | /// The \c Value type of the maps must be convertible to the |
---|
760 | /// \c Flow type of the algorithm. |
---|
761 | /// |
---|
762 | /// \note This function is just a shortcut of calling \ref lowerMap() |
---|
763 | /// and \ref upperMap() separately. |
---|
764 | /// |
---|
765 | /// \return <tt>(*this)</tt> |
---|
766 | template <typename LOWER, typename UPPER> |
---|
767 | NetworkSimplex& boundMaps(const LOWER& lower, const UPPER& upper) { |
---|
768 | return lowerMap(lower).upperMap(upper); |
---|
769 | } |
---|
770 | |
---|
771 | /// \brief Set the costs of the arcs. |
---|
772 | /// |
---|
773 | /// This function sets the costs of the arcs. |
---|
774 | /// If it is not used before calling \ref run(), the costs |
---|
775 | /// will be set to \c 1 on all arcs. |
---|
776 | /// |
---|
777 | /// \param map An arc map storing the costs. |
---|
778 | /// Its \c Value type must be convertible to the \c Cost type |
---|
779 | /// of the algorithm. |
---|
780 | /// |
---|
781 | /// \return <tt>(*this)</tt> |
---|
782 | template<typename COST> |
---|
783 | NetworkSimplex& costMap(const COST& map) { |
---|
784 | delete _pcost; |
---|
785 | _pcost = new CostArcMap(_graph); |
---|
786 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
787 | (*_pcost)[a] = map[a]; |
---|
788 | } |
---|
789 | return *this; |
---|
790 | } |
---|
791 | |
---|
792 | /// \brief Set the supply values of the nodes. |
---|
793 | /// |
---|
794 | /// This function sets the supply values of the nodes. |
---|
795 | /// If neither this function nor \ref stSupply() is used before |
---|
796 | /// calling \ref run(), the supply of each node will be set to zero. |
---|
797 | /// (It makes sense only if non-zero lower bounds are given.) |
---|
798 | /// |
---|
799 | /// \param map A node map storing the supply values. |
---|
800 | /// Its \c Value type must be convertible to the \c Flow type |
---|
801 | /// of the algorithm. |
---|
802 | /// |
---|
803 | /// \return <tt>(*this)</tt> |
---|
804 | template<typename SUP> |
---|
805 | NetworkSimplex& supplyMap(const SUP& map) { |
---|
806 | delete _psupply; |
---|
807 | _pstsup = false; |
---|
808 | _psupply = new FlowNodeMap(_graph); |
---|
809 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
810 | (*_psupply)[n] = map[n]; |
---|
811 | } |
---|
812 | return *this; |
---|
813 | } |
---|
814 | |
---|
815 | /// \brief Set single source and target nodes and a supply value. |
---|
816 | /// |
---|
817 | /// This function sets a single source node and a single target node |
---|
818 | /// and the required flow value. |
---|
819 | /// If neither this function nor \ref supplyMap() is used before |
---|
820 | /// calling \ref run(), the supply of each node will be set to zero. |
---|
821 | /// (It makes sense only if non-zero lower bounds are given.) |
---|
822 | /// |
---|
823 | /// \param s The source node. |
---|
824 | /// \param t The target node. |
---|
825 | /// \param k The required amount of flow from node \c s to node \c t |
---|
826 | /// (i.e. the supply of \c s and the demand of \c t). |
---|
827 | /// |
---|
828 | /// \return <tt>(*this)</tt> |
---|
829 | NetworkSimplex& stSupply(const Node& s, const Node& t, Flow k) { |
---|
830 | delete _psupply; |
---|
831 | _psupply = NULL; |
---|
832 | _pstsup = true; |
---|
833 | _psource = s; |
---|
834 | _ptarget = t; |
---|
835 | _pstflow = k; |
---|
836 | return *this; |
---|
837 | } |
---|
838 | |
---|
839 | /// \brief Set the problem type. |
---|
840 | /// |
---|
841 | /// This function sets the problem type for the algorithm. |
---|
842 | /// If it is not used before calling \ref run(), the \ref GEQ problem |
---|
843 | /// type will be used. |
---|
844 | /// |
---|
845 | /// For more information see \ref ProblemType. |
---|
846 | /// |
---|
847 | /// \return <tt>(*this)</tt> |
---|
848 | NetworkSimplex& problemType(ProblemType problem_type) { |
---|
849 | _ptype = problem_type; |
---|
850 | return *this; |
---|
851 | } |
---|
852 | |
---|
853 | /// \brief Set the flow map. |
