Changeset 2535:716024e7c080 in lemon0.x
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 12/05/07 14:03:19 (13 years ago)
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lemon/capacity_scaling.h
r2533 r2535 26 26 /// flow. 27 27 28 #include <lemon/graph_adaptor.h> 29 #include <lemon/bin_heap.h> 28 30 #include <vector> 29 #include <lemon/graph_adaptor.h>30 #include <lemon/dijkstra.h>31 32 #define WITH_SCALING33 34 #ifdef WITH_SCALING35 #define SCALING_FACTOR 236 #endif37 38 //#define _DEBUG_ITER_39 31 40 32 namespace lemon { … … 47 39 /// flow. 48 40 /// 49 /// \ref lemon::CapacityScaling "CapacityScaling" implements the50 /// capacity scaling version of the successive shortest path51 /// algorithm for finding a minimumcost flow.41 /// \ref CapacityScaling implements the capacity scaling version 42 /// of the successive shortest path algorithm for finding a minimum 43 /// cost flow. 52 44 /// 53 45 /// \param Graph The directed graph type the algorithm runs on. … … 59 51 /// \warning 60 52 ///  Edge capacities and costs should be nonnegative integers. 61 /// 53 /// However \c CostMap::Value should be signed type. 62 54 ///  Supply values should be signed integers. 63 55 ///  \c LowerMap::Value must be convertible to 64 /// 65 /// 56 /// \c CapacityMap::Value and \c CapacityMap::Value must be 57 /// convertible to \c SupplyMap::Value. 66 58 /// 67 59 /// \author Peter Kovacs 68 60 69 61 template < typename Graph, 70 71 72 73 74 62 typename LowerMap = typename Graph::template EdgeMap<int>, 63 typename CapacityMap = LowerMap, 64 typename CostMap = typename Graph::template EdgeMap<int>, 65 typename SupplyMap = typename Graph::template NodeMap 66 <typename CapacityMap::Value> > 75 67 class CapacityScaling 76 68 { … … 88 80 typedef typename Graph::template EdgeMap<Capacity> CapacityRefMap; 89 81 typedef typename Graph::template NodeMap<Supply> SupplyRefMap; 90 91 typedef ResGraphAdaptor< const Graph, Capacity, 92 CapacityRefMap, CapacityRefMap > ResGraph; 93 typedef typename ResGraph::Node ResNode; 94 typedef typename ResGraph::NodeIt ResNodeIt; 95 typedef typename ResGraph::Edge ResEdge; 96 typedef typename ResGraph::EdgeIt ResEdgeIt; 82 typedef typename Graph::template NodeMap<Edge> PredMap; 97 83 98 84 public: 85 86 /// \brief Type to enable or disable capacity scaling. 87 enum ScalingEnum { 88 WITH_SCALING = 0, 89 WITHOUT_SCALING = 1 90 }; 99 91 100 92 /// \brief The type of the flow map. … … 105 97 protected: 106 98 107 /// \brief Map adaptor class for handling reduced edge costs. 108 class ReducedCostMap : public MapBase<ResEdge, Cost> 99 /// \brief Special implementation of the \ref Dijkstra algorithm 100 /// for finding shortest paths in the residual network of the graph 101 /// with respect to the reduced edge costs and modifying the 102 /// node potentials according to the distance of the nodes. 