1 | /* -*- C++ -*- |
---|
2 | * |
---|
3 | * This file is a part of LEMON, a generic C++ optimization library |
---|
4 | * |
---|
5 | * Copyright (C) 2003-2007 |
---|
6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
8 | * |
---|
9 | * Permission to use, modify and distribute this software is granted |
---|
10 | * provided that this copyright notice appears in all copies. For |
---|
11 | * precise terms see the accompanying LICENSE file. |
---|
12 | * |
---|
13 | * This software is provided "AS IS" with no warranty of any kind, |
---|
14 | * express or implied, and with no claim as to its suitability for any |
---|
15 | * purpose. |
---|
16 | * |
---|
17 | */ |
---|
18 | |
---|
19 | #ifndef LEMON_CAPACITY_SCALING_H |
---|
20 | #define LEMON_CAPACITY_SCALING_H |
---|
21 | |
---|
22 | /// \ingroup min_cost_flow |
---|
23 | /// |
---|
24 | /// \file |
---|
25 | /// \brief The capacity scaling algorithm for finding a minimum cost |
---|
26 | /// flow. |
---|
27 | |
---|
28 | #include <vector> |
---|
29 | #include <lemon/dijkstra.h> |
---|
30 | #include <lemon/graph_adaptor.h> |
---|
31 | |
---|
32 | #define WITH_SCALING |
---|
33 | |
---|
34 | namespace lemon { |
---|
35 | |
---|
36 | /// \addtogroup min_cost_flow |
---|
37 | /// @{ |
---|
38 | |
---|
39 | /// \brief Implementation of the capacity scaling version of the |
---|
40 | /// succesive shortest path algorithm for finding a minimum cost flow. |
---|
41 | /// |
---|
42 | /// \ref lemon::CapacityScaling "CapacityScaling" implements a |
---|
43 | /// capacity scaling algorithm for finding a minimum cost flow. |
---|
44 | /// |
---|
45 | /// \param Graph The directed graph type the algorithm runs on. |
---|
46 | /// \param LowerMap The type of the lower bound map. |
---|
47 | /// \param CapacityMap The type of the capacity (upper bound) map. |
---|
48 | /// \param CostMap The type of the cost (length) map. |
---|
49 | /// \param SupplyMap The type of the supply map. |
---|
50 | /// |
---|
51 | /// \warning |
---|
52 | /// - Edge capacities and costs should be nonnegative integers. |
---|
53 | /// However \c CostMap::Value should be signed type. |
---|
54 | /// - Supply values should be integers. |
---|
55 | /// - \c LowerMap::Value must be convertible to |
---|
56 | /// \c CapacityMap::Value and \c CapacityMap::Value must be |
---|
57 | /// convertible to \c SupplyMap::Value. |
---|
58 | /// |
---|
59 | /// \author Peter Kovacs |
---|
60 | |
---|
61 | template < typename Graph, |
---|
62 | typename LowerMap = typename Graph::template EdgeMap<int>, |
---|
63 | typename CapacityMap = LowerMap, |
---|
64 | typename CostMap = typename Graph::template EdgeMap<int>, |
---|
65 | typename SupplyMap = typename Graph::template NodeMap |
---|
66 | <typename CapacityMap::Value> > |
---|
67 | class CapacityScaling |
---|
68 | { |
---|
69 | typedef typename Graph::Node Node; |
---|
70 | typedef typename Graph::NodeIt NodeIt; |
---|
71 | typedef typename Graph::Edge Edge; |
---|
72 | typedef typename Graph::EdgeIt EdgeIt; |
---|
73 | typedef typename Graph::InEdgeIt InEdgeIt; |
---|
74 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
---|
75 | |
---|
76 | typedef typename LowerMap::Value Lower; |
---|
77 | typedef typename CapacityMap::Value Capacity; |
---|
78 | typedef typename CostMap::Value Cost; |
---|
79 | typedef typename SupplyMap::Value Supply; |
