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_CYCLE_CANCELING_H |
---|
20 | #define LEMON_CYCLE_CANCELING_H |
---|
21 | |
---|
22 | /// \ingroup min_cost_flow |
---|
23 | /// |
---|
24 | /// \file |
---|
25 | /// \brief A cycle-canceling algorithm for finding a minimum cost flow. |
---|
26 | |
---|
27 | #include <vector> |
---|
28 | #include <lemon/graph_adaptor.h> |
---|
29 | #include <lemon/circulation.h> |
---|
30 | |
---|
31 | /// \brief The used cycle-canceling method. |
---|
32 | #define LIMITED_CYCLE_CANCELING |
---|
33 | //#define MIN_MEAN_CYCLE_CANCELING |
---|
34 | |
---|
35 | #ifdef LIMITED_CYCLE_CANCELING |
---|
36 | #include <lemon/bellman_ford.h> |
---|
37 | /// \brief The maximum number of iterations for the first execution |
---|
38 | /// of the \ref lemon::BellmanFord "Bellman-Ford" algorithm. |
---|
39 | /// It should be at least 2. |
---|
40 | #define STARTING_LIMIT 2 |
---|
41 | /// \brief The iteration limit for the |
---|
42 | /// \ref lemon::BellmanFord "Bellman-Ford" algorithm is multiplied by |
---|
43 | /// <tt>ALPHA_MUL / ALPHA_DIV</tt> in every round. |
---|
44 | /// <tt>ALPHA_MUL / ALPHA_DIV</tt> must be greater than 1. |
---|
45 | #define ALPHA_MUL 3 |
---|
46 | /// \brief The iteration limit for the |
---|
47 | /// \ref lemon::BellmanFord "Bellman-Ford" algorithm is multiplied by |
---|
48 | /// <tt>ALPHA_MUL / ALPHA_DIV</tt> in every round. |
---|
49 | /// <tt>ALPHA_MUL / ALPHA_DIV</tt> must be greater than 1. |
---|
50 | #define ALPHA_DIV 2 |
---|
51 | |
---|
52 | //#define _ONLY_ONE_CYCLE_ |
---|
53 | //#define _NO_BACK_STEP_ |
---|
54 | //#define _DEBUG_ITER_ |
---|
55 | #endif |
---|
56 | |
---|
57 | #ifdef MIN_MEAN_CYCLE_CANCELING |
---|
58 | #include <lemon/min_mean_cycle.h> |
---|
59 | #include <lemon/path.h> |
---|
60 | #endif |
---|
61 | |
---|
62 | namespace lemon { |
---|
63 | |
---|
64 | /// \addtogroup min_cost_flow |
---|
65 | /// @{ |
---|
66 | |
---|
67 | /// \brief Implementation of a cycle-canceling algorithm for finding |
---|
68 | /// a minimum cost flow. |
---|
69 | /// |
---|
70 | /// \ref lemon::CycleCanceling "CycleCanceling" implements a |
---|
71 | /// cycle-canceling algorithm for finding a minimum cost flow. |
---|
72 | /// |
---|
73 | /// \param Graph The directed graph type the algorithm runs on. |
---|
74 | /// \param LowerMap The type of the lower bound map. |
---|
75 | /// \param CapacityMap The type of the capacity (upper bound) map. |
---|
76 | /// \param CostMap The type of the cost (length) map. |
---|
77 | /// \param SupplyMap The type of the supply map. |
---|
78 | /// |
---|
79 | /// \warning |
---|
80 | /// - Edge capacities and costs should be nonnegative integers. |
---|
81 | /// However \c CostMap::Value should be signed type. |
---|
82 | /// - Supply values should be signed integers. |
---|
83 | /// - \c LowerMap::Value must be convertible to |
---|
84 | /// \c CapacityMap::Value and \c CapacityMap::Value must be |
---|
85 | /// convertible to \c SupplyMap::Value. |
---|
86 | /// |
---|
87 | /// \author Peter Kovacs |
---|
88 | |
---|
89 | template < typename Graph, |
---|
90 | typename LowerMap = typename Graph::template EdgeMap<int>, |
---|