---|
854 | /// |
---|
855 | /// This function sets the flow map. |
---|
856 | /// If it is not used before calling \ref run(), an instance will |
---|
857 | /// be allocated automatically. The destructor deallocates this |
---|
858 | /// automatically allocated map, of course. |
---|
859 | /// |
---|
860 | /// \return <tt>(*this)</tt> |
---|
861 | NetworkSimplex& flowMap(FlowMap& map) { |
---|
862 | if (_local_flow) { |
---|
863 | delete _flow_map; |
---|
864 | _local_flow = false; |
---|
865 | } |
---|
866 | _flow_map = ↦ |
---|
867 | return *this; |
---|
868 | } |
---|
869 | |
---|
870 | /// \brief Set the potential map. |
---|
871 | /// |
---|
872 | /// This function sets the potential map, which is used for storing |
---|
873 | /// the dual solution. |
---|
874 | /// If it is not used before calling \ref run(), an instance will |
---|
875 | /// be allocated automatically. The destructor deallocates this |
---|
876 | /// automatically allocated map, of course. |
---|
877 | /// |
---|
878 | /// \return <tt>(*this)</tt> |
---|
879 | NetworkSimplex& potentialMap(PotentialMap& map) { |
---|
880 | if (_local_potential) { |
---|
881 | delete _potential_map; |
---|
882 | _local_potential = false; |
---|
883 | } |
---|
884 | _potential_map = ↦ |
---|
885 | return *this; |
---|
886 | } |
---|
887 | |
---|
888 | /// @} |
---|
889 | |
---|
890 | /// \name Execution Control |
---|
891 | /// The algorithm can be executed using \ref run(). |
---|
892 | |
---|
893 | /// @{ |
---|
894 | |
---|
895 | /// \brief Run the algorithm. |
---|
896 | /// |
---|
897 | /// This function runs the algorithm. |
---|
898 | /// The paramters can be specified using functions \ref lowerMap(), |
---|
899 | /// \ref upperMap(), \ref capacityMap(), \ref boundMaps(), |
---|
900 | /// \ref costMap(), \ref supplyMap(), \ref stSupply(), |
---|
901 | /// \ref problemType(), \ref flowMap() and \ref potentialMap(). |
---|
902 | /// For example, |
---|
903 | /// \code |
---|
904 | /// NetworkSimplex<ListDigraph> ns(graph); |
---|
905 | /// ns.boundMaps(lower, upper).costMap(cost) |
---|
906 | /// .supplyMap(sup).run(); |
---|
907 | /// \endcode |
---|
908 | /// |
---|
909 | /// This function can be called more than once. All the parameters |
---|
910 | /// that have been given are kept for the next call, unless |
---|
911 | /// \ref reset() is called, thus only the modified parameters |
---|
912 | /// have to be set again. See \ref reset() for examples. |
---|
913 | /// |
---|
914 | /// \param pivot_rule The pivot rule that will be used during the |
---|
915 | /// algorithm. For more information see \ref PivotRule. |
---|
916 | /// |
---|
917 | /// \return \c true if a feasible flow can be found. |
---|
918 | bool run(PivotRule pivot_rule = BLOCK_SEARCH) { |
---|
919 | return init() && start(pivot_rule); |
---|
920 | } |
---|
921 | |
---|
922 | /// \brief Reset all the parameters that have been given before. |
---|
923 | /// |
---|
924 | /// This function resets all the paramaters that have been given |
---|
925 | /// before using functions \ref lowerMap(), \ref upperMap(), |
---|
926 | /// \ref capacityMap(), \ref boundMaps(), \ref costMap(), |
---|
927 | /// \ref supplyMap(), \ref stSupply(), \ref problemType(), |
---|
928 | /// \ref flowMap() and \ref potentialMap(). |
---|
929 | /// |
---|
930 | /// It is useful for multiple run() calls. If this function is not |
---|
931 | /// used, all the parameters given before are kept for the next |
---|
932 | /// \ref run() call. |
---|
933 | /// |
---|
934 | /// For example, |
---|
935 | /// \code |
---|
936 | /// NetworkSimplex<ListDigraph> ns(graph); |
---|
937 | /// |
---|
938 | /// // First run |
---|
939 | /// ns.lowerMap(lower).capacityMap(cap).costMap(cost) |
---|
940 | /// .supplyMap(sup).run(); |
---|
941 | /// |
---|
942 | /// // Run again with modified cost map (reset() is not called, |
---|
943 | /// // so only the cost map have to be set again) |
---|
944 | /// cost[e] += 100; |
---|
945 | /// ns.costMap(cost).run(); |
---|