---|
80 | typedef typename Graph::template EdgeMap<Capacity> CapacityRefMap; |
---|
81 | typedef typename Graph::template NodeMap<Supply> SupplyRefMap; |
---|
82 | |
---|
83 | typedef ResGraphAdaptor< const Graph, Capacity, |
---|
84 | CapacityRefMap, CapacityRefMap > ResGraph; |
---|
85 | typedef typename ResGraph::Node ResNode; |
---|
86 | typedef typename ResGraph::NodeIt ResNodeIt; |
---|
87 | typedef typename ResGraph::Edge ResEdge; |
---|
88 | typedef typename ResGraph::EdgeIt ResEdgeIt; |
---|
89 | |
---|
90 | public: |
---|
91 | |
---|
92 | /// \brief The type of the flow map. |
---|
93 | typedef CapacityRefMap FlowMap; |
---|
94 | /// \brief The type of the potential map. |
---|
95 | typedef typename Graph::template NodeMap<Cost> PotentialMap; |
---|
96 | |
---|
97 | protected: |
---|
98 | |
---|
99 | /// \brief Map adaptor class for handling reduced edge costs. |
---|
100 | class ReducedCostMap : public MapBase<ResEdge, Cost> |
---|
101 | { |
---|
102 | private: |
---|
103 | |
---|
104 | const ResGraph &gr; |
---|
105 | const CostMap &cost_map; |
---|
106 | const PotentialMap &pot_map; |
---|
107 | |
---|
108 | public: |
---|
109 | |
---|
110 | typedef typename MapBase<ResEdge, Cost>::Value Value; |
---|
111 | typedef typename MapBase<ResEdge, Cost>::Key Key; |
---|
112 | |
---|
113 | ReducedCostMap( const ResGraph &_gr, |
---|
114 | const CostMap &_cost, |
---|
115 | const PotentialMap &_pot ) : |
---|
116 | gr(_gr), cost_map(_cost), pot_map(_pot) {} |
---|
117 | |
---|
118 | Value operator[](const Key &e) const { |
---|
119 | return ResGraph::forward(e) ? |
---|
120 | cost_map[e] - pot_map[gr.source(e)] + pot_map[gr.target(e)] : |
---|
121 | -cost_map[e] - pot_map[gr.source(e)] + pot_map[gr.target(e)]; |
---|
122 | } |
---|
123 | |
---|
124 | }; //class ReducedCostMap |
---|
125 | |
---|
126 | /// \brief Map adaptor for \ref lemon::Dijkstra "Dijkstra" class to |
---|
127 | /// update node potentials. |
---|
128 | class PotentialUpdateMap : public MapBase<ResNode, Cost> |
---|
129 | { |
---|
130 | private: |
---|
131 | |
---|
132 | PotentialMap *pot; |
---|
133 | typedef std::pair<ResNode, Cost> Pair; |
---|
134 | std::vector<Pair> data; |
---|
135 | |
---|
136 | public: |
---|
137 | |
---|
138 | typedef typename MapBase<ResNode, Cost>::Value Value; |
---|
139 | typedef typename MapBase<ResNode, Cost>::Key Key; |
---|
140 | |
---|
141 | void potentialMap(PotentialMap &_pot) { |
---|
142 | pot = &_pot; |
---|
143 | } |
---|
144 | |
---|
145 | void init() { |
---|
146 | data.clear(); |
---|
147 | } |
---|
148 | |
---|
149 | void set(const Key &n, const Value &v) { |
---|
150 | data.push_back(Pair(n, v)); |
---|
151 | } |
---|
152 | |
---|
153 | void update() { |
---|
154 | Cost val = data[data.size()-1].second; |
---|
155 | for (int i = 0; i < data.size()-1; ++i) |
---|
156 | (*pot)[data[i].first] += val - data[i].second; |
---|
157 | } |
---|
158 | |
---|
159 | }; //class PotentialUpdateMap |
---|
160 | |
---|
161 | #ifdef WITH_SCALING |
---|
162 | /// \brief Map adaptor class for identifing deficit nodes. |
---|
163 | class DeficitBoolMap : public MapBase<ResNode, bool> |
---|
164 | { |
---|
165 | private: |
---|
166 | |
---|
167 | const SupplyRefMap &imb; |
---|
168 | const Capacity δ |
---|
169 | |
---|
170 | public: |
---|
171 | |
---|