103 class ResidualDijkstra 109 104 { 110 private: 111 112 const ResGraph &gr; 113 const CostMap &cost_map; 114 const PotentialMap &pot_map; 105 typedef typename Graph::template NodeMap<Cost> CostNodeMap; 106 typedef typename Graph::template NodeMap<Edge> PredMap; 107 108 typedef typename Graph::template NodeMap<int> HeapCrossRef; 109 typedef BinHeap<Cost, HeapCrossRef> Heap; 110 111 protected: 112 113 /// \brief The directed graph the algorithm runs on. 114 const Graph &graph; 115 116 /// \brief The flow map. 117 const FlowMap &flow; 118 /// \brief The residual capacity map. 119 const CapacityRefMap &res_cap; 120 /// \brief The cost map. 121 const CostMap &cost; 122 /// \brief The excess map. 123 const SupplyRefMap &excess; 124 125 /// \brief The potential map. 126 PotentialMap &potential; 127 128 /// \brief The distance map. 129 CostNodeMap dist; 130 /// \brief The map of predecessors edges. 131 PredMap &pred; 132 /// \brief The processed (i.e. permanently labeled) nodes. 133 std::vector<Node> proc_nodes; 115 134 116 135 public: 117 136 118 ReducedCostMap( const ResGraph &_gr, 119 const CostMap &_cost, 120 const PotentialMap &_pot ) : 121 gr(_gr), cost_map(_cost), pot_map(_pot) {} 122 123 Cost operator[](const ResEdge &e) const { 124 return ResGraph::forward(e) ? 125 cost_map[e]  pot_map[gr.source(e)] + pot_map[gr.target(e)] : 126 cost_map[e]  pot_map[gr.source(e)] + pot_map[gr.target(e)]; 127 } 128 129 }; //class ReducedCostMap 130 131 /// \brief Map class for the \ref lemon::Dijkstra "Dijkstra" 132 /// algorithm to update node potentials. 133 class PotentialUpdateMap : public MapBase<ResNode, Cost> 134 { 135 private: 136 137 PotentialMap *pot; 138 typedef std::pair<ResNode, Cost> Pair; 139 std::vector<Pair> data; 140 141 public: 142 143 void potentialMap(PotentialMap &_pot) { 144 pot = &_pot; 145 } 146 147 void init() { 148 data.clear(); 149 } 150 151 void set(const ResNode &n, const Cost &v) { 152 data.push_back(Pair(n, v)); 153 } 154 155 void update() { 156 Cost val = data[data.size()1].second; 157 for (int i = 0; i < data.size()1; ++i) 158 (*pot)[data[i].first] += val  data[i].second; 159 } 160 161 }; //class PotentialUpdateMap 162 163 #ifdef WITH_SCALING 164 /// \brief Map adaptor class for identifing deficit nodes. 165 class DeficitBoolMap : public MapBase<ResNode, bool> 166 { 167 private: 168 169 const SupplyRefMap &imb; 170 const Capacity δ 171 172 public: 173 174 DeficitBoolMap(const SupplyRefMap &_imb, const Capacity &_delta) : 175 imb(_imb), delta(_delta) {} 176 177 bool operator[](const ResNode &n) const { 178 return imb[n] <= delta; 179 } 180 181 }; //class DeficitBoolMap 182 183 /// \brief Map adaptor class for filtering edges with at least 184 /// \c delta residual capacity. 185 class DeltaFilterMap : public MapBase<ResEdge, bool> 186 { 187 private: 188 189 const ResGraph &gr; 190 const Capacity δ 191 192 public: 193 194 DeltaFilterMap(const ResGraph &_gr, const Capacity &_delta) : 195 gr(_gr), delta(_delta) {} 196 197 bool operator[](const ResEdge &e) const { 198 return gr.rescap(e) >= delta; 199 } 200 201 }; //class DeltaFilterMap 202 203 typedef EdgeSubGraphAdaptor<const ResGraph, const DeltaFilterMap> 204 DeltaResGraph; 205 206 /// \brief Traits class for \ref lemon::Dijkstra "Dijkstra" class. 207 class ResDijkstraTraits : 208 public DijkstraDefaultTraits<DeltaResGraph, ReducedCostMap> 209 { 210 public: 211 212 typedef PotentialUpdateMap DistMap; 213 214 static DistMap *createDistMap(const DeltaResGraph&) { 215 return new DistMap(); 216 } 217 218 }; //class ResDijkstraTraits 219 220 #else //WITHOUT_CAPACITY_SCALING 221 /// \brief Map adaptor class for identifing deficit nodes. 