946 | /// |
---|
947 | /// // Run again from scratch using reset() |
---|
948 | /// // (the lower bounds will be set to zero on all arcs) |
---|
949 | /// ns.reset(); |
---|
950 | /// ns.capacityMap(cap).costMap(cost) |
---|
951 | /// .supplyMap(sup).run(); |
---|
952 | /// \endcode |
---|
953 | /// |
---|
954 | /// \return <tt>(*this)</tt> |
---|
955 | NetworkSimplex& reset() { |
---|
956 | delete _plower; |
---|
957 | delete _pupper; |
---|
958 | delete _pcost; |
---|
959 | delete _psupply; |
---|
960 | _plower = NULL; |
---|
961 | _pupper = NULL; |
---|
962 | _pcost = NULL; |
---|
963 | _psupply = NULL; |
---|
964 | _pstsup = false; |
---|
965 | _ptype = GEQ; |
---|
966 | if (_local_flow) delete _flow_map; |
---|
967 | if (_local_potential) delete _potential_map; |
---|
968 | _flow_map = NULL; |
---|
969 | _potential_map = NULL; |
---|
970 | _local_flow = false; |
---|
971 | _local_potential = false; |
---|
972 | |
---|
973 | return *this; |
---|
974 | } |
---|
975 | |
---|
976 | /// @} |
---|
977 | |
---|
978 | /// \name Query Functions |
---|
979 | /// The results of the algorithm can be obtained using these |
---|
980 | /// functions.\n |
---|
981 | /// The \ref run() function must be called before using them. |
---|
982 | |
---|
983 | /// @{ |
---|
984 | |
---|
985 | /// \brief Return the total cost of the found flow. |
---|
986 | /// |
---|
987 | /// This function returns the total cost of the found flow. |
---|
988 | /// The complexity of the function is O(e). |
---|
989 | /// |
---|
990 | /// \note The return type of the function can be specified as a |
---|
991 | /// template parameter. For example, |
---|
992 | /// \code |
---|
993 | /// ns.totalCost<double>(); |
---|
994 | /// \endcode |
---|
995 | /// It is useful if the total cost cannot be stored in the \c Cost |
---|
996 | /// type of the algorithm, which is the default return type of the |
---|
997 | /// function. |
---|
998 | /// |
---|
999 | /// \pre \ref run() must be called before using this function. |
---|
1000 | template <typename Num> |
---|
1001 | Num totalCost() const { |
---|
1002 | Num c = 0; |
---|
1003 | if (_pcost) { |
---|
1004 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
1005 | c += (*_flow_map)[e] * (*_pcost)[e]; |
---|
1006 | } else { |
---|
1007 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
1008 | c += (*_flow_map)[e]; |
---|
1009 | } |
---|
1010 | return c; |
---|
1011 | } |
---|
1012 | |
---|
1013 | #ifndef DOXYGEN |
---|
1014 | Cost totalCost() const { |
---|
1015 | return totalCost<Cost>(); |
---|
1016 | } |
---|
1017 | #endif |
---|
1018 | |
---|
1019 | /// \brief Return the flow on the given arc. |
---|
1020 | /// |
---|
1021 | /// This function returns the flow on the given arc. |
---|
1022 | /// |
---|
1023 | /// \pre \ref run() must be called before using this function. |
---|
1024 | Flow flow(const Arc& a) const { |
---|
1025 | return (*_flow_map)[a]; |
---|
1026 | } |
---|
1027 | |
---|
1028 | /// \brief Return a const reference to the flow map. |
---|
1029 | /// |
---|
1030 | /// This function returns a const reference to an arc map storing |
---|
1031 | /// the found flow. |
---|
1032 | /// |
---|
1033 | /// \pre \ref run() must be called before using this function. |
---|
1034 | const FlowMap& flowMap() const { |
---|
1035 | return *_flow_map; |
---|
1036 | } |
---|
1037 | |
---|
1038 | /// \brief Return the potential (dual value) of the given node. |
---|
1039 | /// |
---|
1040 | /// This function returns the potential (dual value) of the |
---|
1041 | /// given node. |
---|
1042 | /// |
---|
1043 | /// \pre \ref run() must be called before using this function. |
---|
1044 | Cost potential(const Node& n) const { |
---|
1045 | return (*_potential_map)[n]; |
---|
1046 | } |
---|
1047 | |
---|
1048 | /// \brief Return a const reference to the potential map |
---|
1049 | /// (the dual solution). |
---|
1050 | /// |
---|
1051 | /// This function returns a const reference to a node map storing |
---|
1052 | /// the found potentials, which form the dual solution of the |