172 | DeficitBoolMap(const SupplyRefMap &_imb, const Capacity &_delta) : |
---|
173 | imb(_imb), delta(_delta) {} |
---|
174 | |
---|
175 | bool operator[](const ResNode &n) const { |
---|
176 | return imb[n] <= -delta; |
---|
177 | } |
---|
178 | |
---|
179 | }; //class DeficitBoolMap |
---|
180 | |
---|
181 | /// \brief Map adaptor class for filtering edges with at least |
---|
182 | /// \c delta residual capacity |
---|
183 | class DeltaFilterMap : public MapBase<ResEdge, bool> |
---|
184 | { |
---|
185 | private: |
---|
186 | |
---|
187 | const ResGraph &gr; |
---|
188 | const Capacity δ |
---|
189 | |
---|
190 | public: |
---|
191 | |
---|
192 | typedef typename MapBase<ResEdge, Cost>::Value Value; |
---|
193 | typedef typename MapBase<ResEdge, Cost>::Key Key; |
---|
194 | |
---|
195 | DeltaFilterMap(const ResGraph &_gr, const Capacity &_delta) : |
---|
196 | gr(_gr), delta(_delta) {} |
---|
197 | |
---|
198 | Value operator[](const Key &e) const { |
---|
199 | return gr.rescap(e) >= delta; |
---|
200 | } |
---|
201 | |
---|
202 | }; //class DeltaFilterMap |
---|
203 | |
---|
204 | typedef EdgeSubGraphAdaptor<const ResGraph, const DeltaFilterMap> |
---|
205 | DeltaResGraph; |
---|
206 | |
---|
207 | /// \brief Traits class for \ref lemon::Dijkstra "Dijkstra" class. |
---|
208 | class ResDijkstraTraits : |
---|
209 | public DijkstraDefaultTraits<DeltaResGraph, ReducedCostMap> |
---|
210 | { |
---|
211 | public: |
---|
212 | |
---|
213 | typedef PotentialUpdateMap DistMap; |
---|
214 | |
---|
215 | static DistMap *createDistMap(const DeltaResGraph&) { |
---|
216 | return new DistMap(); |
---|
217 | } |
---|
218 | |
---|
219 | }; //class ResDijkstraTraits |
---|
220 | |
---|
221 | #else //WITHOUT_CAPACITY_SCALING |
---|
222 | /// \brief Map adaptor class for identifing deficit nodes. |
---|
223 | class DeficitBoolMap : public MapBase<ResNode, bool> |
---|
224 | { |
---|
225 | private: |
---|
226 | |
---|
227 | const SupplyRefMap &imb; |
---|
228 | |
---|
229 | public: |
---|
230 | |
---|
231 | DeficitBoolMap(const SupplyRefMap &_imb) : imb(_imb) {} |
---|
232 | |
---|
233 | bool operator[](const ResNode &n) const { |
---|
234 | return imb[n] < 0; |
---|
235 | } |
---|
236 | |
---|
237 | }; //class DeficitBoolMap |
---|
238 | |
---|
239 | /// \brief Traits class for \ref lemon::Dijkstra "Dijkstra" class. |
---|
240 | class ResDijkstraTraits : |
---|
241 | public DijkstraDefaultTraits<ResGraph, ReducedCostMap> |
---|
242 | { |
---|
243 | public: |
---|
244 | |
---|
245 | typedef PotentialUpdateMap DistMap; |
---|
246 | |
---|
247 | static DistMap *createDistMap(const ResGraph&) { |
---|
248 | return new DistMap(); |
---|
249 | } |
---|
250 | |
---|
251 | }; //class ResDijkstraTraits |
---|
252 | #endif |
---|
253 | |
---|
254 | protected: |
---|
255 | |
---|
256 | /// \brief The directed graph the algorithm runs on. |
---|
257 | const Graph &graph; |
---|
258 | /// \brief The original lower bound map. |
---|
259 | const LowerMap *lower; |
---|
260 | /// \brief The modified capacity map. |
---|
261 | CapacityRefMap capacity; |
---|
262 | /// \brief The cost map. |
---|
263 | const CostMap &cost; |
---|
264 | /// \brief The modified supply map. |
---|
265 | SupplyRefMap supply; |
---|
266 | /// \brief The sum of supply values equals zero. |
---|
267 | bool valid_supply; |
---|
268 | |
---|
269 | /// \brief The edge map of the current flow. |