222 class DeficitBoolMap : public MapBase<ResNode, bool> 223 { 224 private: 225 226 const SupplyRefMap &imb; 227 228 public: 229 230 DeficitBoolMap(const SupplyRefMap &_imb) : imb(_imb) {} 231 232 bool operator[](const ResNode &n) const { 233 return imb[n] < 0; 234 } 235 236 }; //class DeficitBoolMap 237 238 /// \brief Traits class for \ref lemon::Dijkstra "Dijkstra" class. 239 class ResDijkstraTraits : 240 public DijkstraDefaultTraits<ResGraph, ReducedCostMap> 241 { 242 public: 243 244 typedef PotentialUpdateMap DistMap; 245 246 static DistMap *createDistMap(const ResGraph&) { 247 return new DistMap(); 248 } 249 250 }; //class ResDijkstraTraits 251 #endif 137 /// \brief The constructor of the class. 138 ResidualDijkstra( const Graph &_graph, 139 const FlowMap &_flow, 140 const CapacityRefMap &_res_cap, 141 const CostMap &_cost, 142 const SupplyMap &_excess, 143 PotentialMap &_potential, 144 PredMap &_pred ) : 145 graph(_graph), flow(_flow), res_cap(_res_cap), cost(_cost), 146 excess(_excess), potential(_potential), dist(_graph), 147 pred(_pred) 148 {} 149 150 /// \brief Runs the algorithm from the given source node. 151 Node run(Node s, Capacity delta) { 152 HeapCrossRef heap_cross_ref(graph, Heap::PRE_HEAP); 153 Heap heap(heap_cross_ref); 154 heap.push(s, 0); 155 pred[s] = INVALID; 156 proc_nodes.clear(); 157 158 // Processing nodes 159 while (!heap.empty() && excess[heap.top()] > delta) { 160 Node u = heap.top(), v; 161 Cost d = heap.prio()  potential[u], nd; 162 dist[u] = heap.prio(); 163 heap.pop(); 164 proc_nodes.push_back(u); 165 166 // Traversing outgoing edges 167 for (OutEdgeIt e(graph, u); e != INVALID; ++e) { 168 if (res_cap[e] >= delta) { 169 v = graph.target(e); 170 switch(heap.state(v)) { 171 case Heap::PRE_HEAP: 172 heap.push(v, d + cost[e] + potential[v]); 173 pred[v] = e; 174 break; 175 case Heap::IN_HEAP: 176 nd = d + cost[e] + potential[v]; 177 if (nd < heap[v]) { 178 heap.decrease(v, nd); 179 pred[v] = e; 180 } 181 break; 182 case Heap::POST_HEAP: 183 break; 184 } 185 } 186 } 187 188 // Traversing incoming edges 189 for (InEdgeIt e(graph, u); e != INVALID; ++e) { 190 if (flow[e] >= delta) { 191 v = graph.source(e); 192 switch(heap.state(v)) { 193 case Heap::PRE_HEAP: 194 heap.push(v, d  cost[e] + potential[v]); 195 pred[v] = e; 196 break; 197 case Heap::IN_HEAP: 198 nd = d  cost[e] + potential[v]; 199 if (nd < heap[v]) { 200 heap.decrease(v, nd); 201 pred[v] = e; 202 } 203 break; 204 case Heap::POST_HEAP: 205 break; 206 } 207 } 208 } 209 } 210 if (heap.empty()) return INVALID; 211 212 // Updating potentials of processed nodes 213 Node t = heap.top(); 214 Cost dt = heap.prio(); 215 for (int i = 0; i < proc_nodes.size(); ++i) 216 potential[proc_nodes[i]] = dist[proc_nodes[i]]  dt; 217 218 return t; 219 } 220 221 }; //class ResidualDijkstra 252 222 253 223 protected: … … 270 240 /// \brief The potential node map. 271 241 PotentialMap potential; 272 /// \brief The residual graph. 273 ResGraph res_graph; 274 /// \brief The reduced cost map. 275 ReducedCostMap red_cost; 276 277 /// \brief The imbalance map. 278 SupplyRefMap imbalance; 279 /// \brief The excess nodes. 280 std::vector<ResNode> excess_nodes; 242 243 /// \brief The residual capacity map. 244 CapacityRefMap res_cap; 245 /// \brief The excess map. 246 SupplyRefMap excess; 247 /// \brief The excess nodes (i.e. nodes with positive excess). 