1 | /* -*- C++ -*- |
---|
2 | * |
---|
3 | * This file is a part of LEMON, a generic C++ optimization library |
---|
4 | * |
---|
5 | * Copyright (C) 2003-2008 |
---|
6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
8 | * |
---|
9 | * Permission to use, modify and distribute this software is granted |
---|
10 | * provided that this copyright notice appears in all copies. For |
---|
11 | * precise terms see the accompanying LICENSE file. |
---|
12 | * |
---|
13 | * This software is provided "AS IS" with no warranty of any kind, |
---|
14 | * express or implied, and with no claim as to its suitability for any |
---|
15 | * purpose. |
---|
16 | * |
---|
17 | */ |
---|
18 | |
---|
19 | #ifndef LEMON_CAPACITY_SCALING_H |
---|
20 | #define LEMON_CAPACITY_SCALING_H |
---|
21 | |
---|
22 | /// \ingroup min_cost_flow |
---|
23 | /// |
---|
24 | /// \file |
---|
25 | /// \brief Capacity scaling algorithm for finding a minimum cost flow. |
---|
26 | |
---|
27 | #include <vector> |
---|
28 | #include <lemon/bin_heap.h> |
---|
29 | |
---|
30 | namespace lemon { |
---|
31 | |
---|
32 | /// \addtogroup min_cost_flow |
---|
33 | /// @{ |
---|
34 | |
---|
35 | /// \brief Implementation of the capacity scaling algorithm for |
---|
36 | /// finding a minimum cost flow. |
---|
37 | /// |
---|
38 | /// \ref CapacityScaling implements the capacity scaling version |
---|
39 | /// of the successive shortest path algorithm for finding a minimum |
---|
40 | /// cost flow. |
---|
41 | /// |
---|
42 | /// \tparam Digraph The digraph type the algorithm runs on. |
---|
43 | /// \tparam LowerMap The type of the lower bound map. |
---|
44 | /// \tparam CapacityMap The type of the capacity (upper bound) map. |
---|
45 | /// \tparam CostMap The type of the cost (length) map. |
---|
46 | /// \tparam SupplyMap The type of the supply map. |
---|
47 | /// |
---|
48 | /// \warning |
---|
49 | /// - Arc capacities and costs should be \e non-negative \e integers. |
---|
50 | /// - Supply values should be \e signed \e integers. |
---|
51 | /// - The value types of the maps should be convertible to each other. |
---|
52 | /// - \c CostMap::Value must be signed type. |
---|
53 | /// |
---|
54 | /// \author Peter Kovacs |
---|
55 | template < typename Digraph, |
---|
56 | typename LowerMap = typename Digraph::template ArcMap<int>, |
---|
57 | typename CapacityMap = typename Digraph::template ArcMap<int>, |
---|
58 | typename CostMap = typename Digraph::template ArcMap<int>, |
---|
59 | typename SupplyMap = typename Digraph::template NodeMap<int> > |
---|
60 | class CapacityScaling |
---|
61 | { |
---|
62 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
---|
63 | |
---|
64 | typedef typename CapacityMap::Value Capacity; |
---|
65 | typedef typename CostMap::Value Cost; |
---|
66 | typedef typename SupplyMap::Value Supply; |
---|
67 | typedef typename Digraph::template ArcMap<Capacity> CapacityArcMap; |
---|
68 | typedef typename Digraph::template NodeMap<Supply> SupplyNodeMap; |
---|
69 | typedef typename Digraph::template NodeMap<Arc> PredMap; |
---|
70 | |
---|
71 | public: |
---|
72 | |
---|
73 | /// The type of the flow map. |
---|
74 | typedef typename Digraph::template ArcMap<Capacity> FlowMap; |
---|
75 | /// The type of the potential map. |
---|
76 | typedef typename Digraph::template NodeMap<Cost> PotentialMap; |
---|
77 | |
---|
78 | private: |
---|
79 | |
