[880] | 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_CANCEL_AND_TIGHTEN_H |
---|
| 20 | #define LEMON_CANCEL_AND_TIGHTEN_H |
---|
| 21 | |
---|
| 22 | /// \ingroup min_cost_flow |
---|
| 23 | /// |
---|
| 24 | /// \file |
---|
| 25 | /// \brief Cancel and Tighten algorithm for finding a minimum cost flow. |
---|
| 26 | |
---|
| 27 | #include <vector> |
---|
| 28 | |
---|
| 29 | #include <lemon/circulation.h> |
---|
| 30 | #include <lemon/bellman_ford.h> |
---|
| 31 | #include <lemon/howard.h> |
---|
| 32 | #include <lemon/adaptors.h> |
---|
| 33 | #include <lemon/tolerance.h> |
---|
| 34 | #include <lemon/math.h> |
---|
| 35 | |
---|
| 36 | #include <lemon/static_graph.h> |
---|
| 37 | |
---|
| 38 | namespace lemon { |
---|
| 39 | |
---|
| 40 | /// \addtogroup min_cost_flow |
---|
| 41 | /// @{ |
---|
| 42 | |
---|
| 43 | /// \brief Implementation of the Cancel and Tighten algorithm for |
---|
| 44 | /// finding a minimum cost flow. |
---|
| 45 | /// |
---|
| 46 | /// \ref CancelAndTighten implements the Cancel and Tighten algorithm for |
---|
| 47 | /// finding a minimum cost flow. |
---|
| 48 | /// |
---|
| 49 | /// \tparam Digraph The digraph type the algorithm runs on. |
---|
| 50 | /// \tparam LowerMap The type of the lower bound map. |
---|
| 51 | /// \tparam CapacityMap The type of the capacity (upper bound) map. |
---|
| 52 | /// \tparam CostMap The type of the cost (length) map. |
---|
| 53 | /// \tparam SupplyMap The type of the supply map. |
---|
| 54 | /// |
---|
| 55 | /// \warning |
---|
| 56 | /// - Arc capacities and costs should be \e non-negative \e integers. |
---|
| 57 | /// - Supply values should be \e signed \e integers. |
---|
| 58 | /// - The value types of the maps should be convertible to each other. |
---|
| 59 | /// - \c CostMap::Value must be signed type. |
---|
| 60 | /// |
---|
| 61 | /// \author Peter Kovacs |
---|
| 62 | template < typename Digraph, |
---|
| 63 | typename LowerMap = typename Digraph::template ArcMap<int>, |
---|
| 64 | typename CapacityMap = typename Digraph::template ArcMap<int>, |
---|
| 65 | typename CostMap = typename Digraph::template ArcMap<int>, |
---|
| 66 | typename SupplyMap = typename Digraph::template NodeMap<int> > |
---|
| 67 | class CancelAndTighten |
---|
| 68 | { |
---|
| 69 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
---|
| 70 | |
---|
| 71 | typedef typename CapacityMap::Value Capacity; |
---|
| 72 | typedef typename CostMap::Value Cost; |
---|
| 73 | typedef typename SupplyMap::Value Supply; |
---|
| 74 | typedef typename Digraph::template ArcMap<Capacity> CapacityArcMap; |
---|
| 75 | typedef typename Digraph::template NodeMap<Supply> SupplyNodeMap; |
---|
| 76 | |
---|
| 77 | typedef ResidualDigraph< const Digraph, |
---|
| 78 | CapacityArcMap, CapacityArcMap > ResDigraph; |
---|
| 79 | |
---|
| 80 | public: |
---|
| 81 | |
---|
| 82 | /// The type of the flow map. |
---|
| 83 | typedef typename Digraph::template ArcMap<Capacity> FlowMap; |
---|
| 84 | /// The type of the potential map. |
---|
| 85 | typedef typename Digraph::template NodeMap<Cost> PotentialMap; |
---|
| 86 | |
---|
| 87 | private: |
---|
| 88 | |
---|
| 89 | /// \brief Map adaptor class for handling residual arc costs. |
---|
| 90 | /// |
---|
| 91 | /// Map adaptor class for handling residual arc costs. |
---|
| 92 | class ResidualCostMap : public MapBase<typename ResDigraph::Arc, Cost> |
---|
| 93 | { |
---|
| 94 | typedef typename ResDigraph::Arc Arc; |
---|
| 95 | |
---|
| 96 | private: |
---|
| 97 | |
---|
| 98 | const CostMap &_cost_map; |
---|
| 99 | |
---|
| 100 | public: |
---|
| 101 | |
---|
| 102 | ///\e |
---|
| 103 | ResidualCostMap(const CostMap &cost_map) : _cost_map(cost_map) {} |
---|
| 104 | |
---|
| 105 | ///\e |
---|
| 106 | Cost operator[](const Arc &e) const { |
---|
| 107 | return ResDigraph::forward(e) ? _cost_map[e] : -_cost_map[e]; |
---|
| 108 | } |
---|
| 109 | |
---|
| 110 | }; //class ResidualCostMap |
---|
| 111 | |
---|