---|
270 | FlowMap flow; |
---|
271 | /// \brief The potential node map. |
---|
272 | PotentialMap potential; |
---|
273 | /// \brief The residual graph. |
---|
274 | ResGraph res_graph; |
---|
275 | /// \brief The reduced cost map. |
---|
276 | ReducedCostMap red_cost; |
---|
277 | |
---|
278 | /// \brief The imbalance map. |
---|
279 | SupplyRefMap imbalance; |
---|
280 | /// \brief The excess nodes. |
---|
281 | std::vector<ResNode> excess_nodes; |
---|
282 | /// \brief The index of the next excess node. |
---|
283 | int next_node; |
---|
284 | |
---|
285 | #ifdef WITH_SCALING |
---|
286 | typedef Dijkstra<DeltaResGraph, ReducedCostMap, ResDijkstraTraits> |
---|
287 | ResDijkstra; |
---|
288 | /// \brief \ref lemon::Dijkstra "Dijkstra" class for finding |
---|
289 | /// shortest paths in the residual graph with respect to the |
---|
290 | /// reduced edge costs. |
---|
291 | ResDijkstra dijkstra; |
---|
292 | |
---|
293 | /// \brief The delta parameter used for capacity scaling. |
---|
294 | Capacity delta; |
---|
295 | /// \brief Edge filter map. |
---|
296 | DeltaFilterMap delta_filter; |
---|
297 | /// \brief The delta residual graph. |
---|
298 | DeltaResGraph dres_graph; |
---|
299 | /// \brief Map for identifing deficit nodes. |
---|
300 | DeficitBoolMap delta_deficit; |
---|
301 | |
---|
302 | #else //WITHOUT_CAPACITY_SCALING |
---|
303 | typedef Dijkstra<ResGraph, ReducedCostMap, ResDijkstraTraits> |
---|
304 | ResDijkstra; |
---|
305 | /// \brief \ref lemon::Dijkstra "Dijkstra" class for finding |
---|
306 | /// shortest paths in the residual graph with respect to the |
---|
307 | /// reduced edge costs. |
---|
308 | ResDijkstra dijkstra; |
---|
309 | /// \brief Map for identifing deficit nodes. |
---|
310 | DeficitBoolMap has_deficit; |
---|
311 | #endif |
---|
312 | |
---|
313 | /// \brief Pred map for the \ref lemon::Dijkstra "Dijkstra" class. |
---|
314 | typename ResDijkstra::PredMap pred; |
---|
315 | /// \brief Dist map for the \ref lemon::Dijkstra "Dijkstra" class to |
---|
316 | /// update node potentials. |
---|
317 | PotentialUpdateMap updater; |
---|
318 | |
---|
319 | public : |
---|
320 | |
---|
321 | /// \brief General constructor of the class (with lower bounds). |
---|
322 | /// |
---|
323 | /// General constructor of the class (with lower bounds). |
---|
324 | /// |
---|
325 | /// \param _graph The directed graph the algorithm runs on. |
---|
326 | /// \param _lower The lower bounds of the edges. |
---|
327 | /// \param _capacity The capacities (upper bounds) of the edges. |
---|
328 | /// \param _cost The cost (length) values of the edges. |
---|
329 | /// \param _supply The supply values of the nodes (signed). |
---|
330 | CapacityScaling( const Graph &_graph, |
---|
331 | const LowerMap &_lower, |
---|
332 | const CapacityMap &_capacity, |
---|
333 | const CostMap &_cost, |
---|
334 | const SupplyMap &_supply ) : |
---|
335 | graph(_graph), lower(&_lower), capacity(_graph), cost(_cost), |
---|
336 | supply(_graph), flow(_graph, 0), potential(_graph, 0), |
---|
337 | res_graph(_graph, capacity, flow), |
---|
338 | red_cost(res_graph, cost, potential), imbalance(_graph), |
---|
339 | #ifdef WITH_SCALING |
---|
340 | delta(0), delta_filter(res_graph, delta), |
---|
341 | dres_graph(res_graph, delta_filter), |
---|
342 | dijkstra(dres_graph, red_cost), pred(dres_graph), |