---|
80 | /// \brief Special implementation of the \ref Dijkstra algorithm |
---|
81 | /// for finding shortest paths in the residual network. |
---|
82 | /// |
---|
83 | /// \ref ResidualDijkstra is a special implementation of the |
---|
84 | /// \ref Dijkstra algorithm for finding shortest paths in the |
---|
85 | /// residual network of the digraph with respect to the reduced arc |
---|
86 | /// costs and modifying the node potentials according to the |
---|
87 | /// distance of the nodes. |
---|
88 | class ResidualDijkstra |
---|
89 | { |
---|
90 | typedef typename Digraph::template NodeMap<int> HeapCrossRef; |
---|
91 | typedef BinHeap<Cost, HeapCrossRef> Heap; |
---|
92 | |
---|
93 | private: |
---|
94 | |
---|
95 | // The digraph the algorithm runs on |
---|
96 | const Digraph &_graph; |
---|
97 | |
---|
98 | // The main maps |
---|
99 | const FlowMap &_flow; |
---|
100 | const CapacityArcMap &_res_cap; |
---|
101 | const CostMap &_cost; |
---|
102 | const SupplyNodeMap &_excess; |
---|
103 | PotentialMap &_potential; |
---|
104 | |
---|
105 | // The distance map |
---|
106 | PotentialMap _dist; |
---|
107 | // The pred arc map |
---|
108 | PredMap &_pred; |
---|
109 | // The processed (i.e. permanently labeled) nodes |
---|
110 | std::vector<Node> _proc_nodes; |
---|
111 | |
---|
112 | public: |
---|
113 | |
---|
114 | /// Constructor. |
---|
115 | ResidualDijkstra( const Digraph &digraph, |
---|
116 | const FlowMap &flow, |
---|
117 | const CapacityArcMap &res_cap, |
---|
118 | const CostMap &cost, |
---|
119 | const SupplyMap &excess, |
---|
120 | PotentialMap &potential, |
---|
121 | PredMap &pred ) : |
---|
122 | _graph(digraph), _flow(flow), _res_cap(res_cap), _cost(cost), |
---|
123 | _excess(excess), _potential(potential), _dist(digraph), |
---|
124 | _pred(pred) |
---|
125 | {} |
---|
126 | |
---|
127 | /// Run the algorithm from the given source node. |
---|
128 | Node run(Node s, Capacity delta = 1) { |
---|
129 | HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP); |
---|
130 | Heap heap(heap_cross_ref); |
---|
131 | heap.push(s, 0); |
---|
132 | _pred[s] = INVALID; |
---|
133 | _proc_nodes.clear(); |
---|
134 | |
---|
135 | // Processing nodes |
---|
136 | while (!heap.empty() && _excess[heap.top()] > -delta) { |
---|
137 | Node u = heap.top(), v; |
---|
138 | Cost d = heap.prio() + _potential[u], nd; |
---|
139 | _dist[u] = heap.prio(); |
---|
140 | heap.pop(); |
---|
141 | _proc_nodes.push_back(u); |
---|
142 | |
---|
143 | // Traversing outgoing arcs |
---|
144 | for (OutArcIt e(_graph, u); e != INVALID; ++e) { |
---|
145 | if (_res_cap[e] >= delta) { |
---|
146 | v = _graph.target(e); |
---|
147 | switch(heap.state(v)) { |
---|
148 | case Heap::PRE_HEAP: |
---|
149 | heap.push(v, d + _cost[e] - _potential[v]); |
---|
150 | _pred[v] = e; |
---|
151 | break; |
---|
152 | case Heap::IN_HEAP: |
---|
153 | nd = d + _cost[e] - _potential[v]; |
---|
154 | if (nd < heap[v]) { |
---|
155 | heap.decrease(v, nd); |
---|
156 | _pred[v] = e; |
---|
157 | } |
---|
158 | break; |
---|
159 | case Heap::POST_HEAP: |
---|
160 | break; |
---|
161 | } |
---|
162 | } |
---|
163 | } |
---|
164 | |
---|
165 | // Traversing incoming arcs |
---|
166 | for (InArcIt e(_graph, u); e != INVALID; ++e) { |
---|
167 | if (_flow[e] >= delta) { |
---|
168 | v = _graph.source(e); |
---|
169 | switch(heap.state(v)) { |
---|