| 112 | /// \brief Map adaptor class for handling reduced arc costs. |
---|
| 113 | /// |
---|
| 114 | /// Map adaptor class for handling reduced arc costs. |
---|
| 115 | class ReducedCostMap : public MapBase<Arc, Cost> |
---|
| 116 | { |
---|
| 117 | private: |
---|
| 118 | |
---|
| 119 | const Digraph &_gr; |
---|
| 120 | const CostMap &_cost_map; |
---|
| 121 | const PotentialMap &_pot_map; |
---|
| 122 | |
---|
| 123 | public: |
---|
| 124 | |
---|
| 125 | ///\e |
---|
| 126 | ReducedCostMap( const Digraph &gr, |
---|
| 127 | const CostMap &cost_map, |
---|
| 128 | const PotentialMap &pot_map ) : |
---|
| 129 | _gr(gr), _cost_map(cost_map), _pot_map(pot_map) {} |
---|
| 130 | |
---|
| 131 | ///\e |
---|
| 132 | inline Cost operator[](const Arc &e) const { |
---|
| 133 | return _cost_map[e] + _pot_map[_gr.source(e)] |
---|
| 134 | - _pot_map[_gr.target(e)]; |
---|
| 135 | } |
---|
| 136 | |
---|
| 137 | }; //class ReducedCostMap |
---|
| 138 | |
---|
| 139 | struct BFOperationTraits { |
---|
| 140 | static double zero() { return 0; } |
---|
| 141 | |
---|
| 142 | static double infinity() { |
---|
| 143 | return std::numeric_limits<double>::infinity(); |
---|
| 144 | } |
---|
| 145 | |
---|
| 146 | static double plus(const double& left, const double& right) { |
---|
| 147 | return left + right; |
---|
| 148 | } |
---|
| 149 | |
---|
| 150 | static bool less(const double& left, const double& right) { |
---|
| 151 | return left + 1e-6 < right; |
---|
| 152 | } |
---|
| 153 | }; // class BFOperationTraits |
---|
| 154 | |
---|
| 155 | private: |
---|
| 156 | |
---|
| 157 | // The digraph the algorithm runs on |
---|
| 158 | const Digraph &_graph; |
---|
| 159 | // The original lower bound map |
---|
| 160 | const LowerMap *_lower; |
---|
| 161 | // The modified capacity map |
---|
| 162 | CapacityArcMap _capacity; |
---|
| 163 | // The original cost map |
---|
| 164 | const CostMap &_cost; |
---|
| 165 | // The modified supply map |
---|
| 166 | SupplyNodeMap _supply; |
---|
| 167 | bool _valid_supply; |
---|
| 168 | |
---|
| 169 | // Arc map of the current flow |
---|
| 170 | FlowMap *_flow; |
---|
| 171 | bool _local_flow; |
---|
| 172 | // Node map of the current potentials |
---|
| 173 | PotentialMap *_potential; |
---|
| 174 | bool _local_potential; |
---|
| 175 | |
---|
| 176 | // The residual digraph |
---|
| 177 | ResDigraph *_res_graph; |
---|
| 178 | // The residual cost map |
---|
| 179 | ResidualCostMap _res_cost; |
---|
| 180 | |
---|
| 181 | public: |
---|
| 182 | |
---|
| 183 | /// \brief General constructor (with lower bounds). |
---|
| 184 | /// |
---|
| 185 | /// General constructor (with lower bounds). |
---|
| 186 | /// |
---|
| 187 | /// \param digraph The digraph the algorithm runs on. |
---|
| 188 | /// \param lower The lower bounds of the arcs. |
---|
| 189 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
| 190 | /// \param cost The cost (length) values of the arcs. |
---|
| 191 | /// \param supply The supply values of the nodes (signed). |
---|
| 192 | CancelAndTighten( const Digraph &digraph, |
---|
| 193 | const LowerMap &lower, |
---|
| 194 | const CapacityMap &capacity, |
---|
| 195 | const CostMap &cost, |
---|
| 196 | const SupplyMap &supply ) : |
---|
| 197 | _graph(digraph), _lower(&lower), _capacity(digraph), _cost(cost), |
---|
| 198 | _supply(digraph), _flow(NULL), _local_flow(false), |
---|
| 199 | _potential(NULL), _local_potential(false), |
---|
| 200 | _res_graph(NULL), _res_cost(_cost) |
---|
| 201 | { |
---|
| 202 | // Check the sum of supply values |
---|
| 203 | Supply sum = 0; |
---|
| 204 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 205 | _supply[n] = supply[n]; |
---|
| 206 | sum += _supply[n]; |
---|
| 207 | } |
---|
| 208 | _valid_supply = sum == 0; |
---|
| 209 | |
---|
| 210 | // Remove non-zero lower bounds |
---|
| 211 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
| 212 | _capacity[e] = capacity[e]; |
---|
| 213 | if (lower[e] != 0) { |