---|
343 | delta_deficit(imbalance, delta) |
---|
344 | #else //WITHOUT_CAPACITY_SCALING |
---|
345 | dijkstra(res_graph, red_cost), pred(res_graph), |
---|
346 | has_deficit(imbalance) |
---|
347 | #endif |
---|
348 | { |
---|
349 | // Removing nonzero lower bounds |
---|
350 | capacity = subMap(_capacity, _lower); |
---|
351 | Supply sum = 0; |
---|
352 | for (NodeIt n(graph); n != INVALID; ++n) { |
---|
353 | Supply s = _supply[n]; |
---|
354 | for (InEdgeIt e(graph, n); e != INVALID; ++e) |
---|
355 | s += _lower[e]; |
---|
356 | for (OutEdgeIt e(graph, n); e != INVALID; ++e) |
---|
357 | s -= _lower[e]; |
---|
358 | supply[n] = imbalance[n] = s; |
---|
359 | sum += s; |
---|
360 | } |
---|
361 | valid_supply = sum == 0; |
---|
362 | } |
---|
363 | |
---|
364 | /// \brief General constructor of the class (without lower bounds). |
---|
365 | /// |
---|
366 | /// General constructor of the class (without lower bounds). |
---|
367 | /// |
---|
368 | /// \param _graph The directed graph the algorithm runs on. |
---|
369 | /// \param _capacity The capacities (upper bounds) of the edges. |
---|
370 | /// \param _cost The cost (length) values of the edges. |
---|
371 | /// \param _supply The supply values of the nodes (signed). |
---|
372 | CapacityScaling( const Graph &_graph, |
---|
373 | const CapacityMap &_capacity, |
---|
374 | const CostMap &_cost, |
---|
375 | const SupplyMap &_supply ) : |
---|
376 | graph(_graph), lower(NULL), capacity(_capacity), cost(_cost), |
---|
377 | supply(_supply), flow(_graph, 0), potential(_graph, 0), |
---|
378 | res_graph(_graph, capacity, flow), |
---|
379 | red_cost(res_graph, cost, potential), imbalance(_graph), |
---|
380 | #ifdef WITH_SCALING |
---|
381 | delta(0), delta_filter(res_graph, delta), |
---|
382 | dres_graph(res_graph, delta_filter), |
---|
383 | dijkstra(dres_graph, red_cost), pred(dres_graph), |
---|
384 | delta_deficit(imbalance, delta) |
---|
385 | #else //WITHOUT_CAPACITY_SCALING |
---|
386 | dijkstra(res_graph, red_cost), pred(res_graph), |
---|
387 | has_deficit(imbalance) |
---|
388 | #endif |
---|
389 | { |
---|
390 | // Checking the sum of supply values |
---|
391 | Supply sum = 0; |
---|
392 | for (NodeIt n(graph); n != INVALID; ++n) sum += supply[n]; |
---|
393 | valid_supply = sum == 0; |
---|
394 | } |
---|
395 | |
---|
396 | /// \brief Simple constructor of the class (with lower bounds). |
---|
397 | /// |
---|
398 | /// Simple constructor of the class (with lower bounds). |
---|
399 | /// |
---|
400 | /// \param _graph The directed graph the algorithm runs on. |
---|
401 | /// \param _lower The lower bounds of the edges. |
---|
402 | /// \param _capacity The capacities (upper bounds) of the edges. |
---|
403 | /// \param _cost The cost (length) values of the edges. |
---|
404 | /// \param _s The source node. |
---|
405 | /// \param _t The target node. |
---|
406 | /// \param _flow_value The required amount of flow from node \c _s |
---|
407 | /// to node \c _t (i.e. the supply of \c _s and the demand of |
---|
408 | /// \c _t). |
---|
409 | CapacityScaling( const Graph &_graph, |
---|
410 | const LowerMap &_lower, |
---|
411 | const CapacityMap &_capacity, |
---|
412 | const CostMap &_cost, |
---|
413 | Node _s, Node _t, |
---|
414 | Supply _flow_value ) : |
---|
415 | graph(_graph), lower(&_lower), capacity(_graph), cost(_cost), |