170 | case Heap::PRE_HEAP: |
---|
171 | heap.push(v, d - _cost[e] - _potential[v]); |
---|
172 | _pred[v] = e; |
---|
173 | break; |
---|
174 | case Heap::IN_HEAP: |
---|
175 | nd = d - _cost[e] - _potential[v]; |
---|
176 | if (nd < heap[v]) { |
---|
177 | heap.decrease(v, nd); |
---|
178 | _pred[v] = e; |
---|
179 | } |
---|
180 | break; |
---|
181 | case Heap::POST_HEAP: |
---|
182 | break; |
---|
183 | } |
---|
184 | } |
---|
185 | } |
---|
186 | } |
---|
187 | if (heap.empty()) return INVALID; |
---|
188 | |
---|
189 | // Updating potentials of processed nodes |
---|
190 | Node t = heap.top(); |
---|
191 | Cost t_dist = heap.prio(); |
---|
192 | for (int i = 0; i < int(_proc_nodes.size()); ++i) |
---|
193 | _potential[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist; |
---|
194 | |
---|
195 | return t; |
---|
196 | } |
---|
197 | |
---|
198 | }; //class ResidualDijkstra |
---|
199 | |
---|
200 | private: |
---|
201 | |
---|
202 | // The digraph the algorithm runs on |
---|
203 | const Digraph &_graph; |
---|
204 | // The original lower bound map |
---|
205 | const LowerMap *_lower; |
---|
206 | // The modified capacity map |
---|
207 | CapacityArcMap _capacity; |
---|
208 | // The original cost map |
---|
209 | const CostMap &_cost; |
---|
210 | // The modified supply map |
---|
211 | SupplyNodeMap _supply; |
---|
212 | bool _valid_supply; |
---|
213 | |
---|
214 | // Arc map of the current flow |
---|
215 | FlowMap *_flow; |
---|
216 | bool _local_flow; |
---|
217 | // Node map of the current potentials |
---|
218 | PotentialMap *_potential; |
---|
219 | bool _local_potential; |
---|
220 | |
---|
221 | // The residual capacity map |
---|
222 | CapacityArcMap _res_cap; |
---|
223 | // The excess map |
---|
224 | SupplyNodeMap _excess; |
---|
225 | // The excess nodes (i.e. nodes with positive excess) |
---|
226 | std::vector<Node> _excess_nodes; |
---|
227 | // The deficit nodes (i.e. nodes with negative excess) |
---|
228 | std::vector<Node> _deficit_nodes; |
---|
229 | |
---|
230 | // The delta parameter used for capacity scaling |
---|
231 | Capacity _delta; |
---|
232 | // The maximum number of phases |
---|
233 | int _phase_num; |
---|
234 | |
---|
235 | // The pred arc map |
---|
236 | PredMap _pred; |
---|
237 | // Implementation of the Dijkstra algorithm for finding augmenting |
---|
238 | // shortest paths in the residual network |
---|
239 | ResidualDijkstra *_dijkstra; |
---|
240 | |
---|
241 | public: |
---|
242 | |
---|
243 | /// \brief General constructor (with lower bounds). |
---|
244 | /// |
---|
245 | /// General constructor (with lower bounds). |
---|
246 | /// |
---|
247 | /// \param digraph The digraph the algorithm runs on. |
---|
248 | /// \param lower The lower bounds of the arcs. |
---|
249 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
250 | /// \param cost The cost (length) values of the arcs. |
---|
251 | /// \param supply The supply values of the nodes (signed). |
---|
252 | CapacityScaling( const Digraph &digraph, |
---|
253 | const LowerMap &lower, |
---|
254 | const CapacityMap &capacity, |
---|
255 | const CostMap &cost, |
---|
256 | const SupplyMap &supply ) : |
---|
257 | _graph(digraph), _lower(&lower), _capacity(digraph), _cost(cost), |
---|
258 | _supply(digraph), _flow(NULL), _local_flow(false), |
---|
259 | _potential(NULL), _local_potential(false), |
---|