---|
| 214 | _capacity[e] -= lower[e]; |
---|
| 215 | _supply[_graph.source(e)] -= lower[e]; |
---|
| 216 | _supply[_graph.target(e)] += lower[e]; |
---|
| 217 | } |
---|
| 218 | } |
---|
| 219 | } |
---|
| 220 | /* |
---|
| 221 | /// \brief General constructor (without lower bounds). |
---|
| 222 | /// |
---|
| 223 | /// General constructor (without lower bounds). |
---|
| 224 | /// |
---|
| 225 | /// \param digraph The digraph the algorithm runs on. |
---|
| 226 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
| 227 | /// \param cost The cost (length) values of the arcs. |
---|
| 228 | /// \param supply The supply values of the nodes (signed). |
---|
| 229 | CancelAndTighten( const Digraph &digraph, |
---|
| 230 | const CapacityMap &capacity, |
---|
| 231 | const CostMap &cost, |
---|
| 232 | const SupplyMap &supply ) : |
---|
| 233 | _graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost), |
---|
| 234 | _supply(supply), _flow(NULL), _local_flow(false), |
---|
| 235 | _potential(NULL), _local_potential(false), |
---|
| 236 | _res_graph(NULL), _res_cost(_cost) |
---|
| 237 | { |
---|
| 238 | // Check the sum of supply values |
---|
| 239 | Supply sum = 0; |
---|
| 240 | for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n]; |
---|
| 241 | _valid_supply = sum == 0; |
---|
| 242 | } |
---|
| 243 | |
---|
| 244 | /// \brief Simple constructor (with lower bounds). |
---|
| 245 | /// |
---|
| 246 | /// Simple constructor (with lower bounds). |
---|
| 247 | /// |
---|
| 248 | /// \param digraph The digraph the algorithm runs on. |
---|
| 249 | /// \param lower The lower bounds of the arcs. |
---|
| 250 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
| 251 | /// \param cost The cost (length) values of the arcs. |
---|
| 252 | /// \param s The source node. |
---|
| 253 | /// \param t The target node. |
---|
| 254 | /// \param flow_value The required amount of flow from node \c s |
---|
| 255 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
---|
| 256 | CancelAndTighten( const Digraph &digraph, |
---|
| 257 | const LowerMap &lower, |
---|
| 258 | const CapacityMap &capacity, |
---|
| 259 | const CostMap &cost, |
---|
| 260 | Node s, Node t, |
---|
| 261 | Supply flow_value ) : |
---|
| 262 | _graph(digraph), _lower(&lower), _capacity(capacity), _cost(cost), |
---|
| 263 | _supply(digraph, 0), _flow(NULL), _local_flow(false), |
---|
| 264 | _potential(NULL), _local_potential(false), |
---|
| 265 | _res_graph(NULL), _res_cost(_cost) |
---|
| 266 | { |
---|
| 267 | // Remove non-zero lower bounds |
---|
| 268 | _supply[s] = flow_value; |
---|
| 269 | _supply[t] = -flow_value; |
---|
| 270 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
| 271 | if (lower[e] != 0) { |
---|
| 272 | _capacity[e] -= lower[e]; |
---|
| 273 | _supply[_graph.source(e)] -= lower[e]; |
---|
| 274 | _supply[_graph.target(e)] += lower[e]; |
---|
| 275 | } |
---|
| 276 | } |
---|
| 277 | _valid_supply = true; |
---|
| 278 | } |
---|
| 279 | |
---|
| 280 | /// \brief Simple constructor (without lower bounds). |
---|
| 281 | /// |
---|
| 282 | /// Simple constructor (without lower bounds). |
---|
| 283 | /// |
---|
| 284 | /// \param digraph The digraph the algorithm runs on. |
---|
| 285 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
| 286 | /// \param cost The cost (length) values of the arcs. |
---|
| 287 | /// \param s The source node. |
---|
| 288 | /// \param t The target node. |
---|
| 289 | /// \param flow_value The required amount of flow from node \c s |
---|
| 290 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
---|
| 291 | CancelAndTighten( const Digraph &digraph, |
---|
| 292 | const CapacityMap &capacity, |
---|
| 293 | const CostMap &cost, |
---|
| 294 | Node s, Node t, |
---|
| 295 | Supply flow_value ) : |
---|
| 296 | _graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost), |
---|
| 297 | _supply(digraph, 0), _flow(NULL), _local_flow(false), |
---|
| 298 | _potential(NULL), _local_potential(false), |