91 | typename CapacityMap = LowerMap, |
---|
92 | typename CostMap = typename Graph::template EdgeMap<int>, |
---|
93 | typename SupplyMap = typename Graph::template NodeMap |
---|
94 | <typename CapacityMap::Value> > |
---|
95 | class CycleCanceling |
---|
96 | { |
---|
97 | typedef typename Graph::Node Node; |
---|
98 | typedef typename Graph::NodeIt NodeIt; |
---|
99 | typedef typename Graph::Edge Edge; |
---|
100 | typedef typename Graph::EdgeIt EdgeIt; |
---|
101 | typedef typename Graph::InEdgeIt InEdgeIt; |
---|
102 | typedef typename Graph::OutEdgeIt OutEdgeIt; |
---|
103 | |
---|
104 | typedef typename LowerMap::Value Lower; |
---|
105 | typedef typename CapacityMap::Value Capacity; |
---|
106 | typedef typename CostMap::Value Cost; |
---|
107 | typedef typename SupplyMap::Value Supply; |
---|
108 | typedef typename Graph::template EdgeMap<Capacity> CapacityRefMap; |
---|
109 | typedef typename Graph::template NodeMap<Supply> SupplyRefMap; |
---|
110 | |
---|
111 | typedef ResGraphAdaptor< const Graph, Capacity, |
---|
112 | CapacityRefMap, CapacityRefMap > ResGraph; |
---|
113 | typedef typename ResGraph::Node ResNode; |
---|
114 | typedef typename ResGraph::NodeIt ResNodeIt; |
---|
115 | typedef typename ResGraph::Edge ResEdge; |
---|
116 | typedef typename ResGraph::EdgeIt ResEdgeIt; |
---|
117 | |
---|
118 | public: |
---|
119 | |
---|
120 | /// \brief The type of the flow map. |
---|
121 | typedef CapacityRefMap FlowMap; |
---|
122 | |
---|
123 | protected: |
---|
124 | |
---|
125 | /// \brief Map adaptor class for handling residual edge costs. |
---|
126 | class ResCostMap : public MapBase<ResEdge, Cost> |
---|
127 | { |
---|
128 | private: |
---|
129 | |
---|
130 | const CostMap &cost_map; |
---|
131 | |
---|
132 | public: |
---|
133 | |
---|
134 | ResCostMap(const CostMap &_cost) : cost_map(_cost) {} |
---|
135 | |
---|
136 | Cost operator[](const ResEdge &e) const { |
---|
137 | return ResGraph::forward(e) ? cost_map[e] : -cost_map[e]; |
---|
138 | } |
---|
139 | |
---|
140 | }; //class ResCostMap |
---|
141 | |
---|
142 | protected: |
---|
143 | |
---|
144 | /// \brief The directed graph the algorithm runs on. |
---|
145 | const Graph &graph; |
---|
146 | /// \brief The original lower bound map. |
---|
147 | const LowerMap *lower; |
---|
148 | /// \brief The modified capacity map. |
---|
149 | CapacityRefMap capacity; |
---|
150 | /// \brief The cost map. |
---|
151 | const CostMap &cost; |
---|
152 | /// \brief The modified supply map. |
---|
153 | SupplyRefMap supply; |
---|
154 | /// \brief The sum of supply values equals zero. |
---|
155 | bool valid_supply; |
---|
156 | |
---|
157 | /// \brief The current flow. |
---|
158 | FlowMap flow; |
---|
159 | /// \brief The residual graph. |
---|
160 | ResGraph res_graph; |
---|
161 | /// \brief The residual cost map. |
---|
162 | ResCostMap res_cost; |
---|
163 | |
---|
164 | public : |
---|
165 | |
---|
166 | /// \brief General constructor of the class (with lower bounds). |
---|
167 | /// |
---|
168 | /// General constructor of the class (with lower bounds). |
---|
169 | /// |
---|
170 | /// \param _graph The directed graph the algorithm runs on. |
---|