260 | _res_cap(digraph), _excess(digraph), _pred(digraph), _dijkstra(NULL) |
---|
261 | { |
---|
262 | Supply sum = 0; |
---|
263 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
264 | _supply[n] = supply[n]; |
---|
265 | _excess[n] = supply[n]; |
---|
266 | sum += supply[n]; |
---|
267 | } |
---|
268 | _valid_supply = sum == 0; |
---|
269 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
270 | _capacity[a] = capacity[a]; |
---|
271 | _res_cap[a] = capacity[a]; |
---|
272 | } |
---|
273 | |
---|
274 | // Remove non-zero lower bounds |
---|
275 | typename LowerMap::Value lcap; |
---|
276 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
277 | if ((lcap = lower[e]) != 0) { |
---|
278 | _capacity[e] -= lcap; |
---|
279 | _res_cap[e] -= lcap; |
---|
280 | _supply[_graph.source(e)] -= lcap; |
---|
281 | _supply[_graph.target(e)] += lcap; |
---|
282 | _excess[_graph.source(e)] -= lcap; |
---|
283 | _excess[_graph.target(e)] += lcap; |
---|
284 | } |
---|
285 | } |
---|
286 | } |
---|
287 | /* |
---|
288 | /// \brief General constructor (without lower bounds). |
---|
289 | /// |
---|
290 | /// General constructor (without lower bounds). |
---|
291 | /// |
---|
292 | /// \param digraph The digraph the algorithm runs on. |
---|
293 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
294 | /// \param cost The cost (length) values of the arcs. |
---|
295 | /// \param supply The supply values of the nodes (signed). |
---|
296 | CapacityScaling( const Digraph &digraph, |
---|
297 | const CapacityMap &capacity, |
---|
298 | const CostMap &cost, |
---|
299 | const SupplyMap &supply ) : |
---|
300 | _graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost), |
---|
301 | _supply(supply), _flow(NULL), _local_flow(false), |
---|
302 | _potential(NULL), _local_potential(false), |
---|
303 | _res_cap(capacity), _excess(supply), _pred(digraph), _dijkstra(NULL) |
---|
304 | { |
---|
305 | // Check the sum of supply values |
---|
306 | Supply sum = 0; |
---|
307 | for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n]; |
---|
308 | _valid_supply = sum == 0; |
---|
309 | } |
---|
310 | |
---|
311 | /// \brief Simple constructor (with lower bounds). |
---|
312 | /// |
---|
313 | /// Simple constructor (with lower bounds). |
---|
314 | /// |
---|
315 | /// \param digraph The digraph the algorithm runs on. |
---|
316 | /// \param lower The lower bounds of the arcs. |
---|
317 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
318 | /// \param cost The cost (length) values of the arcs. |
---|
319 | /// \param s The source node. |
---|
320 | /// \param t The target node. |
---|
321 | /// \param flow_value The required amount of flow from node \c s |
---|
322 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
---|
323 | CapacityScaling( const Digraph &digraph, |
---|
324 | const LowerMap &lower, |
---|
325 | const CapacityMap &capacity, |
---|
326 | const CostMap &cost, |
---|
327 | Node s, Node t, |
---|
328 | Supply flow_value ) : |
---|
329 | _graph(digraph), _lower(&lower), _capacity(capacity), _cost(cost), |
---|
330 | _supply(digraph, 0), _flow(NULL), _local_flow(false), |
---|
331 | _potential(NULL), _local_potential(false), |
---|
332 | _res_cap(capacity), _excess(digraph, 0), _pred(digraph), _dijkstra(NULL) |
---|
333 | { |
---|
334 | // Remove non-zero lower bounds |
---|
335 | _supply[s] = _excess[s] = flow_value; |
---|
336 | _supply[t] = _excess[t] = -flow_value; |