---|
| 299 | _res_graph(NULL), _res_cost(_cost) |
---|
| 300 | { |
---|
| 301 | _supply[s] = flow_value; |
---|
| 302 | _supply[t] = -flow_value; |
---|
| 303 | _valid_supply = true; |
---|
| 304 | } |
---|
| 305 | */ |
---|
| 306 | /// Destructor. |
---|
| 307 | ~CancelAndTighten() { |
---|
| 308 | if (_local_flow) delete _flow; |
---|
| 309 | if (_local_potential) delete _potential; |
---|
| 310 | delete _res_graph; |
---|
| 311 | } |
---|
| 312 | |
---|
| 313 | /// \brief Set the flow map. |
---|
| 314 | /// |
---|
| 315 | /// Set the flow map. |
---|
| 316 | /// |
---|
| 317 | /// \return \c (*this) |
---|
| 318 | CancelAndTighten& flowMap(FlowMap &map) { |
---|
| 319 | if (_local_flow) { |
---|
| 320 | delete _flow; |
---|
| 321 | _local_flow = false; |
---|
| 322 | } |
---|
| 323 | _flow = ↦ |
---|
| 324 | return *this; |
---|
| 325 | } |
---|
| 326 | |
---|
| 327 | /// \brief Set the potential map. |
---|
| 328 | /// |
---|
| 329 | /// Set the potential map. |
---|
| 330 | /// |
---|
| 331 | /// \return \c (*this) |
---|
| 332 | CancelAndTighten& potentialMap(PotentialMap &map) { |
---|
| 333 | if (_local_potential) { |
---|
| 334 | delete _potential; |
---|
| 335 | _local_potential = false; |
---|
| 336 | } |
---|
| 337 | _potential = ↦ |
---|
| 338 | return *this; |
---|
| 339 | } |
---|
| 340 | |
---|
| 341 | /// \name Execution control |
---|
| 342 | |
---|
| 343 | /// @{ |
---|
| 344 | |
---|
| 345 | /// \brief Run the algorithm. |
---|
| 346 | /// |
---|
| 347 | /// Run the algorithm. |
---|
| 348 | /// |
---|
| 349 | /// \return \c true if a feasible flow can be found. |
---|
| 350 | bool run() { |
---|
| 351 | return init() && start(); |
---|
| 352 | } |
---|
| 353 | |
---|
| 354 | /// @} |
---|
| 355 | |
---|
| 356 | /// \name Query Functions |
---|
| 357 | /// The result of the algorithm can be obtained using these |
---|
| 358 | /// functions.\n |
---|
| 359 | /// \ref lemon::CancelAndTighten::run() "run()" must be called before |
---|
| 360 | /// using them. |
---|
| 361 | |
---|
| 362 | /// @{ |
---|
| 363 | |
---|
| 364 | /// \brief Return a const reference to the arc map storing the |
---|
| 365 | /// found flow. |
---|
| 366 | /// |
---|
| 367 | /// Return a const reference to the arc map storing the found flow. |
---|
| 368 | /// |
---|
| 369 | /// \pre \ref run() must be called before using this function. |
---|
| 370 | const FlowMap& flowMap() const { |
---|
| 371 | return *_flow; |
---|
| 372 | } |
---|
| 373 | |
---|
| 374 | /// \brief Return a const reference to the node map storing the |
---|
| 375 | /// found potentials (the dual solution). |
---|
| 376 | /// |
---|
| 377 | /// Return a const reference to the node map storing the found |
---|
| 378 | /// potentials (the dual solution). |
---|
| 379 | /// |
---|
| 380 | /// \pre \ref run() must be called before using this function. |
---|
| 381 | const PotentialMap& potentialMap() const { |
---|
| 382 | return *_potential; |
---|
| 383 | } |
---|
| 384 | |
---|
| 385 | /// \brief Return the flow on the given arc. |
---|
| 386 | /// |
---|
| 387 | /// Return the flow on the given arc. |
---|
| 388 | /// |
---|
| 389 | /// \pre \ref run() must be called before using this function. |
---|
| 390 | Capacity flow(const Arc& arc) const { |
---|
| 391 | return (*_flow)[arc]; |
---|
| 392 | } |
---|
| 393 | |
---|
| 394 | /// \brief Return the potential of the given node. |
---|
| 395 | /// |
---|
| 396 | /// Return the potential of the given node. |
---|
| 397 | /// |
---|
| 398 | /// \pre \ref run() must be called before using this function. |
---|
| 399 | Cost potential(const Node& node) const { |
---|
| 400 | return (*_potential)[node]; |
---|
| 401 | } |
---|
| 402 | |
---|
| 403 | /// \brief Return the total cost of the found flow. |
---|
| 404 | /// |
---|
| 405 | /// Return the total cost of the found flow. The complexity of the |
---|
| 406 | /// function is \f$ O(e) \f$. |
---|
| 407 | /// |
---|
