[2514] | 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_DINITZ_SLEATOR_TARJAN_H |
---|
| 20 | #define LEMON_DINITZ_SLEATOR_TARJAN_H |
---|
| 21 | |
---|
| 22 | /// \file |
---|
| 23 | /// \ingroup max_flow |
---|
| 24 | /// \brief Implementation the dynamic tree data structure of Sleator |
---|
| 25 | /// and Tarjan. |
---|
| 26 | |
---|
| 27 | #include <lemon/graph_utils.h> |
---|
| 28 | #include <lemon/tolerance.h> |
---|
| 29 | #include <lemon/dynamic_tree.h> |
---|
| 30 | |
---|
| 31 | #include <vector> |
---|
| 32 | #include <limits> |
---|
| 33 | #include <fstream> |
---|
| 34 | |
---|
| 35 | |
---|
| 36 | namespace lemon { |
---|
| 37 | |
---|
| 38 | /// \brief Default traits class of DinitzSleatorTarjan class. |
---|
| 39 | /// |
---|
| 40 | /// Default traits class of DinitzSleatorTarjan class. |
---|
| 41 | /// \param _Graph Graph type. |
---|
| 42 | /// \param _CapacityMap Type of capacity map. |
---|
| 43 | template <typename _Graph, typename _CapacityMap> |
---|
| 44 | struct DinitzSleatorTarjanDefaultTraits { |
---|
| 45 | |
---|
| 46 | /// \brief The graph type the algorithm runs on. |
---|
| 47 | typedef _Graph Graph; |
---|
| 48 | |
---|
| 49 | /// \brief The type of the map that stores the edge capacities. |
---|
| 50 | /// |
---|
| 51 | /// The type of the map that stores the edge capacities. |
---|
| 52 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
---|
| 53 | typedef _CapacityMap CapacityMap; |
---|
| 54 | |
---|
| 55 | /// \brief The type of the length of the edges. |
---|
| 56 | typedef typename CapacityMap::Value Value; |
---|
| 57 | |
---|
| 58 | /// \brief The map type that stores the flow values. |
---|
| 59 | /// |
---|
| 60 | /// The map type that stores the flow values. |
---|
| 61 | /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept. |
---|
| 62 | typedef typename Graph::template EdgeMap<Value> FlowMap; |
---|
| 63 | |
---|
| 64 | /// \brief Instantiates a FlowMap. |
---|
| 65 | /// |
---|
| 66 | /// This function instantiates a \ref FlowMap. |
---|
| 67 | /// \param graph The graph, to which we would like to define the flow map. |
---|
| 68 | static FlowMap* createFlowMap(const Graph& graph) { |
---|
| 69 | return new FlowMap(graph); |
---|
| 70 | } |
---|
| 71 | |
---|
| 72 | /// \brief The tolerance used by the algorithm |
---|
| 73 | /// |
---|
| 74 | /// The tolerance used by the algorithm to handle inexact computation. |
---|
| 75 | typedef Tolerance<Value> Tolerance; |
---|
| 76 | |
---|
| 77 | }; |
---|
| 78 | |
---|
| 79 | /// \ingroup max_flow |
---|
| 80 | /// |
---|
| 81 | /// \brief Dinitz-Sleator-Tarjan algorithms class. |
---|
| 82 | /// |
---|
| 83 | /// This class provides an implementation of the \e |
---|
| 84 | /// Dinitz-Sleator-Tarjan \e algorithm producing a flow of maximum |
---|
| 85 | /// value in a directed graph. The DinitzSleatorTarjan algorithm is |
---|
| 86 | /// the fastest known max flow algorithms wich using blocking |
---|