---|
416 | supply(_graph), flow(_graph, 0), potential(_graph, 0), |
---|
417 | res_graph(_graph, capacity, flow), |
---|
418 | red_cost(res_graph, cost, potential), imbalance(_graph), |
---|
419 | #ifdef WITH_SCALING |
---|
420 | delta(0), delta_filter(res_graph, delta), |
---|
421 | dres_graph(res_graph, delta_filter), |
---|
422 | dijkstra(dres_graph, red_cost), pred(dres_graph), |
---|
423 | delta_deficit(imbalance, delta) |
---|
424 | #else //WITHOUT_CAPACITY_SCALING |
---|
425 | dijkstra(res_graph, red_cost), pred(res_graph), |
---|
426 | has_deficit(imbalance) |
---|
427 | #endif |
---|
428 | { |
---|
429 | // Removing nonzero lower bounds |
---|
430 | capacity = subMap(_capacity, _lower); |
---|
431 | for (NodeIt n(graph); n != INVALID; ++n) { |
---|
432 | Supply s = 0; |
---|
433 | if (n == _s) s = _flow_value; |
---|
434 | if (n == _t) s = -_flow_value; |
---|
435 | for (InEdgeIt e(graph, n); e != INVALID; ++e) |
---|
436 | s += _lower[e]; |
---|
437 | for (OutEdgeIt e(graph, n); e != INVALID; ++e) |
---|
438 | s -= _lower[e]; |
---|
439 | supply[n] = imbalance[n] = s; |
---|
440 | } |
---|
441 | valid_supply = true; |
---|
442 | } |
---|
443 | |
---|
444 | /// \brief Simple constructor of the class (without lower bounds). |
---|
445 | /// |
---|
446 | /// Simple constructor of the class (without lower bounds). |
---|
447 | /// |
---|
448 | /// \param _graph The directed graph the algorithm runs on. |
---|
449 | /// \param _capacity The capacities (upper bounds) of the edges. |
---|
450 | /// \param _cost The cost (length) values of the edges. |
---|
451 | /// \param _s The source node. |
---|
452 | /// \param _t The target node. |
---|
453 | /// \param _flow_value The required amount of flow from node \c _s |
---|
454 | /// to node \c _t (i.e. the supply of \c _s and the demand of |
---|
455 | /// \c _t). |
---|
456 | CapacityScaling( const Graph &_graph, |
---|
457 | const CapacityMap &_capacity, |
---|
458 | const CostMap &_cost, |
---|
459 | Node _s, Node _t, |
---|
460 | Supply _flow_value ) : |
---|
461 | graph(_graph), lower(NULL), capacity(_capacity), cost(_cost), |
---|
462 | supply(_graph, 0), flow(_graph, 0), potential(_graph, 0), |
---|
463 | res_graph(_graph, capacity, flow), |
---|
464 | red_cost(res_graph, cost, potential), imbalance(_graph), |
---|
465 | #ifdef WITH_SCALING |
---|
466 | delta(0), delta_filter(res_graph, delta), |
---|
467 | dres_graph(res_graph, delta_filter), |
---|
468 | dijkstra(dres_graph, red_cost), pred(dres_graph), |
---|
469 | delta_deficit(imbalance, delta) |
---|
470 | #else //WITHOUT_CAPACITY_SCALING |
---|
471 | dijkstra(res_graph, red_cost), pred(res_graph), |
---|
472 | has_deficit(imbalance) |
---|
473 | #endif |
---|
474 | { |
---|
475 | supply[_s] = _flow_value; |
---|
476 | supply[_t] = -_flow_value; |
---|
477 | valid_supply = true; |
---|
478 | } |
---|
479 | |
---|
480 | /// \brief Returns a const reference to the flow map. |
---|
481 | /// |
---|
482 | /// Returns a const reference to the flow map. |
---|
483 | /// |
---|
484 | /// \pre \ref run() must be called before using this function. |
---|
485 | const FlowMap& flowMap() const { |
---|
486 | return flow; |
---|
487 | } |
---|
488 | |
---|
489 | /// \brief Returns a const reference to the potential map (the dual |
---|
490 | /// solution). |
---|