---|
1053 | /// \ref min_cost_flow "minimum cost flow" problem. |
---|
1054 | /// |
---|
1055 | /// \pre \ref run() must be called before using this function. |
---|
1056 | const PotentialMap& potentialMap() const { |
---|
1057 | return *_potential_map; |
---|
1058 | } |
---|
1059 | |
---|
1060 | /// @} |
---|
1061 | |
---|
1062 | private: |
---|
1063 | |
---|
1064 | // Initialize internal data structures |
---|
1065 | bool init() { |
---|
1066 | // Initialize result maps |
---|
1067 | if (!_flow_map) { |
---|
1068 | _flow_map = new FlowMap(_graph); |
---|
1069 | _local_flow = true; |
---|
1070 | } |
---|
1071 | if (!_potential_map) { |
---|
1072 | _potential_map = new PotentialMap(_graph); |
---|
1073 | _local_potential = true; |
---|
1074 | } |
---|
1075 | |
---|
1076 | // Initialize vectors |
---|
1077 | _node_num = countNodes(_graph); |
---|
1078 | _arc_num = countArcs(_graph); |
---|
1079 | int all_node_num = _node_num + 1; |
---|
1080 | int all_arc_num = _arc_num + _node_num; |
---|
1081 | if (_node_num == 0) return false; |
---|
1082 | |
---|
1083 | _arc_ref.resize(_arc_num); |
---|
1084 | _source.resize(all_arc_num); |
---|
1085 | _target.resize(all_arc_num); |
---|
1086 | |
---|
1087 | _cap.resize(all_arc_num); |
---|
1088 | _cost.resize(all_arc_num); |
---|
1089 | _supply.resize(all_node_num); |
---|
1090 | _flow.resize(all_arc_num); |
---|
1091 | _pi.resize(all_node_num); |
---|
1092 | |
---|
1093 | _parent.resize(all_node_num); |
---|
1094 | _pred.resize(all_node_num); |
---|
1095 | _forward.resize(all_node_num); |
---|
1096 | _thread.resize(all_node_num); |
---|
1097 | _rev_thread.resize(all_node_num); |
---|
1098 | _succ_num.resize(all_node_num); |
---|
1099 | _last_succ.resize(all_node_num); |
---|
1100 | _state.resize(all_arc_num); |
---|
1101 | |
---|
1102 | // Initialize node related data |
---|
1103 | bool valid_supply = true; |
---|
1104 | Flow sum_supply = 0; |
---|
1105 | if (!_pstsup && !_psupply) { |
---|
1106 | _pstsup = true; |
---|
1107 | _psource = _ptarget = NodeIt(_graph); |
---|
1108 | _pstflow = 0; |
---|
1109 | } |
---|
1110 | if (_psupply) { |
---|
1111 | int i = 0; |
---|
1112 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
---|
1113 | _node_id[n] = i; |
---|
1114 | _supply[i] = (*_psupply)[n]; |
---|
1115 | sum_supply += _supply[i]; |
---|
1116 | } |
---|
1117 | valid_supply = (_ptype == GEQ && sum_supply <= 0) || |
---|
1118 | (_ptype == LEQ && sum_supply >= 0); |
---|
1119 | } else { |
---|
1120 | int i = 0; |
---|
1121 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
---|
1122 | _node_id[n] = i; |
---|
1123 | _supply[i] = 0; |
---|
1124 | } |
---|
1125 | _supply[_node_id[_psource]] = _pstflow; |
---|
1126 | _supply[_node_id[_ptarget]] = -_pstflow; |
---|
1127 | } |
---|
1128 | if (!valid_supply) return false; |
---|
1129 | |
---|
1130 | // Infinite capacity value |
---|
1131 | Flow inf_cap = |
---|
1132 | std::numeric_limits<Flow>::has_infinity ? |
---|
1133 | std::numeric_limits<Flow>::infinity() : |
---|
1134 | std::numeric_limits<Flow>::max(); |
---|
1135 | |
---|
1136 | // Initialize artifical cost |
---|
1137 | Cost art_cost; |
---|
1138 | if (std::numeric_limits<Cost>::is_exact) { |
---|
1139 | art_cost = std::numeric_limits<Cost>::max() / 4 + 1; |
---|
1140 | } else { |
---|
1141 | art_cost = std::numeric_limits<Cost>::min(); |
---|
1142 | for (int i = 0; i != _arc_num; ++i) { |
---|
1143 | if (_cost[i] > art_cost) art_cost = _cost[i]; |
---|
1144 | } |
---|
1145 | art_cost = (art_cost + 1) * _node_num; |
---|
1146 | } |
---|
1147 | |
---|
1148 | // Run Circulation to check if a feasible solution exists |
---|
1149 | typedef ConstMap<Arc, Flow> ConstArcMap; |
---|
1150 | FlowNodeMap *csup = NULL; |
---|
1151 | bool local_csup = false; |
---|
1152 | if (_psupply) { |
---|
1153 | csup = _psupply; |
---|
1154 | } else { |
---|
1155 | csup = new FlowNodeMap(_graph, 0); |
---|
1156 | (*csup)[_psource] = _pstflow; |
---|
1157 | (*csup)[_ptarget] = -_pstflow; |
---|