| 87 | /// flow. It is an improvement of the Dinitz algorithm by using the |
---|
| 88 | /// \ref DynamicTree "dynamic tree" data structure of Sleator and |
---|
| 89 | /// Tarjan. |
---|
| 90 | /// |
---|
| 91 | /// This blocking flow algorithms builds a layered graph according |
---|
| 92 | /// to \ref Bfs "breadth-first search" distance from the target node |
---|
| 93 | /// in the reversed residual graph. The layered graph contains each |
---|
| 94 | /// residual edge which steps one level down. After that the |
---|
| 95 | /// algorithm constructs a blocking flow on the layered graph and |
---|
| 96 | /// augments the overall flow with it. The number of the levels in |
---|
| 97 | /// the layered graph is strictly increasing in each augmenting |
---|
| 98 | /// phase therefore the number of the augmentings is at most |
---|
| 99 | /// \f$n-1\f$. The length of each phase is at most |
---|
| 100 | /// \f$O(m\log(n))\f$, that the overall time complexity is |
---|
| 101 | /// \f$O(nm\log(n))\f$. |
---|
| 102 | /// |
---|
| 103 | /// \param _Graph The directed graph type the algorithm runs on. |
---|
| 104 | /// \param _CapacityMap The capacity map type. |
---|
| 105 | /// \param _Traits Traits class to set various data types used by |
---|
| 106 | /// the algorithm. The default traits class is \ref |
---|
| 107 | /// DinitzSleatorTarjanDefaultTraits. See \ref |
---|
| 108 | /// DinitzSleatorTarjanDefaultTraits for the documentation of a |
---|
| 109 | /// Dinitz-Sleator-Tarjan traits class. |
---|
| 110 | /// |
---|
| 111 | /// \author Tamas Hamori and Balazs Dezso |
---|
| 112 | #ifdef DOXYGEN |
---|
| 113 | template <typename _Graph, typename _CapacityMap, typename _Traits> |
---|
| 114 | #else |
---|
| 115 | template <typename _Graph, |
---|
| 116 | typename _CapacityMap = typename _Graph::template EdgeMap<int>, |
---|
| 117 | typename _Traits = |
---|
| 118 | DinitzSleatorTarjanDefaultTraits<_Graph, _CapacityMap> > |
---|
| 119 | #endif |
---|
| 120 | class DinitzSleatorTarjan { |
---|
| 121 | public: |
---|
| 122 | |
---|
| 123 | typedef _Traits Traits; |
---|
| 124 | typedef typename Traits::Graph Graph; |
---|
| 125 | typedef typename Traits::CapacityMap CapacityMap; |
---|
| 126 | typedef typename Traits::Value Value; |
---|
| 127 | |
---|
| 128 | typedef typename Traits::FlowMap FlowMap; |
---|
| 129 | typedef typename Traits::Tolerance Tolerance; |
---|
| 130 | |
---|
| 131 | |
---|
| 132 | private: |
---|
| 133 | |
---|
| 134 | GRAPH_TYPEDEFS(typename Graph); |
---|
| 135 | |
---|
| 136 | |
---|
| 137 | typedef typename Graph::template NodeMap<int> LevelMap; |
---|
| 138 | typedef typename Graph::template NodeMap<int> IntNodeMap; |
---|
| 139 | typedef typename Graph::template NodeMap<Edge> EdgeNodeMap; |
---|
| 140 | typedef DynamicTree<Value, IntNodeMap, Tolerance, false> DynTree; |
---|
| 141 | |
---|
| 142 | private: |
---|
| 143 | |
---|
| 144 | const Graph& _graph; |
---|
| 145 | const CapacityMap* _capacity; |
