| 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 |