1158 | local_csup = true; |
---|
1159 | } |
---|
1160 | bool circ_result = false; |
---|
1161 | if (_ptype == GEQ || (_ptype == LEQ && sum_supply == 0)) { |
---|
1162 | // GEQ problem type |
---|
1163 | if (_plower) { |
---|
1164 | if (_pupper) { |
---|
1165 | Circulation<GR, FlowArcMap, FlowArcMap, FlowNodeMap> |
---|
1166 | circ(_graph, *_plower, *_pupper, *csup); |
---|
1167 | circ_result = circ.run(); |
---|
1168 | } else { |
---|
1169 | Circulation<GR, FlowArcMap, ConstArcMap, FlowNodeMap> |
---|
1170 | circ(_graph, *_plower, ConstArcMap(inf_cap), *csup); |
---|
1171 | circ_result = circ.run(); |
---|
1172 | } |
---|
1173 | } else { |
---|
1174 | if (_pupper) { |
---|
1175 | Circulation<GR, ConstArcMap, FlowArcMap, FlowNodeMap> |
---|
1176 | circ(_graph, ConstArcMap(0), *_pupper, *csup); |
---|
1177 | circ_result = circ.run(); |
---|
1178 | } else { |
---|
1179 | Circulation<GR, ConstArcMap, ConstArcMap, FlowNodeMap> |
---|
1180 | circ(_graph, ConstArcMap(0), ConstArcMap(inf_cap), *csup); |
---|
1181 | circ_result = circ.run(); |
---|
1182 | } |
---|
1183 | } |
---|
1184 | } else { |
---|
1185 | // LEQ problem type |
---|
1186 | typedef ReverseDigraph<const GR> RevGraph; |
---|
1187 | typedef NegMap<FlowNodeMap> NegNodeMap; |
---|
1188 | RevGraph rgraph(_graph); |
---|
1189 | NegNodeMap neg_csup(*csup); |
---|
1190 | if (_plower) { |
---|
1191 | if (_pupper) { |
---|
1192 | Circulation<RevGraph, FlowArcMap, FlowArcMap, NegNodeMap> |
---|
1193 | circ(rgraph, *_plower, *_pupper, neg_csup); |
---|
1194 | circ_result = circ.run(); |
---|
1195 | } else { |
---|
1196 | Circulation<RevGraph, FlowArcMap, ConstArcMap, NegNodeMap> |
---|
1197 | circ(rgraph, *_plower, ConstArcMap(inf_cap), neg_csup); |
---|
1198 | circ_result = circ.run(); |
---|
1199 | } |
---|
1200 | } else { |
---|
1201 | if (_pupper) { |
---|
1202 | Circulation<RevGraph, ConstArcMap, FlowArcMap, NegNodeMap> |
---|
1203 | circ(rgraph, ConstArcMap(0), *_pupper, neg_csup); |
---|
1204 | circ_result = circ.run(); |
---|
1205 | } else { |
---|
1206 | Circulation<RevGraph, ConstArcMap, ConstArcMap, NegNodeMap> |
---|
1207 | circ(rgraph, ConstArcMap(0), ConstArcMap(inf_cap), neg_csup); |
---|
1208 | circ_result = circ.run(); |
---|
1209 | } |
---|
1210 | } |
---|
1211 | } |
---|
1212 | if (local_csup) delete csup; |
---|
1213 | if (!circ_result) return false; |
---|
1214 | |
---|
1215 | // Set data for the artificial root node |
---|
1216 | _root = _node_num; |
---|
1217 | _parent[_root] = -1; |
---|
1218 | _pred[_root] = -1; |
---|
1219 | _thread[_root] = 0; |
---|
1220 | _rev_thread[0] = _root; |
---|
1221 | _succ_num[_root] = all_node_num; |
---|
1222 | _last_succ[_root] = _root - 1; |
---|
1223 | _supply[_root] = -sum_supply; |
---|
1224 | if (sum_supply < 0) { |
---|
1225 | _pi[_root] = -art_cost; |
---|
1226 | } else { |
---|
1227 | _pi[_root] = art_cost; |
---|
1228 | } |
---|
1229 | |
---|
1230 | // Store the arcs in a mixed order |
---|
1231 | int k = std::max(int(std::sqrt(double(_arc_num))), 10); |
---|
1232 | int i = 0; |
---|
1233 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
1234 | _arc_ref[i] = e; |
---|
1235 | if ((i += k) >= _arc_num) i = (i % k) + 1; |
---|
1236 | } |
---|
1237 | |
---|
1238 | // Initialize arc maps |
---|
1239 | if (_pupper && _pcost) { |
---|
1240 | for (int i = 0; i != _arc_num; ++i) { |
---|
1241 | Arc e = _arc_ref[i]; |
---|
1242 | _source[i] = _node_id[_graph.source(e)]; |
---|
1243 | _target[i] = _node_id[_graph.target(e)]; |
---|
1244 | _cap[i] = (*_pupper)[e]; |
---|
1245 | _cost[i] = (*_pcost)[e]; |
---|
1246 | _flow[i] = 0; |
---|
1247 | _state[i] = STATE_LOWER; |
---|
1248 | } |
---|
1249 | } else { |
---|
1250 | for (int i = 0; i != _arc_num; ++i) { |
---|
1251 | Arc e = _arc_ref[i]; |
---|
1252 | _source[i] = _node_id[_graph.source(e)]; |
---|
1253 | _target[i] = _node_id[_graph.target(e)]; |
---|
1254 | _flow[i] = 0; |
---|
1255 | _state[i] = STATE_LOWER; |
---|
1256 | } |
---|
1257 | if (_pupper) { |
---|
1258 | for (int i = 0; i != _arc_num; ++i) |