171 | /// \param _lower The lower bounds of the edges. |
---|
172 | /// \param _capacity The capacities (upper bounds) of the edges. |
---|
173 | /// \param _cost The cost (length) values of the edges. |
---|
174 | /// \param _supply The supply values of the nodes (signed). |
---|
175 | CycleCanceling( const Graph &_graph, |
---|
176 | const LowerMap &_lower, |
---|
177 | const CapacityMap &_capacity, |
---|
178 | const CostMap &_cost, |
---|
179 | const SupplyMap &_supply ) : |
---|
180 | graph(_graph), lower(&_lower), capacity(_graph), cost(_cost), |
---|
181 | supply(_graph), flow(_graph, 0), |
---|
182 | res_graph(_graph, capacity, flow), res_cost(cost) |
---|
183 | { |
---|
184 | // Removing nonzero lower bounds |
---|
185 | capacity = subMap(_capacity, _lower); |
---|
186 | Supply sum = 0; |
---|
187 | for (NodeIt n(graph); n != INVALID; ++n) { |
---|
188 | Supply s = _supply[n]; |
---|
189 | for (InEdgeIt e(graph, n); e != INVALID; ++e) |
---|
190 | s += _lower[e]; |
---|
191 | for (OutEdgeIt e(graph, n); e != INVALID; ++e) |
---|
192 | s -= _lower[e]; |
---|
193 | sum += (supply[n] = s); |
---|
194 | } |
---|
195 | valid_supply = sum == 0; |
---|
196 | } |
---|
197 | |
---|
198 | /// \brief General constructor of the class (without lower bounds). |
---|
199 | /// |
---|
200 | /// General constructor of the class (without lower bounds). |
---|
201 | /// |
---|
202 | /// \param _graph The directed graph the algorithm runs on. |
---|
203 | /// \param _capacity The capacities (upper bounds) of the edges. |
---|
204 | /// \param _cost The cost (length) values of the edges. |
---|
205 | /// \param _supply The supply values of the nodes (signed). |
---|
206 | CycleCanceling( const Graph &_graph, |
---|
207 | const CapacityMap &_capacity, |
---|
208 | const CostMap &_cost, |
---|
209 | const SupplyMap &_supply ) : |
---|
210 | graph(_graph), lower(NULL), capacity(_capacity), cost(_cost), |
---|
211 | supply(_supply), flow(_graph, 0), |
---|
212 | res_graph(_graph, capacity, flow), res_cost(cost) |
---|
213 | { |
---|
214 | // Checking the sum of supply values |
---|
215 | Supply sum = 0; |
---|
216 | for (NodeIt n(graph); n != INVALID; ++n) sum += supply[n]; |
---|
217 | valid_supply = sum == 0; |
---|
218 | } |
---|
219 | |
---|
220 | |
---|
221 | /// \brief Simple constructor of the class (with lower bounds). |
---|
222 | /// |
---|
223 | /// Simple constructor of the class (with lower bounds). |
---|
224 | /// |
---|
225 | /// \param _graph The directed graph the algorithm runs on. |
---|
226 | /// \param _lower The lower bounds of the edges. |
---|
227 | /// \param _capacity The capacities (upper bounds) of the edges. |
---|
228 | /// \param _cost The cost (length) values of the edges. |
---|
229 | /// \param _s The source node. |
---|
230 | /// \param _t The target node. |
---|
231 | /// \param _flow_value The required amount of flow from node \c _s |
---|
232 | /// to node \c _t (i.e. the supply of \c _s and the demand of |
---|
233 | /// \c _t). |
---|
234 | CycleCanceling( const Graph &_graph, |
---|
235 | const LowerMap &_lower, |
---|
236 | const CapacityMap &_capacity, |
---|
237 | const CostMap &_cost, |
---|
238 | Node _s, Node _t, |
---|