---|
| 146 | |
---|
| 147 | Node _source, _target; |
---|
| 148 | |
---|
| 149 | FlowMap* _flow; |
---|
| 150 | bool _local_flow; |
---|
| 151 | |
---|
| 152 | IntNodeMap* _level; |
---|
| 153 | EdgeNodeMap* _dt_edges; |
---|
| 154 | |
---|
| 155 | IntNodeMap* _dt_index; |
---|
| 156 | DynTree* _dt; |
---|
| 157 | |
---|
[2519] | 158 | std::vector<Node> _queue; |
---|
| 159 | |
---|
[2514] | 160 | Tolerance _tolerance; |
---|
| 161 | |
---|
| 162 | Value _flow_value; |
---|
| 163 | Value _max_value; |
---|
| 164 | |
---|
| 165 | |
---|
| 166 | public: |
---|
| 167 | |
---|
| 168 | typedef DinitzSleatorTarjan Create; |
---|
| 169 | |
---|
| 170 | ///\name Named template parameters |
---|
| 171 | |
---|
| 172 | ///@{ |
---|
| 173 | |
---|
| 174 | template <typename _FlowMap> |
---|
| 175 | struct DefFlowMapTraits : public Traits { |
---|
| 176 | typedef _FlowMap FlowMap; |
---|
| 177 | static FlowMap *createFlowMap(const Graph&) { |
---|
| 178 | throw UninitializedParameter(); |
---|
| 179 | } |
---|
| 180 | }; |
---|
| 181 | |
---|
| 182 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
| 183 | /// FlowMap type |
---|
| 184 | /// |
---|
| 185 | /// \ref named-templ-param "Named parameter" for setting FlowMap |
---|
| 186 | /// type |
---|
| 187 | template <typename _FlowMap> |
---|
| 188 | struct DefFlowMap |
---|
| 189 | : public DinitzSleatorTarjan<Graph, CapacityMap, |
---|
| 190 | DefFlowMapTraits<_FlowMap> > { |
---|
| 191 | typedef DinitzSleatorTarjan<Graph, CapacityMap, |
---|
| 192 | DefFlowMapTraits<_FlowMap> > Create; |
---|
| 193 | }; |
---|
| 194 | |
---|
| 195 | template <typename _Elevator> |
---|
| 196 | struct DefElevatorTraits : public Traits { |
---|
| 197 | typedef _Elevator Elevator; |
---|
| 198 | static Elevator *createElevator(const Graph&, int) { |
---|
| 199 | throw UninitializedParameter(); |
---|
| 200 | } |
---|
| 201 | }; |
---|
| 202 | |
---|
| 203 | /// @} |
---|
| 204 | |
---|
| 205 | /// \brief \ref Exception for the case when the source equals the target. |
---|
| 206 | /// |
---|
| 207 | /// \ref Exception for the case when the source equals the target. |
---|
| 208 | /// |
---|
| 209 | class InvalidArgument : public lemon::LogicError { |
---|
| 210 | public: |
---|
| 211 | virtual const char* what() const throw() { |
---|
| 212 | return "lemon::DinitzSleatorTarjan::InvalidArgument"; |
---|
| 213 | } |
---|
| 214 | }; |
---|
| 215 | |
---|
| 216 | /// \brief The constructor of the class. |
---|
| 217 | /// |
---|
| 218 | /// The constructor of the class. |
---|
| 219 | /// \param graph The directed graph the algorithm runs on. |
---|
| 220 | /// \param capacity The capacity of the edges. |
---|
| 221 | /// \param source The source node. |
---|
| 222 | /// \param target The target node. |
---|
| 223 | DinitzSleatorTarjan(const Graph& graph, const CapacityMap& capacity, |
---|
| 224 | Node source, Node target) |
---|
| 225 | : _graph(graph), _capacity(&capacity), |