---|
1259 | _cap[i] = (*_pupper)[_arc_ref[i]]; |
---|
1260 | } else { |
---|
1261 | for (int i = 0; i != _arc_num; ++i) |
---|
1262 | _cap[i] = inf_cap; |
---|
1263 | } |
---|
1264 | if (_pcost) { |
---|
1265 | for (int i = 0; i != _arc_num; ++i) |
---|
1266 | _cost[i] = (*_pcost)[_arc_ref[i]]; |
---|
1267 | } else { |
---|
1268 | for (int i = 0; i != _arc_num; ++i) |
---|
1269 | _cost[i] = 1; |
---|
1270 | } |
---|
1271 | } |
---|
1272 | |
---|
1273 | // Remove non-zero lower bounds |
---|
1274 | if (_plower) { |
---|
1275 | for (int i = 0; i != _arc_num; ++i) { |
---|
1276 | Flow c = (*_plower)[_arc_ref[i]]; |
---|
1277 | if (c != 0) { |
---|
1278 | _cap[i] -= c; |
---|
1279 | _supply[_source[i]] -= c; |
---|
1280 | _supply[_target[i]] += c; |
---|
1281 | } |
---|
1282 | } |
---|
1283 | } |
---|
1284 | |
---|
1285 | // Add artificial arcs and initialize the spanning tree data structure |
---|
1286 | for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { |
---|
1287 | _thread[u] = u + 1; |
---|
1288 | _rev_thread[u + 1] = u; |
---|
1289 | _succ_num[u] = 1; |
---|
1290 | _last_succ[u] = u; |
---|
1291 | _parent[u] = _root; |
---|
1292 | _pred[u] = e; |
---|
1293 | _cost[e] = art_cost; |
---|
1294 | _cap[e] = inf_cap; |
---|
1295 | _state[e] = STATE_TREE; |
---|
1296 | if (_supply[u] > 0 || (_supply[u] == 0 && sum_supply <= 0)) { |
---|
1297 | _flow[e] = _supply[u]; |
---|
1298 | _forward[u] = true; |
---|
1299 | _pi[u] = -art_cost + _pi[_root]; |
---|
1300 | } else { |
---|
1301 | _flow[e] = -_supply[u]; |
---|
1302 | _forward[u] = false; |
---|
1303 | _pi[u] = art_cost + _pi[_root]; |
---|
1304 | } |
---|
1305 | } |
---|
1306 | |
---|
1307 | return true; |
---|
1308 | } |
---|
1309 | |
---|
1310 | // Find the join node |
---|
1311 | void findJoinNode() { |
---|
1312 | int u = _source[in_arc]; |
---|
1313 | int v = _target[in_arc]; |
---|
1314 | while (u != v) { |
---|
1315 | if (_succ_num[u] < _succ_num[v]) { |
---|
1316 | u = _parent[u]; |
---|
1317 | } else { |
---|
1318 | v = _parent[v]; |
---|
1319 | } |
---|
1320 | } |
---|
1321 | join = u; |
---|
1322 | } |
---|
1323 | |
---|
1324 | // Find the leaving arc of the cycle and returns true if the |
---|
1325 | // leaving arc is not the same as the entering arc |
---|
1326 | bool findLeavingArc() { |
---|
1327 | // Initialize first and second nodes according to the direction |
---|
1328 | // of the cycle |
---|
1329 | if (_state[in_arc] == STATE_LOWER) { |
---|
1330 | first = _source[in_arc]; |
---|
1331 | second = _target[in_arc]; |
---|
1332 | } else { |
---|
1333 | first = _target[in_arc]; |
---|
1334 | second = _source[in_arc]; |
---|
1335 | } |
---|
1336 | delta = _cap[in_arc]; |
---|
1337 | int result = 0; |
---|
1338 | Flow d; |
---|
1339 | int e; |
---|
1340 | |
---|
1341 | // Search the cycle along the path form the first node to the root |
---|
1342 | for (int u = first; u != join; u = _parent[u]) { |
---|
1343 | e = _pred[u]; |
---|
1344 | d = _forward[u] ? _flow[e] : _cap[e] - _flow[e]; |
---|
1345 | if (d < delta) { |
---|
1346 | delta = d; |
---|
1347 | u_out = u; |
---|
1348 | result = 1; |
---|
1349 | } |
---|
1350 | } |
---|
1351 | // Search the cycle along the path form the second node to the root |
---|
1352 | for (int u = second; u != join; u = _parent[u]) { |
---|
1353 | e = _pred[u]; |
---|
1354 | d = _forward[u] ? _cap[e] - _flow[e] : _flow[e]; |
---|
1355 | if (d <= delta) { |
---|
1356 | delta = d; |
---|
1357 | u_out = u; |
---|
1358 | result = 2; |
---|
1359 | } |
---|
1360 | } |
---|
1361 | |
---|
1362 | if (result == 1) { |
---|
1363 | u_in = first; |
---|
1364 | v_in = second; |
---|
1365 | } else { |
---|
1366 | u_in = second; |
---|
1367 | v_in = first; |
---|
1368 | } |
---|
1369 | return result != 0; |
---|
1370 | } |
---|
1371 | |
---|
1372 | // Change _flow and _state vectors |
---|
1373 | void changeFlow(bool change) { |
---|
1374 | // Augment along the cycle |
---|
1375 | if (delta > 0) { |
---|
1376 | Flow val = _state[in_arc] * delta; |