239 | Supply _flow_value ) : |
---|
240 | graph(_graph), lower(&_lower), capacity(_graph), cost(_cost), |
---|
241 | supply(_graph), flow(_graph, 0), |
---|
242 | res_graph(_graph, capacity, flow), res_cost(cost) |
---|
243 | { |
---|
244 | // Removing nonzero lower bounds |
---|
245 | capacity = subMap(_capacity, _lower); |
---|
246 | for (NodeIt n(graph); n != INVALID; ++n) { |
---|
247 | Supply s = 0; |
---|
248 | if (n == _s) s = _flow_value; |
---|
249 | if (n == _t) s = -_flow_value; |
---|
250 | for (InEdgeIt e(graph, n); e != INVALID; ++e) |
---|
251 | s += _lower[e]; |
---|
252 | for (OutEdgeIt e(graph, n); e != INVALID; ++e) |
---|
253 | s -= _lower[e]; |
---|
254 | supply[n] = s; |
---|
255 | } |
---|
256 | valid_supply = true; |
---|
257 | } |
---|
258 | |
---|
259 | /// \brief Simple constructor of the class (without lower bounds). |
---|
260 | /// |
---|
261 | /// Simple constructor of the class (without lower bounds). |
---|
262 | /// |
---|
263 | /// \param _graph The directed graph the algorithm runs on. |
---|
264 | /// \param _capacity The capacities (upper bounds) of the edges. |
---|
265 | /// \param _cost The cost (length) values of the edges. |
---|
266 | /// \param _s The source node. |
---|
267 | /// \param _t The target node. |
---|
268 | /// \param _flow_value The required amount of flow from node \c _s |
---|
269 | /// to node \c _t (i.e. the supply of \c _s and the demand of |
---|
270 | /// \c _t). |
---|
271 | CycleCanceling( const Graph &_graph, |
---|
272 | const CapacityMap &_capacity, |
---|
273 | const CostMap &_cost, |
---|
274 | Node _s, Node _t, |
---|
275 | Supply _flow_value ) : |
---|
276 | graph(_graph), lower(NULL), capacity(_capacity), cost(_cost), |
---|
277 | supply(_graph, 0), flow(_graph, 0), |
---|
278 | res_graph(_graph, capacity, flow), res_cost(cost) |
---|
279 | { |
---|
280 | supply[_s] = _flow_value; |
---|
281 | supply[_t] = -_flow_value; |
---|
282 | valid_supply = true; |
---|
283 | } |
---|
284 | |
---|
285 | /// \brief Returns a const reference to the flow map. |
---|
286 | /// |
---|
287 | /// Returns a const reference to the flow map. |
---|
288 | /// |
---|
289 | /// \pre \ref run() must be called before using this function. |
---|
290 | const FlowMap& flowMap() const { |
---|
291 | return flow; |
---|
292 | } |
---|
293 | |
---|
294 | /// \brief Returns the total cost of the found flow. |
---|
295 | /// |
---|
296 | /// Returns the total cost of the found flow. The complexity of the |
---|
297 | /// function is \f$ O(e) \f$. |
---|
298 | /// |
---|
299 | /// \pre \ref run() must be called before using this function. |
---|
300 | Cost totalCost() const { |
---|
301 | Cost c = 0; |
---|
302 | for (EdgeIt e(graph); e != INVALID; ++e) |
---|
303 | c += flow[e] * cost[e]; |
---|
304 | return c; |
---|
305 | } |
---|
306 | |
---|
307 | /// \brief Runs the algorithm. |
---|
308 | /// |
---|
309 | /// Runs the algorithm. |
---|
310 | /// |
---|
311 | /// \return \c true if a feasible flow can be found. |
---|
312 | bool run() { |
---|
313 | return init() && start(); |
---|
314 | } |
---|
315 | |
---|
316 | protected: |
---|
317 | |
---|
318 | /// \brief Initializes the algorithm. |
---|