| 408 | /// \pre \ref run() must be called before using this function. |
---|
| 409 | Cost totalCost() const { |
---|
| 410 | Cost c = 0; |
---|
| 411 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
| 412 | c += (*_flow)[e] * _cost[e]; |
---|
| 413 | return c; |
---|
| 414 | } |
---|
| 415 | |
---|
| 416 | /// @} |
---|
| 417 | |
---|
| 418 | private: |
---|
| 419 | |
---|
| 420 | /// Initialize the algorithm. |
---|
| 421 | bool init() { |
---|
| 422 | if (!_valid_supply) return false; |
---|
| 423 | |
---|
| 424 | // Initialize flow and potential maps |
---|
| 425 | if (!_flow) { |
---|
| 426 | _flow = new FlowMap(_graph); |
---|
| 427 | _local_flow = true; |
---|
| 428 | } |
---|
| 429 | if (!_potential) { |
---|
| 430 | _potential = new PotentialMap(_graph); |
---|
| 431 | _local_potential = true; |
---|
| 432 | } |
---|
| 433 | |
---|
| 434 | _res_graph = new ResDigraph(_graph, _capacity, *_flow); |
---|
| 435 | |
---|
| 436 | // Find a feasible flow using Circulation |
---|
| 437 | Circulation< Digraph, ConstMap<Arc, Capacity>, |
---|
| 438 | CapacityArcMap, SupplyMap > |
---|
| 439 | circulation( _graph, constMap<Arc>(Capacity(0)), |
---|
| 440 | _capacity, _supply ); |
---|
| 441 | return circulation.flowMap(*_flow).run(); |
---|
| 442 | } |
---|
| 443 | |
---|
| 444 | bool start() { |
---|
| 445 | const double LIMIT_FACTOR = 0.01; |
---|
| 446 | const int MIN_LIMIT = 3; |
---|
| 447 | |
---|
| 448 | typedef typename Digraph::template NodeMap<double> FloatPotentialMap; |
---|
| 449 | typedef typename Digraph::template NodeMap<int> LevelMap; |
---|
| 450 | typedef typename Digraph::template NodeMap<bool> BoolNodeMap; |
---|
| 451 | typedef typename Digraph::template NodeMap<Node> PredNodeMap; |
---|
| 452 | typedef typename Digraph::template NodeMap<Arc> PredArcMap; |
---|
| 453 | typedef typename ResDigraph::template ArcMap<double> ResShiftCostMap; |
---|
| 454 | FloatPotentialMap pi(_graph); |
---|
| 455 | LevelMap level(_graph); |
---|
| 456 | BoolNodeMap reached(_graph); |
---|
| 457 | BoolNodeMap processed(_graph); |
---|
| 458 | PredNodeMap pred_node(_graph); |
---|
| 459 | PredArcMap pred_arc(_graph); |
---|
| 460 | int node_num = countNodes(_graph); |
---|
| 461 | typedef std::pair<Arc, bool> pair; |
---|
| 462 | std::vector<pair> stack(node_num); |
---|
| 463 | std::vector<Node> proc_vector(node_num); |
---|
| 464 | ResShiftCostMap shift_cost(*_res_graph); |
---|
| 465 | |
---|
| 466 | Tolerance<double> tol; |
---|
| 467 | tol.epsilon(1e-6); |
---|
| 468 | |
---|
| 469 | Timer t1, t2, t3; |
---|
| 470 | t1.reset(); |
---|
| 471 | t2.reset(); |
---|
| 472 | t3.reset(); |
---|
| 473 | |
---|
| 474 | // Initialize epsilon and the node potentials |
---|
| 475 | double epsilon = 0; |
---|
| 476 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
| 477 | if (_capacity[e] - (*_flow)[e] > 0 && _cost[e] < -epsilon) |
---|
| 478 | epsilon = -_cost[e]; |
---|
| 479 | else if ((*_flow)[e] > 0 && _cost[e] > epsilon) |
---|
| 480 | epsilon = _cost[e]; |
---|
| 481 | } |
---|
| 482 | for (NodeIt v(_graph); v != INVALID; ++v) { |
---|
| 483 | pi[v] = 0; |
---|
| 484 | } |
---|
| 485 | |
---|
| 486 | // Start phases |
---|
| 487 | int limit = int(LIMIT_FACTOR * node_num); |
---|
| 488 | if (limit < MIN_LIMIT) limit = MIN_LIMIT; |
---|
| 489 | int iter = limit; |
---|
| 490 | while (epsilon * node_num >= 1) { |
---|
| 491 | t1.start(); |
---|
| 492 | // Find and cancel cycles in the admissible digraph using DFS |
---|
| 493 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 494 | reached[n] = false; |
---|
| 495 | processed[n] = false; |
---|
| 496 | } |
---|
| 497 | int stack_head = -1; |
---|
| 498 | int proc_head = -1; |
---|
| 499 | |
---|
| 500 | for (NodeIt start(_graph); start != INVALID; ++start) { |
---|
| 501 | if (reached[start]) continue; |
---|
| 502 | |
---|
| 503 | // New start node |
---|
| 504 | reached[start] = true; |
---|
| 505 | pred_arc[start] = INVALID; |
---|
| 506 | pred_node[start] = INVALID; |