---|
1377 | _flow[in_arc] += val; |
---|
1378 | for (int u = _source[in_arc]; u != join; u = _parent[u]) { |
---|
1379 | _flow[_pred[u]] += _forward[u] ? -val : val; |
---|
1380 | } |
---|
1381 | for (int u = _target[in_arc]; u != join; u = _parent[u]) { |
---|
1382 | _flow[_pred[u]] += _forward[u] ? val : -val; |
---|
1383 | } |
---|
1384 | } |
---|
1385 | // Update the state of the entering and leaving arcs |
---|
1386 | if (change) { |
---|
1387 | _state[in_arc] = STATE_TREE; |
---|
1388 | _state[_pred[u_out]] = |
---|
1389 | (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER; |
---|
1390 | } else { |
---|
1391 | _state[in_arc] = -_state[in_arc]; |
---|
1392 | } |
---|
1393 | } |
---|
1394 | |
---|
1395 | // Update the tree structure |
---|
1396 | void updateTreeStructure() { |
---|
1397 | int u, w; |
---|
1398 | int old_rev_thread = _rev_thread[u_out]; |
---|
1399 | int old_succ_num = _succ_num[u_out]; |
---|
1400 | int old_last_succ = _last_succ[u_out]; |
---|
1401 | v_out = _parent[u_out]; |
---|
1402 | |
---|
1403 | u = _last_succ[u_in]; // the last successor of u_in |
---|
1404 | right = _thread[u]; // the node after it |
---|
1405 | |
---|
1406 | // Handle the case when old_rev_thread equals to v_in |
---|
1407 | // (it also means that join and v_out coincide) |
---|
1408 | if (old_rev_thread == v_in) { |
---|
1409 | last = _thread[_last_succ[u_out]]; |
---|
1410 | } else { |
---|
1411 | last = _thread[v_in]; |
---|
1412 | } |
---|
1413 | |
---|
1414 | // Update _thread and _parent along the stem nodes (i.e. the nodes |
---|
1415 | // between u_in and u_out, whose parent have to be changed) |
---|
1416 | _thread[v_in] = stem = u_in; |
---|
1417 | _dirty_revs.clear(); |
---|
1418 | _dirty_revs.push_back(v_in); |
---|
1419 | par_stem = v_in; |
---|
1420 | while (stem != u_out) { |
---|
1421 | // Insert the next stem node into the thread list |
---|
1422 | new_stem = _parent[stem]; |
---|
1423 | _thread[u] = new_stem; |
---|
1424 | _dirty_revs.push_back(u); |
---|
1425 | |
---|
1426 | // Remove the subtree of stem from the thread list |
---|
1427 | w = _rev_thread[stem]; |
---|
1428 | _thread[w] = right; |
---|
1429 | _rev_thread[right] = w; |
---|
1430 | |
---|
1431 | // Change the parent node and shift stem nodes |
---|
1432 | _parent[stem] = par_stem; |
---|
1433 | par_stem = stem; |
---|
1434 | stem = new_stem; |
---|
1435 | |
---|
1436 | // Update u and right |
---|
1437 | u = _last_succ[stem] == _last_succ[par_stem] ? |
---|
1438 | _rev_thread[par_stem] : _last_succ[stem]; |
---|
1439 | right = _thread[u]; |
---|
1440 | } |
---|
1441 | _parent[u_out] = par_stem; |
---|
1442 | _thread[u] = last; |
---|
1443 | _rev_thread[last] = u; |
---|
1444 | _last_succ[u_out] = u; |
---|
1445 | |
---|
1446 | // Remove the subtree of u_out from the thread list except for |
---|
1447 | // the case when old_rev_thread equals to v_in |
---|
1448 | // (it also means that join and v_out coincide) |
---|
1449 | if (old_rev_thread != v_in) { |
---|
1450 | _thread[old_rev_thread] = right; |
---|
1451 | _rev_thread[right] = old_rev_thread; |
---|
1452 | } |
---|
1453 | |
---|
1454 | // Update _rev_thread using the new _thread values |
---|
1455 | for (int i = 0; i < int(_dirty_revs.size()); ++i) { |
---|
1456 | u = _dirty_revs[i]; |
---|
1457 | _rev_thread[_thread[u]] = u; |
---|
1458 | } |
---|
1459 | |
---|
1460 | // Update _pred, _forward, _last_succ and _succ_num for the |
---|
1461 | // stem nodes from u_out to u_in |
---|
1462 | int tmp_sc = 0, tmp_ls = _last_succ[u_out]; |
---|
1463 | u = u_out; |
---|
1464 | while (u != u_in) { |
---|
1465 | w = _parent[u]; |
---|
1466 | _pred[u] = _pred[w]; |
---|
1467 | _forward[u] = !_forward[w]; |
---|
1468 | tmp_sc += _succ_num[u] - _succ_num[w]; |
---|
1469 | _succ_num[u] = tmp_sc; |
---|
1470 | _last_succ[w] = tmp_ls; |
---|
1471 | u = w; |
---|
1472 | } |
---|
1473 | _pred[u_in] = in_arc; |
---|
1474 | _forward[u_in] = (u_in == _source[in_arc]); |
---|
1475 | _succ_num[u_in] = old_succ_num; |
---|