319 | bool init() { |
---|
320 | // Checking the sum of supply values |
---|
321 | Supply sum = 0; |
---|
322 | for (NodeIt n(graph); n != INVALID; ++n) sum += supply[n]; |
---|
323 | if (sum != 0) return false; |
---|
324 | |
---|
325 | // Finding a feasible flow |
---|
326 | Circulation< Graph, ConstMap<Edge, Capacity>, CapacityRefMap, |
---|
327 | SupplyMap > |
---|
328 | circulation( graph, constMap<Edge>((Capacity)0), capacity, |
---|
329 | supply ); |
---|
330 | circulation.flowMap(flow); |
---|
331 | return circulation.run() == -1; |
---|
332 | } |
---|
333 | |
---|
334 | #ifdef LIMITED_CYCLE_CANCELING |
---|
335 | /// \brief Executes a cycle-canceling algorithm using |
---|
336 | /// \ref lemon::BellmanFord "Bellman-Ford" algorithm with limited |
---|
337 | /// iteration count. |
---|
338 | bool start() { |
---|
339 | typename BellmanFord<ResGraph, ResCostMap>::PredMap pred(res_graph); |
---|
340 | typename ResGraph::template NodeMap<int> visited(res_graph); |
---|
341 | std::vector<ResEdge> cycle; |
---|
342 | int node_num = countNodes(graph); |
---|
343 | |
---|
344 | #ifdef _DEBUG_ITER_ |
---|
345 | int cycle_num = 0; |
---|
346 | #endif |
---|
347 | int length_bound = STARTING_LIMIT; |
---|
348 | bool optimal = false; |
---|
349 | while (!optimal) { |
---|
350 | BellmanFord<ResGraph, ResCostMap> bf(res_graph, res_cost); |
---|
351 | bf.predMap(pred); |
---|
352 | bf.init(0); |
---|
353 | int iter_num = 0; |
---|
354 | bool cycle_found = false; |
---|
355 | while (!cycle_found) { |
---|
356 | #ifdef _NO_BACK_STEP_ |
---|
357 | int curr_iter_num = length_bound <= node_num ? |
---|
358 | length_bound - iter_num : node_num - iter_num; |
---|
359 | #else |
---|
360 | int curr_iter_num = iter_num + length_bound <= node_num ? |
---|
361 | length_bound : node_num - iter_num; |
---|
362 | #endif |
---|
363 | iter_num += curr_iter_num; |
---|
364 | int real_iter_num = curr_iter_num; |
---|
365 | for (int i = 0; i < curr_iter_num; ++i) { |
---|
366 | if (bf.processNextWeakRound()) { |
---|
367 | real_iter_num = i; |
---|
368 | break; |
---|
369 | } |
---|
370 | } |
---|
371 | if (real_iter_num < curr_iter_num) { |
---|
372 | optimal = true; |
---|
373 | break; |
---|
374 | } else { |
---|
375 | // Searching for node disjoint negative cycles |
---|
376 | for (ResNodeIt n(res_graph); n != INVALID; ++n) |
---|
377 | visited[n] = 0; |
---|
378 | int id = 0; |
---|
379 | for (ResNodeIt n(res_graph); n != INVALID; ++n) { |
---|
380 | if (visited[n] > 0) continue; |
---|
381 | visited[n] = ++id; |
---|
382 | ResNode u = pred[n] == INVALID ? |
---|
383 | INVALID : res_graph.source(pred[n]); |
---|
384 | while (u != INVALID && visited[u] == 0) { |
---|
385 | visited[u] = id; |
---|
386 | u = pred[u] == INVALID ? |
---|
387 | INVALID : res_graph.source(pred[u]); |
---|
388 | } |
---|
389 | if (u != INVALID && visited[u] == id) { |
---|
390 | // Finding the negative cycle |
---|
391 | cycle_found = true; |
---|
392 | cycle.clear(); |
---|
393 | ResEdge e = pred[u]; |
---|
394 | cycle.push_back(e); |
---|
395 | Capacity d = res_graph.rescap(e); |
---|
396 | while (res_graph.source(e) != u) { |
---|
397 | cycle.push_back(e = pred[res_graph.source(e)]); |