---|
| 507 | |
---|
| 508 | // Find the first admissible residual outgoing arc |
---|
| 509 | double p = pi[start]; |
---|
| 510 | Arc e; |
---|
| 511 | _graph.firstOut(e, start); |
---|
| 512 | while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 || |
---|
| 513 | !tol.negative(_cost[e] + p - pi[_graph.target(e)])) ) |
---|
| 514 | _graph.nextOut(e); |
---|
| 515 | if (e != INVALID) { |
---|
| 516 | stack[++stack_head] = pair(e, true); |
---|
| 517 | goto next_step_1; |
---|
| 518 | } |
---|
| 519 | _graph.firstIn(e, start); |
---|
| 520 | while ( e != INVALID && ((*_flow)[e] == 0 || |
---|
| 521 | !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) ) |
---|
| 522 | _graph.nextIn(e); |
---|
| 523 | if (e != INVALID) { |
---|
| 524 | stack[++stack_head] = pair(e, false); |
---|
| 525 | goto next_step_1; |
---|
| 526 | } |
---|
| 527 | processed[start] = true; |
---|
| 528 | proc_vector[++proc_head] = start; |
---|
| 529 | continue; |
---|
| 530 | next_step_1: |
---|
| 531 | |
---|
| 532 | while (stack_head >= 0) { |
---|
| 533 | Arc se = stack[stack_head].first; |
---|
| 534 | bool sf = stack[stack_head].second; |
---|
| 535 | Node u, v; |
---|
| 536 | if (sf) { |
---|
| 537 | u = _graph.source(se); |
---|
| 538 | v = _graph.target(se); |
---|
| 539 | } else { |
---|
| 540 | u = _graph.target(se); |
---|
| 541 | v = _graph.source(se); |
---|
| 542 | } |
---|
| 543 | |
---|
| 544 | if (!reached[v]) { |
---|
| 545 | // A new node is reached |
---|
| 546 | reached[v] = true; |
---|
| 547 | pred_node[v] = u; |
---|
| 548 | pred_arc[v] = se; |
---|
| 549 | // Find the first admissible residual outgoing arc |
---|
| 550 | double p = pi[v]; |
---|
| 551 | Arc e; |
---|
| 552 | _graph.firstOut(e, v); |
---|
| 553 | while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 || |
---|
| 554 | !tol.negative(_cost[e] + p - pi[_graph.target(e)])) ) |
---|
| 555 | _graph.nextOut(e); |
---|
| 556 | if (e != INVALID) { |
---|
| 557 | stack[++stack_head] = pair(e, true); |
---|
| 558 | goto next_step_2; |
---|
| 559 | } |
---|
| 560 | _graph.firstIn(e, v); |
---|
| 561 | while ( e != INVALID && ((*_flow)[e] == 0 || |
---|
| 562 | !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) ) |
---|
| 563 | _graph.nextIn(e); |
---|
| 564 | stack[++stack_head] = pair(e, false); |
---|
| 565 | next_step_2: ; |
---|
| 566 | } else { |
---|
| 567 | if (!processed[v]) { |
---|
| 568 | // A cycle is found |
---|
| 569 | Node n, w = u; |
---|
| 570 | Capacity d, delta = sf ? _capacity[se] - (*_flow)[se] : |
---|
| 571 | (*_flow)[se]; |
---|
| 572 | for (n = u; n != v; n = pred_node[n]) { |
---|
| 573 | d = _graph.target(pred_arc[n]) == n ? |
---|
| 574 | _capacity[pred_arc[n]] - (*_flow)[pred_arc[n]] : |
---|
| 575 | (*_flow)[pred_arc[n]]; |
---|
| 576 | if (d <= delta) { |
---|
| 577 | delta = d; |
---|
| 578 | w = pred_node[n]; |
---|
| 579 | } |
---|
| 580 | } |
---|
| 581 | |
---|
| 582 | /* |
---|
| 583 | std::cout << "CYCLE FOUND: "; |
---|
| 584 | if (sf) |
---|
| 585 | std::cout << _cost[se] + pi[_graph.source(se)] - pi[_graph.target(se)]; |
---|
| 586 | else |
---|
| 587 | std::cout << _graph.id(se) << ":" << -(_cost[se] + pi[_graph.source(se)] - pi[_graph.target(se)]); |
---|
| 588 | for (n = u; n != v; n = pred_node[n]) { |
---|
| 589 | if (_graph.target(pred_arc[n]) == n) |
---|
| 590 | std::cout << " " << _cost[pred_arc[n]] + pi[_graph.source(pred_arc[n])] - pi[_graph.target(pred_arc[n])]; |
---|
| 591 | else |
---|
| 592 | std::cout << " " << -(_cost[pred_arc[n]] + pi[_graph.source(pred_arc[n])] - pi[_graph.target(pred_arc[n])]); |
---|
| 593 | } |
---|
| 594 | std::cout << "\n"; |
---|
| 595 | */ |
---|
| 596 | // Augment along the cycle |
---|
| 597 | (*_flow)[se] = sf ? (*_flow)[se] + delta : |
---|
| 598 | (*_flow)[se] - delta; |
---|
| 599 | for (n = u; n != v; n = pred_node[n]) { |
---|
| 600 | if (_graph.target(pred_arc[n]) == n) |
---|
| 601 | (*_flow)[pred_arc[n]] += delta; |
---|
| 602 | else |
---|