---|
337 | typename LowerMap::Value lcap; |
---|
338 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
339 | if ((lcap = lower[e]) != 0) { |
---|
340 | _capacity[e] -= lcap; |
---|
341 | _res_cap[e] -= lcap; |
---|
342 | _supply[_graph.source(e)] -= lcap; |
---|
343 | _supply[_graph.target(e)] += lcap; |
---|
344 | _excess[_graph.source(e)] -= lcap; |
---|
345 | _excess[_graph.target(e)] += lcap; |
---|
346 | } |
---|
347 | } |
---|
348 | _valid_supply = true; |
---|
349 | } |
---|
350 | |
---|
351 | /// \brief Simple constructor (without lower bounds). |
---|
352 | /// |
---|
353 | /// Simple constructor (without lower bounds). |
---|
354 | /// |
---|
355 | /// \param digraph The digraph the algorithm runs on. |
---|
356 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
357 | /// \param cost The cost (length) values of the arcs. |
---|
358 | /// \param s The source node. |
---|
359 | /// \param t The target node. |
---|
360 | /// \param flow_value The required amount of flow from node \c s |
---|
361 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
---|
362 | CapacityScaling( const Digraph &digraph, |
---|
363 | const CapacityMap &capacity, |
---|
364 | const CostMap &cost, |
---|
365 | Node s, Node t, |
---|
366 | Supply flow_value ) : |
---|
367 | _graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost), |
---|
368 | _supply(digraph, 0), _flow(NULL), _local_flow(false), |
---|
369 | _potential(NULL), _local_potential(false), |
---|
370 | _res_cap(capacity), _excess(digraph, 0), _pred(digraph), _dijkstra(NULL) |
---|
371 | { |
---|
372 | _supply[s] = _excess[s] = flow_value; |
---|
373 | _supply[t] = _excess[t] = -flow_value; |
---|
374 | _valid_supply = true; |
---|
375 | } |
---|
376 | */ |
---|
377 | /// Destructor. |
---|
378 | ~CapacityScaling() { |
---|
379 | if (_local_flow) delete _flow; |
---|
380 | if (_local_potential) delete _potential; |
---|
381 | delete _dijkstra; |
---|
382 | } |
---|
383 | |
---|
384 | /// \brief Set the flow map. |
---|
385 | /// |
---|
386 | /// Set the flow map. |
---|
387 | /// |
---|
388 | /// \return \c (*this) |
---|
389 | CapacityScaling& flowMap(FlowMap &map) { |
---|
390 | if (_local_flow) { |
---|
391 | delete _flow; |
---|
392 | _local_flow = false; |
---|
393 | } |
---|
394 | _flow = ↦ |
---|
395 | return *this; |
---|
396 | } |
---|
397 | |
---|
398 | /// \brief Set the potential map. |
---|
399 | /// |
---|
400 | /// Set the potential map. |
---|
401 | /// |
---|
402 | /// \return \c (*this) |
---|
403 | CapacityScaling& potentialMap(PotentialMap &map) { |
---|
404 | if (_local_potential) { |
---|
405 | delete _potential; |
---|
406 | _local_potential = false; |
---|
407 | } |
---|
408 | _potential = ↦ |
---|
409 | return *this; |
---|
410 | } |
---|
411 | |
---|
412 | /// \name Execution control |
---|
413 | |
---|
414 | /// @{ |
---|
415 | |
---|
416 | /// \brief Run the algorithm. |
---|
417 | /// |
---|
418 | /// This function runs the algorithm. |
---|
419 | /// |
---|
420 | /// \param scaling Enable or disable capacity scaling. |
---|
421 | /// If the maximum arc capacity and/or the amount of total supply |
---|
422 | /// is rather small, the algorithm could be slightly faster without |
---|
423 | /// scaling. |
---|
424 | /// |
---|
425 | /// \return \c true if a feasible flow can be found. |
---|
426 | bool run(bool scaling = true) { |