---|
| 226 | _source(source), _target(target), |
---|
| 227 | _flow(0), _local_flow(false), |
---|
| 228 | _level(0), _dt_edges(0), |
---|
[2519] | 229 | _dt_index(0), _dt(0), _queue(), |
---|
[2514] | 230 | _tolerance(), _flow_value(), _max_value() |
---|
| 231 | { |
---|
| 232 | if (_source == _target) { |
---|
| 233 | throw InvalidArgument(); |
---|
| 234 | } |
---|
| 235 | } |
---|
| 236 | |
---|
| 237 | /// \brief Destrcutor. |
---|
| 238 | /// |
---|
| 239 | /// Destructor. |
---|
| 240 | ~DinitzSleatorTarjan() { |
---|
| 241 | destroyStructures(); |
---|
| 242 | } |
---|
| 243 | |
---|
| 244 | /// \brief Sets the capacity map. |
---|
| 245 | /// |
---|
| 246 | /// Sets the capacity map. |
---|
| 247 | /// \return \c (*this) |
---|
| 248 | DinitzSleatorTarjan& capacityMap(const CapacityMap& map) { |
---|
| 249 | _capacity = ↦ |
---|
| 250 | return *this; |
---|
| 251 | } |
---|
| 252 | |
---|
| 253 | /// \brief Sets the flow map. |
---|
| 254 | /// |
---|
| 255 | /// Sets the flow map. |
---|
| 256 | /// \return \c (*this) |
---|
| 257 | DinitzSleatorTarjan& flowMap(FlowMap& map) { |
---|
| 258 | if (_local_flow) { |
---|
| 259 | delete _flow; |
---|
| 260 | _local_flow = false; |
---|
| 261 | } |
---|
| 262 | _flow = ↦ |
---|
| 263 | return *this; |
---|
| 264 | } |
---|
| 265 | |
---|
| 266 | /// \brief Returns the flow map. |
---|
| 267 | /// |
---|
| 268 | /// \return The flow map. |
---|
| 269 | const FlowMap& flowMap() { |
---|
| 270 | return *_flow; |
---|
| 271 | } |
---|
| 272 | |
---|
| 273 | /// \brief Sets the source node. |
---|
| 274 | /// |
---|
| 275 | /// Sets the source node. |
---|
| 276 | /// \return \c (*this) |
---|
| 277 | DinitzSleatorTarjan& source(const Node& node) { |
---|
| 278 | _source = node; |
---|
| 279 | return *this; |
---|
| 280 | } |
---|
| 281 | |
---|
| 282 | /// \brief Sets the target node. |
---|
| 283 | /// |
---|
| 284 | /// Sets the target node. |
---|
| 285 | /// \return \c (*this) |
---|
| 286 | DinitzSleatorTarjan& target(const Node& node) { |
---|
| 287 | _target = node; |
---|
| 288 | return *this; |
---|
| 289 | } |
---|
| 290 | |
---|
| 291 | /// \brief Sets the tolerance used by algorithm. |
---|
| 292 | /// |
---|
| 293 | /// Sets the tolerance used by algorithm. |
---|
| 294 | DinitzSleatorTarjan& tolerance(const Tolerance& tolerance) const { |
---|
| 295 | _tolerance = tolerance; |
---|
| 296 | if (_dt) { |
---|
| 297 | _dt.tolerance(_tolerance); |
---|
| 298 | } |
---|
| 299 | return *this; |
---|
| 300 | } |
---|
| 301 | |
---|
| 302 | /// \brief Returns the tolerance used by algorithm. |
---|
| 303 | /// |
---|
| 304 | /// Returns the tolerance used by algorithm. |
---|
| 305 | const Tolerance& tolerance() const { |
---|
| 306 | return tolerance; |
---|
| 307 | } |
---|
| 308 | |
---|
| 309 | private: |
---|
| 310 | |
---|
| 311 | void createStructures() { |
---|
| 312 | if (!_flow) { |
---|
| 313 | _flow = Traits::createFlowMap(_graph); |
---|