| 603 | (*_flow)[pred_arc[n]] -= delta; |
---|
| 604 | } |
---|
| 605 | for (n = u; stack_head > 0 && n != w; n = pred_node[n]) { |
---|
| 606 | --stack_head; |
---|
| 607 | reached[n] = false; |
---|
| 608 | } |
---|
| 609 | u = w; |
---|
| 610 | } |
---|
| 611 | v = u; |
---|
| 612 | |
---|
| 613 | // Find the next admissible residual outgoing arc |
---|
| 614 | double p = pi[v]; |
---|
| 615 | Arc e = stack[stack_head].first; |
---|
| 616 | if (!stack[stack_head].second) { |
---|
| 617 | _graph.nextIn(e); |
---|
| 618 | goto in_arc_3; |
---|
| 619 | } |
---|
| 620 | _graph.nextOut(e); |
---|
| 621 | while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 || |
---|
| 622 | !tol.negative(_cost[e] + p - pi[_graph.target(e)])) ) |
---|
| 623 | _graph.nextOut(e); |
---|
| 624 | if (e != INVALID) { |
---|
| 625 | stack[stack_head] = pair(e, true); |
---|
| 626 | goto next_step_3; |
---|
| 627 | } |
---|
| 628 | _graph.firstIn(e, v); |
---|
| 629 | in_arc_3: |
---|
| 630 | while ( e != INVALID && ((*_flow)[e] == 0 || |
---|
| 631 | !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) ) |
---|
| 632 | _graph.nextIn(e); |
---|
| 633 | stack[stack_head] = pair(e, false); |
---|
| 634 | next_step_3: ; |
---|
| 635 | } |
---|
| 636 | |
---|
| 637 | while (stack_head >= 0 && stack[stack_head].first == INVALID) { |
---|
| 638 | processed[v] = true; |
---|
| 639 | proc_vector[++proc_head] = v; |
---|
| 640 | if (--stack_head >= 0) { |
---|
| 641 | v = stack[stack_head].second ? |
---|
| 642 | _graph.source(stack[stack_head].first) : |
---|
| 643 | _graph.target(stack[stack_head].first); |
---|
| 644 | // Find the next admissible residual outgoing arc |
---|
| 645 | double p = pi[v]; |
---|
| 646 | Arc e = stack[stack_head].first; |
---|
| 647 | if (!stack[stack_head].second) { |
---|
| 648 | _graph.nextIn(e); |
---|
| 649 | goto in_arc_4; |
---|
| 650 | } |
---|
| 651 | _graph.nextOut(e); |
---|
| 652 | while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 || |
---|
| 653 | !tol.negative(_cost[e] + p - pi[_graph.target(e)])) ) |
---|
| 654 | _graph.nextOut(e); |
---|
| 655 | if (e != INVALID) { |
---|
| 656 | stack[stack_head] = pair(e, true); |
---|
| 657 | goto next_step_4; |
---|
| 658 | } |
---|
| 659 | _graph.firstIn(e, v); |
---|
| 660 | in_arc_4: |
---|
| 661 | while ( e != INVALID && ((*_flow)[e] == 0 || |
---|
| 662 | !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) ) |
---|
| 663 | _graph.nextIn(e); |
---|
| 664 | stack[stack_head] = pair(e, false); |
---|
| 665 | next_step_4: ; |
---|
| 666 | } |
---|
| 667 | } |
---|
| 668 | } |
---|
| 669 | } |
---|
| 670 | t1.stop(); |
---|
| 671 | |
---|
| 672 | // Tighten potentials and epsilon |
---|
| 673 | if (--iter > 0) { |
---|
| 674 | // Compute levels |
---|
| 675 | t2.start(); |
---|
| 676 | for (int i = proc_head; i >= 0; --i) { |
---|
| 677 | Node v = proc_vector[i]; |
---|
| 678 | double p = pi[v]; |
---|
| 679 | int l = 0; |
---|
| 680 | for (InArcIt e(_graph, v); e != INVALID; ++e) { |
---|
| 681 | Node u = _graph.source(e); |
---|
| 682 | if ( _capacity[e] - (*_flow)[e] > 0 && |
---|
| 683 | tol.negative(_cost[e] + pi[u] - p) && |
---|
| 684 | level[u] + 1 > l ) l = level[u] + 1; |
---|
| 685 | } |
---|
| 686 | for (OutArcIt e(_graph, v); e != INVALID; ++e) { |
---|
| 687 | Node u = _graph.target(e); |
---|
| 688 | if ( (*_flow)[e] > 0 && |
---|
| 689 | tol.negative(-_cost[e] + pi[u] - p) && |
---|
| 690 | level[u] + 1 > l ) l = level[u] + 1; |
---|
| 691 | } |
---|
| 692 | level[v] = l; |
---|
| 693 | } |
---|
| 694 | |
---|
| 695 | // Modify potentials |
---|
| 696 | double p, q = -1; |
---|
| 697 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
| 698 | Node u = _graph.source(e); |
---|
| 699 | Node v = _graph.target(e); |
---|
| 700 | if (_capacity[e] - (*_flow)[e] > 0 && level[u] - level[v] > 0) { |
---|
| 701 | p = (_cost[e] + pi[u] - pi[v] + epsilon) / |
---|
| 702 | (level[u] - level[v] + 1); |
---|
| 703 | if (q < 0 || p < q) q = p; |