---|
427 | return init(scaling) && start(); |
---|
428 | } |
---|
429 | |
---|
430 | /// @} |
---|
431 | |
---|
432 | /// \name Query Functions |
---|
433 | /// The results of the algorithm can be obtained using these |
---|
434 | /// functions.\n |
---|
435 | /// \ref lemon::CapacityScaling::run() "run()" must be called before |
---|
436 | /// using them. |
---|
437 | |
---|
438 | /// @{ |
---|
439 | |
---|
440 | /// \brief Return a const reference to the arc map storing the |
---|
441 | /// found flow. |
---|
442 | /// |
---|
443 | /// Return a const reference to the arc map storing the found flow. |
---|
444 | /// |
---|
445 | /// \pre \ref run() must be called before using this function. |
---|
446 | const FlowMap& flowMap() const { |
---|
447 | return *_flow; |
---|
448 | } |
---|
449 | |
---|
450 | /// \brief Return a const reference to the node map storing the |
---|
451 | /// found potentials (the dual solution). |
---|
452 | /// |
---|
453 | /// Return a const reference to the node map storing the found |
---|
454 | /// potentials (the dual solution). |
---|
455 | /// |
---|
456 | /// \pre \ref run() must be called before using this function. |
---|
457 | const PotentialMap& potentialMap() const { |
---|
458 | return *_potential; |
---|
459 | } |
---|
460 | |
---|
461 | /// \brief Return the flow on the given arc. |
---|
462 | /// |
---|
463 | /// Return the flow on the given arc. |
---|
464 | /// |
---|
465 | /// \pre \ref run() must be called before using this function. |
---|
466 | Capacity flow(const Arc& arc) const { |
---|
467 | return (*_flow)[arc]; |
---|
468 | } |
---|
469 | |
---|
470 | /// \brief Return the potential of the given node. |
---|
471 | /// |
---|
472 | /// Return the potential of the given node. |
---|
473 | /// |
---|
474 | /// \pre \ref run() must be called before using this function. |
---|
475 | Cost potential(const Node& node) const { |
---|
476 | return (*_potential)[node]; |
---|
477 | } |
---|
478 | |
---|
479 | /// \brief Return the total cost of the found flow. |
---|
480 | /// |
---|
481 | /// Return the total cost of the found flow. The complexity of the |
---|
482 | /// function is \f$ O(e) \f$. |
---|
483 | /// |
---|
484 | /// \pre \ref run() must be called before using this function. |
---|
485 | Cost totalCost() const { |
---|
486 | Cost c = 0; |
---|
487 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
488 | c += (*_flow)[e] * _cost[e]; |
---|
489 | return c; |
---|
490 | } |
---|
491 | |
---|
492 | /// @} |
---|
493 | |
---|
494 | private: |
---|
495 | |
---|
496 | /// Initialize the algorithm. |
---|
497 | bool init(bool scaling) { |
---|
498 | if (!_valid_supply) return false; |
---|
499 | |
---|
500 | // Initializing maps |
---|
501 | if (!_flow) { |
---|
502 | _flow = new FlowMap(_graph); |
---|
503 | _local_flow = true; |
---|
504 | } |
---|
505 | if (!_potential) { |
---|
506 | _potential = new PotentialMap(_graph); |
---|
507 | _local_potential = true; |
---|
508 | } |
---|
509 | for (ArcIt e(_graph); e != INVALID; ++e) (*_flow)[e] = 0; |
---|
510 | for (NodeIt n(_graph); n != INVALID; ++n) (*_potential)[n] = 0; |
---|
511 | |
---|
512 | _dijkstra = new ResidualDijkstra( _graph, *_flow, _res_cap, _cost, |
---|
513 | _excess, *_potential, _pred ); |
---|
514 | |
---|
515 | // Initializing delta value |
---|
516 | if (scaling) { |
---|
517 | // With scaling |
---|