| 314 | _local_flow = true; |
---|
| 315 | } |
---|
| 316 | if (!_level) { |
---|
| 317 | _level = new LevelMap(_graph); |
---|
| 318 | } |
---|
| 319 | if (!_dt_index && !_dt) { |
---|
| 320 | _dt_index = new IntNodeMap(_graph); |
---|
| 321 | _dt = new DynTree(*_dt_index, _tolerance); |
---|
| 322 | } |
---|
| 323 | if (!_dt_edges) { |
---|
| 324 | _dt_edges = new EdgeNodeMap(_graph); |
---|
| 325 | } |
---|
[2519] | 326 | _queue.resize(countNodes(_graph)); |
---|
[2514] | 327 | _max_value = _dt->maxValue(); |
---|
| 328 | } |
---|
| 329 | |
---|
| 330 | void destroyStructures() { |
---|
| 331 | if (_local_flow) { |
---|
| 332 | delete _flow; |
---|
| 333 | } |
---|
| 334 | if (_level) { |
---|
| 335 | delete _level; |
---|
| 336 | } |
---|
| 337 | if (_dt) { |
---|
| 338 | delete _dt; |
---|
| 339 | } |
---|
| 340 | if (_dt_index) { |
---|
| 341 | delete _dt_index; |
---|
| 342 | } |
---|
| 343 | if (_dt_edges) { |
---|
| 344 | delete _dt_edges; |
---|
| 345 | } |
---|
| 346 | } |
---|
| 347 | |
---|
| 348 | bool createLayeredGraph() { |
---|
| 349 | |
---|
| 350 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 351 | _level->set(n, -2); |
---|
| 352 | } |
---|
| 353 | |
---|
| 354 | int level = 0; |
---|
| 355 | |
---|
[2519] | 356 | _queue[0] = _target; |
---|
[2514] | 357 | _level->set(_target, level); |
---|
[2519] | 358 | |
---|
| 359 | int first = 0, last = 1, limit = 0; |
---|
[2514] | 360 | |
---|
[2519] | 361 | while (first != last && (*_level)[_source] == -2) { |
---|
| 362 | if (first == limit) { |
---|
| 363 | limit = last; |
---|
| 364 | ++level; |
---|
| 365 | } |
---|
[2514] | 366 | |
---|
[2519] | 367 | Node n = _queue[first++]; |
---|
[2514] | 368 | |
---|
[2519] | 369 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
| 370 | Node v = _graph.target(e); |
---|
| 371 | if ((*_level)[v] != -2) continue; |
---|
| 372 | Value rem = (*_flow)[e]; |
---|
| 373 | if (!_tolerance.positive(rem)) continue; |
---|
| 374 | _level->set(v, level); |
---|
| 375 | _queue[last++] = v; |
---|
[2514] | 376 | } |
---|
[2519] | 377 | |
---|
| 378 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
| 379 | Node v = _graph.source(e); |
---|
| 380 | if ((*_level)[v] != -2) continue; |
---|
| 381 | Value rem = (*_capacity)[e] - (*_flow)[e]; |
---|
| 382 | if (!_tolerance.positive(rem)) continue; |
---|
| 383 | _level->set(v, level); |
---|
| 384 | _queue[last++] = v; |
---|
| 385 | } |
---|
[2514] | 386 | } |
---|
| 387 | return (*_level)[_source] != -2; |
---|
| 388 | } |
---|
| 389 | |
---|
| 390 | void initEdges() { |
---|
| 391 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 392 | _graph.firstOut((*_dt_edges)[n], n); |
---|
| 393 | } |
---|
| 394 | } |
---|
| 395 | |
---|
| 396 | |
---|
| 397 | void augmentPath() { |
---|
| 398 | Value rem; |
---|
| 399 | Node n = _dt->findCost(_source, rem); |
---|
| 400 | _flow_value += rem; |
---|
| 401 | _dt->addCost(_source, - rem); |
---|
| 402 | |
---|