248 std::vector<Node> excess_nodes; 281 249 /// \brief The index of the next excess node. 282 250 int next_node; 283 251 284 #ifdef WITH_SCALING 285 typedef Dijkstra<DeltaResGraph, ReducedCostMap, ResDijkstraTraits> 286 ResDijkstra; 287 /// \brief \ref lemon::Dijkstra "Dijkstra" class for finding 288 /// shortest paths in the residual graph with respect to the 289 /// reduced edge costs. 290 ResDijkstra dijkstra; 291 252 /// \brief The scaling status (enabled or disabled). 253 ScalingEnum scaling; 292 254 /// \brief The delta parameter used for capacity scaling. 293 255 Capacity delta; 294 /// \brief Edge filter map for filtering edges with at least 295 /// \c delta residual capacity. 296 DeltaFilterMap delta_filter; 297 /// \brief The delta residual graph (i.e. the subgraph of the 298 /// residual graph consisting of edges with at least \c delta 299 /// residual capacity). 300 DeltaResGraph dres_graph; 301 /// \brief Map for identifing deficit nodes. 302 DeficitBoolMap delta_deficit; 303 256 /// \brief The maximum number of phases. 257 Capacity phase_num; 304 258 /// \brief The deficit nodes. 305 std::vector<ResNode> deficit_nodes; 306 307 #else //WITHOUT_CAPACITY_SCALING 308 typedef Dijkstra<ResGraph, ReducedCostMap, ResDijkstraTraits> 309 ResDijkstra; 310 /// \brief \ref lemon::Dijkstra "Dijkstra" class for finding 311 /// shortest paths in the residual graph with respect to the 312 /// reduced edge costs. 313 ResDijkstra dijkstra; 314 /// \brief Map for identifing deficit nodes. 315 DeficitBoolMap has_deficit; 316 #endif 317 318 /// \brief Pred map for the \ref lemon::Dijkstra "Dijkstra" class. 319 typename ResDijkstra::PredMap pred; 320 /// \brief Dist map for the \ref lemon::Dijkstra "Dijkstra" class to 321 /// update node potentials. 322 PotentialUpdateMap updater; 259 std::vector<Node> deficit_nodes; 260 261 /// \brief Implementation of the \ref Dijkstra algorithm for 262 /// finding augmenting shortest paths in the residual network. 263 ResidualDijkstra dijkstra; 264 /// \brief The map of predecessors edges. 265 PredMap pred; 323 266 324 267 public : … … 334 277 /// \param _supply The supply values of the nodes (signed). 335 278 CapacityScaling( const Graph &_graph, 336 337 338 339 279 const LowerMap &_lower, 280 const CapacityMap &_capacity, 281 const CostMap &_cost, 282 const SupplyMap &_supply ) : 340 283 graph(_graph), lower(&_lower), capacity(_graph), cost(_cost), 341 284 supply(_graph), flow(_graph, 0), potential(_graph, 0), 342 res_graph(_graph, capacity, flow), 343 red_cost(res_graph, cost, potential), imbalance(_graph), 344 #ifdef WITH_SCALING 345 delta(0), delta_filter(res_graph, delta), 346 dres_graph(res_graph, delta_filter), 347 dijkstra(dres_graph, red_cost), pred(dres_graph), 348 delta_deficit(imbalance, delta) 349 #else //WITHOUT_CAPACITY_SCALING 350 dijkstra(res_graph, red_cost), pred(res_graph), 351 has_deficit(imbalance) 352 #endif 285 res_cap(_graph), excess(_graph), pred(_graph), 286 dijkstra(graph, flow, res_cap, cost, excess, potential, pred) 353 287 { 354 288 // Removing nonzero lower bounds 355 289 capacity = subMap(_capacity, _lower); 290 res_cap = capacity; 356 291 Supply sum = 0; 357 292 for (NodeIt n(graph); n != INVALID; ++n) { 358 359 360 361 362 363 364 293 Supply s = _supply[n]; 294 for (InEdgeIt e(graph, n); e != INVALID; ++e) 295 s += _lower[e]; 296 for (OutEdgeIt e(graph, n); e != INVALID; ++e) 297 s = _lower[e]; 298 supply[n] = s; 299 sum += s; 365 300 } 366 301 valid_supply = sum == 0; … … 376 311 /// \param _supply The supply values of the nodes (signed). 