1476 | |
---|
1477 | // Set limits for updating _last_succ form v_in and v_out |
---|
1478 | // towards the root |
---|
1479 | int up_limit_in = -1; |
---|
1480 | int up_limit_out = -1; |
---|
1481 | if (_last_succ[join] == v_in) { |
---|
1482 | up_limit_out = join; |
---|
1483 | } else { |
---|
1484 | up_limit_in = join; |
---|
1485 | } |
---|
1486 | |
---|
1487 | // Update _last_succ from v_in towards the root |
---|
1488 | for (u = v_in; u != up_limit_in && _last_succ[u] == v_in; |
---|
1489 | u = _parent[u]) { |
---|
1490 | _last_succ[u] = _last_succ[u_out]; |
---|
1491 | } |
---|
1492 | // Update _last_succ from v_out towards the root |
---|
1493 | if (join != old_rev_thread && v_in != old_rev_thread) { |
---|
1494 | for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; |
---|
1495 | u = _parent[u]) { |
---|
1496 | _last_succ[u] = old_rev_thread; |
---|
1497 | } |
---|
1498 | } else { |
---|
1499 | for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; |
---|
1500 | u = _parent[u]) { |
---|
1501 | _last_succ[u] = _last_succ[u_out]; |
---|
1502 | } |
---|
1503 | } |
---|
1504 | |
---|
1505 | // Update _succ_num from v_in to join |
---|
1506 | for (u = v_in; u != join; u = _parent[u]) { |
---|
1507 | _succ_num[u] += old_succ_num; |
---|
1508 | } |
---|
1509 | // Update _succ_num from v_out to join |
---|
1510 | for (u = v_out; u != join; u = _parent[u]) { |
---|
1511 | _succ_num[u] -= old_succ_num; |
---|
1512 | } |
---|
1513 | } |
---|
1514 | |
---|
1515 | // Update potentials |
---|
1516 | void updatePotential() { |
---|
1517 | Cost sigma = _forward[u_in] ? |
---|
1518 | _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] : |
---|
1519 | _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]]; |
---|
1520 | // Update potentials in the subtree, which has been moved |
---|
1521 | int end = _thread[_last_succ[u_in]]; |
---|
1522 | for (int u = u_in; u != end; u = _thread[u]) { |
---|
1523 | _pi[u] += sigma; |
---|
1524 | } |
---|
1525 | } |
---|
1526 | |
---|
1527 | // Execute the algorithm |
---|
1528 | bool start(PivotRule pivot_rule) { |
---|
1529 | // Select the pivot rule implementation |
---|
1530 | switch (pivot_rule) { |
---|
1531 | case FIRST_ELIGIBLE: |
---|
1532 | return start<FirstEligiblePivotRule>(); |
---|
1533 | case BEST_ELIGIBLE: |
---|
1534 | return start<BestEligiblePivotRule>(); |
---|
1535 | case BLOCK_SEARCH: |
---|
1536 | return start<BlockSearchPivotRule>(); |
---|
1537 | case CANDIDATE_LIST: |
---|
1538 | return start<CandidateListPivotRule>(); |
---|
1539 | case ALTERING_LIST: |
---|
1540 | return start<AlteringListPivotRule>(); |
---|
1541 | } |
---|
1542 | return false; |
---|
1543 | } |
---|
1544 | |
---|
1545 | template <typename PivotRuleImpl> |
---|
1546 | bool start() { |
---|
1547 | PivotRuleImpl pivot(*this); |
---|
1548 | |
---|
1549 | // Execute the Network Simplex algorithm |
---|
1550 | while (pivot.findEnteringArc()) { |
---|
1551 | findJoinNode(); |
---|
1552 | bool change = findLeavingArc(); |
---|
1553 | changeFlow(change); |
---|
1554 | if (change) { |
---|
1555 | updateTreeStructure(); |
---|
1556 | updatePotential(); |
---|
1557 | } |
---|
1558 | } |
---|
1559 | |
---|
1560 | // Copy flow values to _flow_map |
---|
1561 | if (_plower) { |
---|
1562 | for (int i = 0; i != _arc_num; ++i) { |
---|
1563 | Arc e = _arc_ref[i]; |
---|
1564 | _flow_map->set(e, (*_plower)[e] + _flow[i]); |
---|
1565 | } |
---|
1566 | } else { |
---|
1567 | for (int i = 0; i != _arc_num; ++i) { |
---|
1568 | _flow_map->set(_arc_ref[i], _flow[i]); |
---|
1569 | } |
---|
1570 | } |
---|
1571 | // Copy potential values to _potential_map |
---|
1572 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
1573 | _potential_map->set(n, _pi[_node_id[n]]); |
---|
1574 | } |
---|
1575 | |
---|
1576 | return true; |
---|
1577 | } |
---|
1578 | |
---|
1579 | }; //class NetworkSimplex |
---|
1580 | |
---|
1581 | ///@} |
---|
1582 | |
---|
1583 | } //namespace lemon |
---|
1584 | |
---|
1585 | #endif //LEMON_NETWORK_SIMPLEX_H |
---|