518 | Supply max_sup = 0, max_dem = 0; |
---|
519 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
520 | if ( _supply[n] > max_sup) max_sup = _supply[n]; |
---|
521 | if (-_supply[n] > max_dem) max_dem = -_supply[n]; |
---|
522 | } |
---|
523 | Capacity max_cap = 0; |
---|
524 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
525 | if (_capacity[e] > max_cap) max_cap = _capacity[e]; |
---|
526 | } |
---|
527 | max_sup = std::min(std::min(max_sup, max_dem), max_cap); |
---|
528 | _phase_num = 0; |
---|
529 | for (_delta = 1; 2 * _delta <= max_sup; _delta *= 2) |
---|
530 | ++_phase_num; |
---|
531 | } else { |
---|
532 | // Without scaling |
---|
533 | _delta = 1; |
---|
534 | } |
---|
535 | |
---|
536 | return true; |
---|
537 | } |
---|
538 | |
---|
539 | bool start() { |
---|
540 | if (_delta > 1) |
---|
541 | return startWithScaling(); |
---|
542 | else |
---|
543 | return startWithoutScaling(); |
---|
544 | } |
---|
545 | |
---|
546 | /// Execute the capacity scaling algorithm. |
---|
547 | bool startWithScaling() { |
---|
548 | // Processing capacity scaling phases |
---|
549 | Node s, t; |
---|
550 | int phase_cnt = 0; |
---|
551 | int factor = 4; |
---|
552 | while (true) { |
---|
553 | // Saturating all arcs not satisfying the optimality condition |
---|
554 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
555 | Node u = _graph.source(e), v = _graph.target(e); |
---|
556 | Cost c = _cost[e] + (*_potential)[u] - (*_potential)[v]; |
---|
557 | if (c < 0 && _res_cap[e] >= _delta) { |
---|
558 | _excess[u] -= _res_cap[e]; |
---|
559 | _excess[v] += _res_cap[e]; |
---|
560 | (*_flow)[e] = _capacity[e]; |
---|
561 | _res_cap[e] = 0; |
---|
562 | } |
---|
563 | else if (c > 0 && (*_flow)[e] >= _delta) { |
---|
564 | _excess[u] += (*_flow)[e]; |
---|
565 | _excess[v] -= (*_flow)[e]; |
---|
566 | (*_flow)[e] = 0; |
---|
567 | _res_cap[e] = _capacity[e]; |
---|
568 | } |
---|
569 | } |
---|
570 | |
---|
571 | // Finding excess nodes and deficit nodes |
---|
572 | _excess_nodes.clear(); |
---|
573 | _deficit_nodes.clear(); |
---|
574 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
575 | if (_excess[n] >= _delta) _excess_nodes.push_back(n); |
---|
576 | if (_excess[n] <= -_delta) _deficit_nodes.push_back(n); |
---|
577 | } |
---|
578 | int next_node = 0, next_def_node = 0; |
---|
579 | |
---|
580 | // Finding augmenting shortest paths |
---|
581 | while (next_node < int(_excess_nodes.size())) { |
---|
582 | // Checking deficit nodes |
---|
583 | if (_delta > 1) { |
---|
584 | bool delta_deficit = false; |
---|
585 | for ( ; next_def_node < int(_deficit_nodes.size()); |
---|
586 | ++next_def_node ) { |
---|
587 | if (_excess[_deficit_nodes[next_def_node]] <= -_delta) { |
---|
588 | delta_deficit = true; |
---|
589 | break; |
---|
590 | } |
---|
591 | } |
---|
592 | if (!delta_deficit) break; |
---|
593 | } |
---|
594 | |
---|
595 | // Running Dijkstra |
---|
596 | s = _excess_nodes[next_node]; |
---|
597 | if ((t = _dijkstra->run(s, _delta)) == INVALID) { |
---|
598 | if (_delta > 1) { |
---|
599 | ++next_node; |
---|
600 | continue; |
---|
601 | } |
---|
602 | return false; |
---|
603 | } |
---|
604 | |
---|
605 | // Augmenting along a shortest path from s to t. |
---|
606 | Capacity d = std::min(_excess[s], -_excess[t]); |
---|
607 | Node u = t; |
---|
608 | Arc e; |
---|
609 | if (d > _delta) { |
---|