377 312 CapacityScaling( const Graph &_graph, 378 379 380 313 const CapacityMap &_capacity, 314 const CostMap &_cost, 315 const SupplyMap &_supply ) : 381 316 graph(_graph), lower(NULL), capacity(_capacity), cost(_cost), 382 317 supply(_supply), flow(_graph, 0), potential(_graph, 0), 383 res_graph(_graph, capacity, flow), 384 red_cost(res_graph, cost, potential), imbalance(_graph), 385 #ifdef WITH_SCALING 386 delta(0), delta_filter(res_graph, delta), 387 dres_graph(res_graph, delta_filter), 388 dijkstra(dres_graph, red_cost), pred(dres_graph), 389 delta_deficit(imbalance, delta) 390 #else //WITHOUT_CAPACITY_SCALING 391 dijkstra(res_graph, red_cost), pred(res_graph), 392 has_deficit(imbalance) 393 #endif 318 res_cap(_capacity), excess(_graph), pred(_graph), 319 dijkstra(graph, flow, res_cap, cost, excess, potential) 394 320 { 395 321 // Checking the sum of supply values … … 413 339 /// \c _t). 414 340 CapacityScaling( const Graph &_graph, 415 416 417 418 419 341 const LowerMap &_lower, 342 const CapacityMap &_capacity, 343 const CostMap &_cost, 344 Node _s, Node _t, 345 Supply _flow_value ) : 420 346 graph(_graph), lower(&_lower), capacity(_graph), cost(_cost), 421 347 supply(_graph), flow(_graph, 0), potential(_graph, 0), 422 res_graph(_graph, capacity, flow), 423 red_cost(res_graph, cost, potential), imbalance(_graph), 424 #ifdef WITH_SCALING 425 delta(0), delta_filter(res_graph, delta), 426 dres_graph(res_graph, delta_filter), 427 dijkstra(dres_graph, red_cost), pred(dres_graph), 428 delta_deficit(imbalance, delta) 429 #else //WITHOUT_CAPACITY_SCALING 430 dijkstra(res_graph, red_cost), pred(res_graph), 431 has_deficit(imbalance) 432 #endif 348 res_cap(_graph), excess(_graph), pred(_graph), 349 dijkstra(graph, flow, res_cap, cost, excess, potential) 433 350 { 434 351 // Removing nonzero lower bounds 435 352 capacity = subMap(_capacity, _lower); 353 res_cap = capacity; 436 354 for (NodeIt n(graph); n != INVALID; ++n) { 437 438 439 440 441 442 443 444 355 Supply s = 0; 356 if (n == _s) s = _flow_value; 357 if (n == _t) s = _flow_value; 358 for (InEdgeIt e(graph, n); e != INVALID; ++e) 359 s += _lower[e]; 360 for (OutEdgeIt e(graph, n); e != INVALID; ++e) 361 s = _lower[e]; 362 supply[n] = s; 445 363 } 446 364 valid_supply = true; … … 460 378 /// \c _t). 461 379 CapacityScaling( const Graph &_graph, 462 463 464 465 380 const CapacityMap &_capacity, 381 const CostMap &_cost, 382 Node _s, Node _t, 383 Supply _flow_value ) : 466 384 graph(_graph), lower(NULL), capacity(_capacity), cost(_cost), 467 385 supply(_graph, 0), flow(_graph, 0), potential(_graph, 0), 468 res_graph(_graph, capacity, flow), 469 red_cost(res_graph, cost, potential), imbalance(_graph), 470 #ifdef WITH_SCALING 471 delta(0), delta_filter(res_graph, delta), 472 dres_graph(res_graph, delta_filter), 473 dijkstra(dres_graph, red_cost), pred(dres_graph), 474 delta_deficit(imbalance, delta) 475 #else //WITHOUT_CAPACITY_SCALING 476 dijkstra(res_graph, red_cost), pred(res_graph), 477 has_deficit(imbalance) 478 #endif 386 res_cap(_capacity), excess(_graph), pred(_graph), 387 dijkstra(graph, flow, res_cap, cost, excess, potential) 479 388 { 480 389 supply[_s] = _flow_value; … … 512 421 Cost c = 0; 513 422 for (EdgeIt e(graph); e != INVALID; ++e) 514 423 c += flow[e] * cost[e]; 515 424 return c; 516 425 } … … 520 429 /// Runs the algorithm. 