---|
| 704 | } |
---|
| 705 | else if ((*_flow)[e] > 0 && level[v] - level[u] > 0) { |
---|
| 706 | p = (-_cost[e] - pi[u] + pi[v] + epsilon) / |
---|
| 707 | (level[v] - level[u] + 1); |
---|
| 708 | if (q < 0 || p < q) q = p; |
---|
| 709 | } |
---|
| 710 | } |
---|
| 711 | for (NodeIt v(_graph); v != INVALID; ++v) { |
---|
| 712 | pi[v] -= q * level[v]; |
---|
| 713 | } |
---|
| 714 | |
---|
| 715 | // Modify epsilon |
---|
| 716 | epsilon = 0; |
---|
| 717 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
| 718 | double curr = _cost[e] + pi[_graph.source(e)] |
---|
| 719 | - pi[_graph.target(e)]; |
---|
| 720 | if (_capacity[e] - (*_flow)[e] > 0 && curr < -epsilon) |
---|
| 721 | epsilon = -curr; |
---|
| 722 | else if ((*_flow)[e] > 0 && curr > epsilon) |
---|
| 723 | epsilon = curr; |
---|
| 724 | } |
---|
| 725 | t2.stop(); |
---|
| 726 | } else { |
---|
| 727 | // Set epsilon to the minimum cycle mean |
---|
| 728 | t3.start(); |
---|
| 729 | |
---|
| 730 | /**/ |
---|
| 731 | StaticDigraph static_graph; |
---|
| 732 | typename ResDigraph::template NodeMap<typename StaticDigraph::Node> node_ref(*_res_graph); |
---|
| 733 | typename ResDigraph::template ArcMap<typename StaticDigraph::Arc> arc_ref(*_res_graph); |
---|
| 734 | static_graph.build(*_res_graph, node_ref, arc_ref); |
---|
| 735 | typename StaticDigraph::template NodeMap<double> static_pi(static_graph); |
---|
| 736 | typename StaticDigraph::template ArcMap<double> static_cost(static_graph); |
---|
| 737 | |
---|
| 738 | for (typename ResDigraph::ArcIt e(*_res_graph); e != INVALID; ++e) |
---|
| 739 | static_cost[arc_ref[e]] = _res_cost[e]; |
---|
| 740 | |
---|
| 741 | Howard<StaticDigraph, typename StaticDigraph::template ArcMap<double> > |
---|
| 742 | mmc(static_graph, static_cost); |
---|
| 743 | mmc.findMinMean(); |
---|
| 744 | epsilon = -mmc.cycleMean(); |
---|
| 745 | /**/ |
---|
| 746 | |
---|
| 747 | /* |
---|
| 748 | Howard<ResDigraph, ResidualCostMap> mmc(*_res_graph, _res_cost); |
---|
| 749 | mmc.findMinMean(); |
---|
| 750 | epsilon = -mmc.cycleMean(); |
---|
| 751 | */ |
---|
| 752 | |
---|
| 753 | // Compute feasible potentials for the current epsilon |
---|
| 754 | for (typename StaticDigraph::ArcIt e(static_graph); e != INVALID; ++e) |
---|
| 755 | static_cost[e] += epsilon; |
---|
| 756 | typename BellmanFord<StaticDigraph, typename StaticDigraph::template ArcMap<double> >:: |
---|
| 757 | template SetDistMap<typename StaticDigraph::template NodeMap<double> >:: |
---|
| 758 | template SetOperationTraits<BFOperationTraits>::Create |
---|
| 759 | bf(static_graph, static_cost); |
---|
| 760 | bf.distMap(static_pi).init(0); |
---|
| 761 | bf.start(); |
---|
| 762 | for (NodeIt n(_graph); n != INVALID; ++n) |
---|
| 763 | pi[n] = static_pi[node_ref[n]]; |
---|
| 764 | |
---|
| 765 | /* |
---|
| 766 | for (typename ResDigraph::ArcIt e(*_res_graph); e != INVALID; ++e) |
---|
| 767 | shift_cost[e] = _res_cost[e] + epsilon; |
---|
| 768 | typename BellmanFord<ResDigraph, ResShiftCostMap>:: |
---|
| 769 | template SetDistMap<FloatPotentialMap>:: |
---|
| 770 | template SetOperationTraits<BFOperationTraits>::Create |
---|
| 771 | bf(*_res_graph, shift_cost); |
---|
| 772 | bf.distMap(pi).init(0); |
---|
| 773 | bf.start(); |
---|
| 774 | */ |
---|
| 775 | |
---|
| 776 | iter = limit; |
---|
| 777 | t3.stop(); |
---|
| 778 | } |
---|
| 779 | } |
---|
| 780 | |
---|
| 781 | // std::cout << t1.realTime() << " " << t2.realTime() << " " << t3.realTime() << "\n"; |
---|
| 782 | |
---|
| 783 | // Handle non-zero lower bounds |
---|
| 784 | if (_lower) { |
---|
| 785 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
| 786 | (*_flow)[e] += (*_lower)[e]; |
---|
| 787 | } |
---|
| 788 | return true; |
---|
| 789 | } |
---|
| 790 | |
---|
| 791 | }; //class CancelAndTighten |
---|
| 792 | |
---|
| 793 | ///@} |
---|
| 794 | |
---|
| 795 | } //namespace lemon |
---|
| 796 | |
---|
| 797 | #endif //LEMON_CANCEL_AND_TIGHTEN_H |
---|