| 403 | _dt->cut(n); |
---|
| 404 | _dt->addCost(n, _max_value); |
---|
| 405 | |
---|
| 406 | Edge e = (*_dt_edges)[n]; |
---|
| 407 | if (_graph.source(e) == n) { |
---|
| 408 | _flow->set(e, (*_capacity)[e]); |
---|
| 409 | |
---|
| 410 | _graph.nextOut(e); |
---|
| 411 | if (e == INVALID) { |
---|
| 412 | _graph.firstIn(e, n); |
---|
| 413 | } |
---|
| 414 | } else { |
---|
| 415 | _flow->set(e, 0); |
---|
| 416 | _graph.nextIn(e); |
---|
| 417 | } |
---|
| 418 | _dt_edges->set(n, e); |
---|
| 419 | |
---|
| 420 | } |
---|
| 421 | |
---|
| 422 | bool advance(Node n) { |
---|
| 423 | Edge e = (*_dt_edges)[n]; |
---|
| 424 | if (e == INVALID) return false; |
---|
| 425 | |
---|
| 426 | Node u; |
---|
| 427 | Value rem; |
---|
| 428 | if (_graph.source(e) == n) { |
---|
| 429 | u = _graph.target(e); |
---|
| 430 | while ((*_level)[n] != (*_level)[u] + 1 || |
---|
| 431 | !_tolerance.positive((*_capacity)[e] - (*_flow)[e])) { |
---|
| 432 | _graph.nextOut(e); |
---|
| 433 | if (e == INVALID) break; |
---|
| 434 | u = _graph.target(e); |
---|
| 435 | } |
---|
| 436 | if (e != INVALID) { |
---|
| 437 | rem = (*_capacity)[e] - (*_flow)[e]; |
---|
| 438 | } else { |
---|
| 439 | _graph.firstIn(e, n); |
---|
| 440 | if (e == INVALID) { |
---|
| 441 | _dt_edges->set(n, INVALID); |
---|
| 442 | return false; |
---|
| 443 | } |
---|
| 444 | u = _graph.source(e); |
---|
| 445 | while ((*_level)[n] != (*_level)[u] + 1 || |
---|
| 446 | !_tolerance.positive((*_flow)[e])) { |
---|
| 447 | _graph.nextIn(e); |
---|
| 448 | if (e == INVALID) { |
---|
| 449 | _dt_edges->set(n, INVALID); |
---|
| 450 | return false; |
---|
| 451 | } |
---|
| 452 | u = _graph.source(e); |
---|
| 453 | } |
---|
| 454 | rem = (*_flow)[e]; |
---|
| 455 | } |
---|
| 456 | } else { |
---|
| 457 | u = _graph.source(e); |
---|
| 458 | while ((*_level)[n] != (*_level)[u] + 1 || |
---|
| 459 | !_tolerance.positive((*_flow)[e])) { |
---|
| 460 | _graph.nextIn(e); |
---|
| 461 | if (e == INVALID) { |
---|
| 462 | _dt_edges->set(n, INVALID); |
---|
| 463 | return false; |
---|
| 464 | } |
---|
| 465 | u = _graph.source(e); |
---|
| 466 | } |
---|
| 467 | rem = (*_flow)[e]; |
---|
| 468 | } |
---|
| 469 | |
---|
| 470 | _dt->addCost(n, - std::numeric_limits<Value>::max()); |
---|
| 471 | _dt->addCost(n, rem); |
---|
| 472 | _dt->link(n, u); |
---|
| 473 | _dt_edges->set(n, e); |
---|
| 474 | return true; |
---|
| 475 | } |
---|
| 476 | |
---|
| 477 | void retreat(Node n) { |
---|
| 478 | _level->set(n, -1); |
---|
| 479 | |
---|
| 480 | for (OutEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
| 481 | Node u = _graph.target(e); |
---|
| 482 | if ((*_dt_edges)[u] == e && _dt->findRoot(u) == n) { |
---|
| 483 | Value rem; |
---|
| 484 | _dt->findCost(u, rem); |
---|
| 485 | _flow->set(e, rem); |
---|
| 486 | _dt->cut(u); |
---|
| 487 | _dt->addCost(u, - rem); |
---|
| 488 | _dt->addCost(u, _max_value); |
---|
| 489 | } |
---|
| 490 | } |
---|