521 430 /// 431 /// \param scaling_mode The scaling mode. In case of WITH_SCALING 432 /// capacity scaling is enabled in the algorithm (this is the 433 /// default value) otherwise it is disabled. 434 /// If the maximum edge capacity and/or the amount of total supply 435 /// is small, the algorithm could be faster without scaling. 436 /// 522 437 /// \return \c true if a feasible flow can be found. 523 bool run( ) {524 return init( ) && start();438 bool run(int scaling_mode = WITH_SCALING) { 439 return init(scaling_mode) && start(); 525 440 } 526 441 … … 528 443 529 444 /// \brief Initializes the algorithm. 530 bool init( ) {445 bool init(int scaling_mode) { 531 446 if (!valid_supply) return false; 532 imbalance = supply; 533 534 // Initalizing Dijkstra class 535 updater.potentialMap(potential); 536 dijkstra.distMap(updater).predMap(pred); 537 538 #ifdef WITH_SCALING 447 excess = supply; 448 539 449 // Initilaizing delta value 540 Supply max_sup = 0, max_dem = 0; 541 for (NodeIt n(graph); n != INVALID; ++n) { 542 if (supply[n] > max_sup) max_sup = supply[n]; 543 if (supply[n] < max_dem) max_dem = supply[n]; 544 } 545 if (max_dem < max_sup) max_sup = max_dem; 546 for ( delta = 1; SCALING_FACTOR * delta < max_sup; 547 delta *= SCALING_FACTOR ) ; 548 #endif 450 if (scaling_mode == WITH_SCALING) { 451 // With scaling 452 Supply max_sup = 0, max_dem = 0; 453 for (NodeIt n(graph); n != INVALID; ++n) { 454 if ( supply[n] > max_sup) max_sup = supply[n]; 455 if (supply[n] > max_dem) max_dem = supply[n]; 456 } 457 if (max_dem < max_sup) max_sup = max_dem; 458 phase_num = 0; 459 for (delta = 1; 2 * delta <= max_sup; delta *= 2) 460 ++phase_num; 461 } else { 462 // Without scaling 463 delta = 1; 464 } 549 465 return true; 550 466 } 551 467 552 #ifdef WITH_SCALING 468 /// \brief Executes the algorithm. 469 bool start() { 470 if (delta > 1) 471 return startWithScaling(); 472 else 473 return startWithoutScaling(); 474 } 475 553 476 /// \brief Executes the capacity scaling version of the successive 554 477 /// shortest path algorithm. 555 bool start() { 556 typedef typename DeltaResGraph::EdgeIt DeltaResEdgeIt; 557 typedef typename DeltaResGraph::Edge DeltaResEdge; 558 #ifdef _DEBUG_ITER_ 559 int dijk_num = 0; 560 #endif 561 478 bool startWithScaling() { 562 479 // Processing capacity scaling phases 563 ResNode s, t; 564 for ( ; delta >= 1; delta = delta < SCALING_FACTOR && delta > 1 ? 565 1 : delta / SCALING_FACTOR ) 566 { 567 // Saturating edges not satisfying the optimality condition 568 Capacity r; 569 for (DeltaResEdgeIt e(dres_graph); e != INVALID; ++e) { 570 if (red_cost[e] < 0) { 571 res_graph.augment(e, r = res_graph.rescap(e)); 572 imbalance[dres_graph.source(e)] = r; 573 imbalance[dres_graph.target(e)] += r; 574 } 575 } 576 577 // Finding excess nodes 578 excess_nodes.clear(); 579 deficit_nodes.clear(); 580 for (ResNodeIt n(res_graph); n != INVALID; ++n) { 581 if (imbalance[n] >= delta) excess_nodes.push_back(n); 582 if (imbalance[n] <= delta) deficit_nodes.push_back(n); 583 } 584 next_node = 0; 585 586 // Finding shortest paths 587 while (next_node < excess_nodes.size()) { 588 // Checking deficit nodes 589 if (delta > 1) { 590 bool delta_def = false; 591 for (int i = 0; i < deficit_nodes.size(); ++i) { 592 if (imbalance[deficit_nodes[i]] <= delta) { 593 delta_def = true; 594 break; 595 } 596 } 597 if (!delta_def) break; 598 } 599 600 // Running Dijkstra 601 s = excess_nodes[next_node]; 602 updater.init(); 603 dijkstra.init(); 604 dijkstra.addSource(s); 605 #ifdef _DEBUG_ITER_ 606 ++dijk_num; 607 #endif 608 if ((t = dijkstra.start(delta_deficit)) == INVALID) { 609 if (delta > 1) { 610 ++next_node; 611 continue; 612 } 613 return false; 614 } 615 616 // Updating node potentials 617 updater.update(); 618 619 // Augment along a shortest path from s to t 620 Capacity d = imbalance[s] < imbalance[t] ? 621 imbalance[s] : imbalance[t]; 622 ResNode u = t; 623 ResEdge e; 624 if (d > delta) { 625 while ((e = pred[u]) != INVALID) { 626 if (res_graph.rescap(e) < d) d = res_graph.rescap(e); 627 u = dres_graph.source(e); 628 } 629 } 630 u = t; 631 while ((e = pred[u]) != INVALID) { 632 res_graph.augment(e, d); 633 u = dres_graph.source(e); 634 } 635 imbalance[s] = d; 636 imbalance[t] += d; 637 if (imbalance[s] < delta) ++next_node; 638 } 639 } 640 #ifdef _DEBUG_ITER_ 641 std::cout << "Capacity Scaling algorithm finished with running Dijkstra algorithm " 642 << dijk_num << " times." << std::endl; 643 #endif 480 Node s, t; 481 int phase_cnt = 0; 482 int factor = 4; 483 while (true) { 484 // Saturating all edges not satisfying the optimality condition 485 for (EdgeIt e(graph); e != INVALID; ++e) { 486 Node u = graph.source(e), v = graph.target(e); 487 Cost c = cost[e]  potential[u] + potential[v]; 488 if (c < 0 && res_cap[e] >= delta) { 489 excess[u] = res_cap[e]; 490 excess[v] += res_cap[e]; 491 flow[e] = capacity[e]; 492 res_cap[e] = 0; 493 } 494 else if (c > 0 && flow[e] >= delta) { 495 excess[u] += flow[e]; 496 excess[v] = flow[e]; 497 flow[e] = 0; 498 res_cap[e] = capacity[e]; 499 } 500 } 501 502 // Finding excess nodes and deficit nodes 503 excess_nodes.clear(); 504 deficit_nodes.clear(); 505 for (NodeIt n(graph); n != INVALID; ++n) { 506 if (excess[n] >= delta) excess_nodes.push_back(n); 507 if (excess[n] <= delta) deficit_nodes.push_back(n); 508 } 509 next_node = 0; 510 511 // Finding augmenting shortest paths 512 while (next_node < excess_nodes.size()) { 513 // Checking deficit nodes 514 if (delta > 1) { 515 bool delta_deficit = false; 516 for (int i = 0; i < deficit_nodes.size(); ++i) { 517 if (excess[deficit_nodes[i]] <= delta) { 518 delta_deficit = true; 519 break; 520 } 521 } 522 if (!delta_deficit) break; 523 } 524 525 // Running Dijkstra 526 s = excess_nodes[next_node]; 527 if ((t = dijkstra.run(s, delta)) == INVALID) { 528 if (delta > 1) { 529 ++next_node; 530 continue; 531 } 532 return false; 533 } 534 535 // Augmenting along a shortest path from s to t. 536 Capacity d = excess[s] < excess[t] ? excess[s] : excess[t]; 537 Node u = t; 538 Edge e; 539 if (d > delta) { 540 while ((e = pred[u]) != INVALID) { 541 Capacity rc; 542 if (u == graph.target(e)) { 543 rc = res_cap[e]; 544 u = graph.source(e); 