491 | /// |
---|
492 | /// Returns a const reference to the potential map (the dual |
---|
493 | /// solution). |
---|
494 | /// |
---|
495 | /// \pre \ref run() must be called before using this function. |
---|
496 | const PotentialMap& potentialMap() const { |
---|
497 | return potential; |
---|
498 | } |
---|
499 | |
---|
500 | /// \brief Returns the total cost of the found flow. |
---|
501 | /// |
---|
502 | /// Returns the total cost of the found flow. The complexity of the |
---|
503 | /// function is \f$ O(e) \f$. |
---|
504 | /// |
---|
505 | /// \pre \ref run() must be called before using this function. |
---|
506 | Cost totalCost() const { |
---|
507 | Cost c = 0; |
---|
508 | for (EdgeIt e(graph); e != INVALID; ++e) |
---|
509 | c += flow[e] * cost[e]; |
---|
510 | return c; |
---|
511 | } |
---|
512 | |
---|
513 | /// \brief Runs the successive shortest path algorithm. |
---|
514 | /// |
---|
515 | /// Runs the successive shortest path algorithm. |
---|
516 | /// |
---|
517 | /// \return \c true if a feasible flow can be found. |
---|
518 | bool run() { |
---|
519 | return init() && start(); |
---|
520 | } |
---|
521 | |
---|
522 | protected: |
---|
523 | |
---|
524 | /// \brief Initializes the algorithm. |
---|
525 | bool init() { |
---|
526 | if (!valid_supply) return false; |
---|
527 | |
---|
528 | // Initalizing Dijkstra class |
---|
529 | updater.potentialMap(potential); |
---|
530 | dijkstra.distMap(updater).predMap(pred); |
---|
531 | |
---|
532 | #ifdef WITH_SCALING |
---|
533 | // Initilaizing delta value |
---|
534 | Capacity max_cap = 0; |
---|
535 | for (EdgeIt e(graph); e != INVALID; ++e) { |
---|
536 | if (capacity[e] > max_cap) max_cap = capacity[e]; |
---|
537 | } |
---|
538 | for (delta = 1; 2 * delta < max_cap; delta *= 2) ; |
---|
539 | #endif |
---|
540 | return true; |
---|
541 | } |
---|
542 | |
---|
543 | #ifdef WITH_SCALING |
---|
544 | /// \brief Executes the capacity scaling version of the successive |
---|
545 | /// shortest path algorithm. |
---|
546 | bool start() { |
---|
547 | typedef typename DeltaResGraph::EdgeIt DeltaResEdgeIt; |
---|
548 | typedef typename DeltaResGraph::Edge DeltaResEdge; |
---|
549 | |
---|
550 | // Processing capacity scaling phases |
---|
551 | ResNode s, t; |
---|
552 | for ( ; delta >= 1; delta = delta < 4 && delta > 1 ? |
---|
553 | 1 : delta / 4 ) |
---|
554 | { |
---|
555 | // Saturating edges not satisfying the optimality condition |
---|
556 | Capacity r; |
---|
557 | for (DeltaResEdgeIt e(dres_graph); e != INVALID; ++e) { |
---|
558 | if (red_cost[e] < 0) { |
---|
559 | res_graph.augment(e, r = res_graph.rescap(e)); |
---|
560 | imbalance[dres_graph.target(e)] += r; |
---|
561 | imbalance[dres_graph.source(e)] -= r; |
---|
562 | } |
---|
563 | } |
---|
564 | |
---|
565 | // Finding excess nodes |
---|
566 | excess_nodes.clear(); |
---|
567 | for (ResNodeIt n(res_graph); n != INVALID; ++n) { |
---|
568 | if (imbalance[n] >= delta) excess_nodes.push_back(n); |
---|
569 | } |
---|
570 | next_node = 0; |
---|
571 | |
---|
572 | // Finding successive shortest paths |
---|
573 | while (next_node < excess_nodes.size()) { |
---|
574 | // Running Dijkstra |
---|
575 | s = excess_nodes[next_node]; |
---|
576 | updater.init(); |
---|
577 | dijkstra.init(); |
---|
578 | dijkstra.addSource(s); |
---|
579 | if ((t = dijkstra.start(delta_deficit)) == INVALID) { |