610 | while ((e = _pred[u]) != INVALID) { |
---|
611 | Capacity rc; |
---|
612 | if (u == _graph.target(e)) { |
---|
613 | rc = _res_cap[e]; |
---|
614 | u = _graph.source(e); |
---|
615 | } else { |
---|
616 | rc = (*_flow)[e]; |
---|
617 | u = _graph.target(e); |
---|
618 | } |
---|
619 | if (rc < d) d = rc; |
---|
620 | } |
---|
621 | } |
---|
622 | u = t; |
---|
623 | while ((e = _pred[u]) != INVALID) { |
---|
624 | if (u == _graph.target(e)) { |
---|
625 | (*_flow)[e] += d; |
---|
626 | _res_cap[e] -= d; |
---|
627 | u = _graph.source(e); |
---|
628 | } else { |
---|
629 | (*_flow)[e] -= d; |
---|
630 | _res_cap[e] += d; |
---|
631 | u = _graph.target(e); |
---|
632 | } |
---|
633 | } |
---|
634 | _excess[s] -= d; |
---|
635 | _excess[t] += d; |
---|
636 | |
---|
637 | if (_excess[s] < _delta) ++next_node; |
---|
638 | } |
---|
639 | |
---|
640 | if (_delta == 1) break; |
---|
641 | if (++phase_cnt > _phase_num / 4) factor = 2; |
---|
642 | _delta = _delta <= factor ? 1 : _delta / factor; |
---|
643 | } |
---|
644 | |
---|
645 | // Handling non-zero lower bounds |
---|
646 | if (_lower) { |
---|
647 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
648 | (*_flow)[e] += (*_lower)[e]; |
---|
649 | } |
---|
650 | return true; |
---|
651 | } |
---|
652 | |
---|
653 | /// Execute the successive shortest path algorithm. |
---|
654 | bool startWithoutScaling() { |
---|
655 | // Finding excess nodes |
---|
656 | for (NodeIt n(_graph); n != INVALID; ++n) |
---|
657 | if (_excess[n] > 0) _excess_nodes.push_back(n); |
---|
658 | if (_excess_nodes.size() == 0) return true; |
---|
659 | int next_node = 0; |
---|
660 | |
---|
661 | // Finding shortest paths |
---|
662 | Node s, t; |
---|
663 | while ( _excess[_excess_nodes[next_node]] > 0 || |
---|
664 | ++next_node < int(_excess_nodes.size()) ) |
---|
665 | { |
---|
666 | // Running Dijkstra |
---|
667 | s = _excess_nodes[next_node]; |
---|
668 | if ((t = _dijkstra->run(s)) == INVALID) return false; |
---|
669 | |
---|
670 | // Augmenting along a shortest path from s to t |
---|
671 | Capacity d = std::min(_excess[s], -_excess[t]); |
---|
672 | Node u = t; |
---|
673 | Arc e; |
---|
674 | if (d > 1) { |
---|
675 | while ((e = _pred[u]) != INVALID) { |
---|
676 | Capacity rc; |
---|
677 | if (u == _graph.target(e)) { |
---|
678 | rc = _res_cap[e]; |
---|
679 | u = _graph.source(e); |
---|
680 | } else { |
---|
681 | rc = (*_flow)[e]; |
---|
682 | u = _graph.target(e); |
---|
683 | } |
---|
684 | if (rc < d) d = rc; |
---|
685 | } |
---|
686 | } |
---|
687 | u = t; |
---|
688 | while ((e = _pred[u]) != INVALID) { |
---|
689 | if (u == _graph.target(e)) { |
---|
690 | (*_flow)[e] += d; |
---|
691 | _res_cap[e] -= d; |
---|
692 | u = _graph.source(e); |
---|
693 | } else { |
---|
694 | (*_flow)[e] -= d; |
---|
695 | _res_cap[e] += d; |
---|
696 | u = _graph.target(e); |
---|
697 | } |
---|
698 | } |
---|
699 | _excess[s] -= d; |
---|
700 | _excess[t] += d; |
---|
701 | } |
---|
702 | |
---|
703 | // Handling non-zero lower bounds |
---|
704 | if (_lower) { |
---|
705 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
706 | (*_flow)[e] += (*_lower)[e]; |
---|
707 | } |
---|
708 | return true; |
---|
709 | } |
---|
710 | |
---|
711 | }; //class CapacityScaling |
---|
712 | |
---|
713 | ///@} |
---|
714 | |
---|
715 | } //namespace lemon |
---|
716 | |
---|
717 | #endif //LEMON_CAPACITY_SCALING_H |
---|