545 } else { 546 rc = flow[e]; 547 u = graph.target(e); 548 } 549 if (rc < d) d = rc; 550 } 551 } 552 u = t; 553 while ((e = pred[u]) != INVALID) { 554 if (u == graph.target(e)) { 555 flow[e] += d; 556 res_cap[e] = d; 557 u = graph.source(e); 558 } else { 559 flow[e] = d; 560 res_cap[e] += d; 561 u = graph.target(e); 562 } 563 } 564 excess[s] = d; 565 excess[t] += d; 566 567 if (excess[s] < delta) ++next_node; 568 } 569 570 if (delta == 1) break; 571 if (++phase_cnt > phase_num / 4) factor = 2; 572 delta = delta <= factor ? 1 : delta / factor; 573 } 644 574 645 575 // Handling nonzero lower bounds 646 576 if (lower) { 647 648 577 for (EdgeIt e(graph); e != INVALID; ++e) 578 flow[e] += (*lower)[e]; 649 579 } 650 580 return true; 651 581 } 652 582 653 #else //WITHOUT_CAPACITY_SCALING654 583 /// \brief Executes the successive shortest path algorithm without 655 584 /// capacity scaling. 656 bool start () {585 bool startWithoutScaling() { 657 586 // Finding excess nodes 658 for ( ResNodeIt n(res_graph); n != INVALID; ++n) {659 if (imbalance[n] > 0) excess_nodes.push_back(n);587 for (NodeIt n(graph); n != INVALID; ++n) { 588 if (excess[n] > 0) excess_nodes.push_back(n); 660 589 } 661 590 if (excess_nodes.size() == 0) return true; … … 663 592 664 593 // Finding shortest paths 665 ResNode s, t;666 while ( imbalance[excess_nodes[next_node]] > 0 667 594 Node s, t; 595 while ( excess[excess_nodes[next_node]] > 0  596 ++next_node < excess_nodes.size() ) 668 597 { 669 // Running Dijkstra 670 s = excess_nodes[next_node]; 671 updater.init(); 672 dijkstra.init(); 673 dijkstra.addSource(s); 674 if ((t = dijkstra.start(has_deficit)) == INVALID) 675 return false; 676 677 // Updating node potentials 678 updater.update(); 679 680 // Augmenting along a shortest path from s to t 681 Capacity delta = imbalance[s] < imbalance[t] ? 682 imbalance[s] : imbalance[t]; 683 ResNode u = t; 684 ResEdge e; 685 while ((e = pred[u]) != INVALID) { 686 if (res_graph.rescap(e) < delta) delta = res_graph.rescap(e); 687 u = res_graph.source(e); 688 } 689 u = t; 690 while ((e = pred[u]) != INVALID) { 691 res_graph.augment(e, delta); 692 u = res_graph.source(e); 693 } 694 imbalance[s] = delta; 695 imbalance[t] += delta; 598 // Running Dijkstra 599 s = excess_nodes[next_node]; 600 if ((t = dijkstra.run(s, 1)) == INVALID) 601 return false; 602 603 // Augmenting along a shortest path from s to t 604 Capacity d = excess[s] < excess[t] ? excess[s] : excess[t]; 605 Node u = t; 606 Edge e; 607 while ((e = pred[u]) != INVALID) { 608 Capacity rc; 609 if (u == graph.target(e)) { 610 rc = res_cap[e]; 611 u = graph.source(e); 612 } else { 613 rc = flow[e]; 614 u = graph.target(e); 615 } 616 if (rc < d) d = rc; 617 } 618 u = t; 619 while ((e = pred[u]) != INVALID) { 620 if (u == graph.target(e)) { 621 flow[e] += d; 622 res_cap[e] = d; 623 u = graph.source(e); 624 } else { 625 flow[e] = d; 626 res_cap[e] += d; 627 u = graph.target(e); 628 } 629 } 630 excess[s] = d; 631 excess[t] += d; 696 632 } 697 633 698 634 // Handling nonzero lower bounds 699 635 if (lower) { 700 701 636 for (EdgeIt e(graph); e != INVALID; ++e) 637 flow[e] += (*lower)[e]; 702 638 } 703 639 return true; 704 640 } 705 #endif706 641 707 642 }; //class CapacityScaling
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