---|
580 | if (delta > 1) { |
---|
581 | ++next_node; |
---|
582 | continue; |
---|
583 | } |
---|
584 | return false; |
---|
585 | } |
---|
586 | |
---|
587 | // Updating node potentials |
---|
588 | updater.update(); |
---|
589 | |
---|
590 | // Augment along a shortest path from s to t |
---|
591 | Capacity d = imbalance[s] < -imbalance[t] ? |
---|
592 | imbalance[s] : -imbalance[t]; |
---|
593 | ResNode u = t; |
---|
594 | ResEdge e; |
---|
595 | if (d > delta) { |
---|
596 | while ((e = pred[u]) != INVALID) { |
---|
597 | if (res_graph.rescap(e) < d) d = res_graph.rescap(e); |
---|
598 | u = dres_graph.source(e); |
---|
599 | } |
---|
600 | } |
---|
601 | u = t; |
---|
602 | while ((e = pred[u]) != INVALID) { |
---|
603 | res_graph.augment(e, d); |
---|
604 | u = dres_graph.source(e); |
---|
605 | } |
---|
606 | imbalance[s] -= d; |
---|
607 | imbalance[t] += d; |
---|
608 | if (imbalance[s] < delta) ++next_node; |
---|
609 | } |
---|
610 | } |
---|
611 | |
---|
612 | // Handling nonzero lower bounds |
---|
613 | if (lower) { |
---|
614 | for (EdgeIt e(graph); e != INVALID; ++e) |
---|
615 | flow[e] += (*lower)[e]; |
---|
616 | } |
---|
617 | return true; |
---|
618 | } |
---|
619 | |
---|
620 | #else //WITHOUT_CAPACITY_SCALING |
---|
621 | /// \brief Executes the successive shortest path algorithm without |
---|
622 | /// capacity scaling. |
---|
623 | bool start() { |
---|
624 | // Finding excess nodes |
---|
625 | for (ResNodeIt n(res_graph); n != INVALID; ++n) { |
---|
626 | if (imbalance[n] > 0) excess_nodes.push_back(n); |
---|
627 | } |
---|
628 | if (excess_nodes.size() == 0) return true; |
---|
629 | next_node = 0; |
---|
630 | |
---|
631 | // Finding successive shortest paths |
---|
632 | ResNode s, t; |
---|
633 | while ( imbalance[excess_nodes[next_node]] > 0 || |
---|
634 | ++next_node < excess_nodes.size() ) |
---|
635 | { |
---|
636 | // Running Dijkstra |
---|
637 | s = excess_nodes[next_node]; |
---|
638 | updater.init(); |
---|
639 | dijkstra.init(); |
---|
640 | dijkstra.addSource(s); |
---|
641 | if ((t = dijkstra.start(has_deficit)) == INVALID) |
---|
642 | return false; |
---|
643 | |
---|
644 | // Updating node potentials |
---|
645 | updater.update(); |
---|
646 | |
---|
647 | // Augmenting along a shortest path from s to t |
---|
648 | Capacity delta = imbalance[s] < -imbalance[t] ? |
---|
649 | imbalance[s] : -imbalance[t]; |
---|
650 | ResNode u = t; |
---|
651 | ResEdge e; |
---|
652 | while ((e = pred[u]) != INVALID) { |
---|
653 | if (res_graph.rescap(e) < delta) delta = res_graph.rescap(e); |
---|
654 | u = res_graph.source(e); |
---|
655 | } |
---|
656 | u = t; |
---|
657 | while ((e = pred[u]) != INVALID) { |
---|
658 | res_graph.augment(e, delta); |
---|
659 | u = res_graph.source(e); |
---|
660 | } |
---|
661 | imbalance[s] -= delta; |
---|
662 | imbalance[t] += delta; |
---|
663 | } |
---|
664 | |
---|
665 | // Handling nonzero lower bounds |
---|
666 | if (lower) { |
---|
667 | for (EdgeIt e(graph); e != INVALID; ++e) |
---|
668 | flow[e] += (*lower)[e]; |
---|
669 | } |
---|
670 | return true; |
---|
671 | } |
---|
672 | #endif |
---|
673 | |
---|
674 | }; //class CapacityScaling |
---|
675 | |
---|
676 | ///@} |
---|
677 | |
---|
678 | } //namespace lemon |
---|
679 | |
---|
680 | #endif //LEMON_CAPACITY_SCALING_H |
---|