---|
398 | if (res_graph.rescap(e) < d) |
---|
399 | d = res_graph.rescap(e); |
---|
400 | } |
---|
401 | #ifdef _DEBUG_ITER_ |
---|
402 | ++cycle_num; |
---|
403 | #endif |
---|
404 | // Augmenting along the cycle |
---|
405 | for (int i = 0; i < cycle.size(); ++i) |
---|
406 | res_graph.augment(cycle[i], d); |
---|
407 | #ifdef _ONLY_ONE_CYCLE_ |
---|
408 | break; |
---|
409 | #endif |
---|
410 | } |
---|
411 | } |
---|
412 | } |
---|
413 | |
---|
414 | if (!cycle_found) |
---|
415 | length_bound = length_bound * ALPHA_MUL / ALPHA_DIV; |
---|
416 | } |
---|
417 | } |
---|
418 | |
---|
419 | #ifdef _DEBUG_ITER_ |
---|
420 | std::cout << "Limited cycle-canceling algorithm finished. " |
---|
421 | << "Found " << cycle_num << " negative cycles." |
---|
422 | << std::endl; |
---|
423 | #endif |
---|
424 | |
---|
425 | // Handling nonzero lower bounds |
---|
426 | if (lower) { |
---|
427 | for (EdgeIt e(graph); e != INVALID; ++e) |
---|
428 | flow[e] += (*lower)[e]; |
---|
429 | } |
---|
430 | return true; |
---|
431 | } |
---|
432 | #endif |
---|
433 | |
---|
434 | #ifdef MIN_MEAN_CYCLE_CANCELING |
---|
435 | /// \brief Executes the minimum mean cycle-canceling algorithm |
---|
436 | /// using \ref lemon::MinMeanCycle "MinMeanCycle" class. |
---|
437 | bool start() { |
---|
438 | typedef Path<ResGraph> ResPath; |
---|
439 | MinMeanCycle<ResGraph, ResCostMap> mmc(res_graph, res_cost); |
---|
440 | ResPath cycle; |
---|
441 | |
---|
442 | #ifdef _DEBUG_ITER_ |
---|
443 | int cycle_num = 0; |
---|
444 | #endif |
---|
445 | mmc.cyclePath(cycle).init(); |
---|
446 | if (mmc.findMinMean()) { |
---|
447 | while (mmc.cycleLength() < 0) { |
---|
448 | #ifdef _DEBUG_ITER_ |
---|
449 | ++iter; |
---|
450 | #endif |
---|
451 | // Finding the cycle |
---|
452 | mmc.findCycle(); |
---|
453 | |
---|
454 | // Finding the largest flow amount that can be augmented |
---|
455 | // along the cycle |
---|
456 | Capacity delta = 0; |
---|
457 | for (typename ResPath::EdgeIt e(cycle); e != INVALID; ++e) { |
---|
458 | if (delta == 0 || res_graph.rescap(e) < delta) |
---|
459 | delta = res_graph.rescap(e); |
---|
460 | } |
---|
461 | |
---|
462 | // Augmenting along the cycle |
---|
463 | for (typename ResPath::EdgeIt e(cycle); e != INVALID; ++e) |
---|
464 | res_graph.augment(e, delta); |
---|
465 | |
---|
466 | // Finding the minimum cycle mean for the modified residual |
---|
467 | // graph |
---|
468 | mmc.reset(); |
---|
469 | if (!mmc.findMinMean()) break; |
---|
470 | } |
---|
471 | } |
---|
472 | |
---|
473 | #ifdef _DEBUG_ITER_ |
---|
474 | std::cout << "Minimum mean cycle-canceling algorithm finished. " |
---|
475 | << "Found " << cycle_num << " negative cycles." |
---|
476 | << std::endl; |
---|
477 | #endif |
---|
478 | |
---|
479 | // Handling nonzero lower bounds |
---|
480 | if (lower) { |
---|
481 | for (EdgeIt e(graph); e != INVALID; ++e) |
---|
482 | flow[e] += (*lower)[e]; |
---|
483 | } |
---|
484 | return true; |
---|
485 | } |
---|
486 | #endif |
---|
487 | |
---|
488 | }; //class CycleCanceling |
---|
489 | |
---|
490 | ///@} |
---|
491 | |
---|
492 | } //namespace lemon |
---|
493 | |
---|
494 | #endif //LEMON_CYCLE_CANCELING_H |
---|