| 491 | for (InEdgeIt e(_graph, n); e != INVALID; ++e) { |
---|
| 492 | Node u = _graph.source(e); |
---|
| 493 | if ((*_dt_edges)[u] == e && _dt->findRoot(u) == n) { |
---|
| 494 | Value rem; |
---|
| 495 | _dt->findCost(u, rem); |
---|
| 496 | _flow->set(e, (*_capacity)[e] - rem); |
---|
| 497 | _dt->cut(u); |
---|
| 498 | _dt->addCost(u, - rem); |
---|
| 499 | _dt->addCost(u, _max_value); |
---|
| 500 | } |
---|
| 501 | } |
---|
| 502 | } |
---|
| 503 | |
---|
| 504 | void extractTrees() { |
---|
| 505 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 506 | |
---|
| 507 | Node w = _dt->findRoot(n); |
---|
| 508 | |
---|
| 509 | while (w != n) { |
---|
| 510 | |
---|
| 511 | Value rem; |
---|
| 512 | Node u = _dt->findCost(n, rem); |
---|
| 513 | |
---|
| 514 | _dt->cut(u); |
---|
| 515 | _dt->addCost(u, - rem); |
---|
| 516 | _dt->addCost(u, _max_value); |
---|
| 517 | |
---|
| 518 | Edge e = (*_dt_edges)[u]; |
---|
| 519 | _dt_edges->set(u, INVALID); |
---|
| 520 | |
---|
| 521 | if (u == _graph.source(e)) { |
---|
| 522 | _flow->set(e, (*_capacity)[e] - rem); |
---|
| 523 | } else { |
---|
| 524 | _flow->set(e, rem); |
---|
| 525 | } |
---|
| 526 | |
---|
| 527 | w = _dt->findRoot(n); |
---|
| 528 | } |
---|
| 529 | } |
---|
| 530 | } |
---|
| 531 | |
---|
| 532 | |
---|
| 533 | public: |
---|
| 534 | |
---|
| 535 | /// \name Execution control The simplest way to execute the |
---|
| 536 | /// algorithm is to use the \c run() member functions. |
---|
| 537 | /// \n |
---|
| 538 | /// If you need more control on initial solution or |
---|
| 539 | /// execution then you have to call one \ref init() function and then |
---|
| 540 | /// the start() or multiple times the \c augment() member function. |
---|
| 541 | |
---|
| 542 | ///@{ |
---|
| 543 | |
---|
| 544 | /// \brief Initializes the algorithm |
---|
| 545 | /// |
---|
| 546 | /// It sets the flow to empty flow. |
---|
| 547 | void init() { |
---|
| 548 | createStructures(); |
---|
| 549 | |
---|
| 550 | _dt->clear(); |
---|
| 551 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 552 | _dt->makeTree(n); |
---|
| 553 | _dt->addCost(n, _max_value); |
---|
| 554 | } |
---|
| 555 | |
---|
| 556 | for (EdgeIt it(_graph); it != INVALID; ++it) { |
---|
| 557 | _flow->set(it, 0); |
---|
| 558 | } |
---|
| 559 | _flow_value = 0; |
---|
| 560 | } |
---|
| 561 | |
---|
| 562 | /// \brief Initializes the algorithm |
---|
| 563 | /// |
---|
| 564 | /// Initializes the flow to the \c flowMap. The \c flowMap should |
---|
| 565 | /// contain a feasible flow, ie. in each node excluding the source |
---|
| 566 | /// and the target the incoming flow should be equal to the |
---|
| 567 | /// outgoing flow. |
---|
| 568 | template <typename FlowMap> |
---|
| 569 | void flowInit(const FlowMap& flowMap) { |
---|
| 570 | createStructures(); |
---|
| 571 | |
---|
| 572 | _dt->clear(); |
---|
| 573 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 574 | _dt->makeTree(n); |
---|
| 575 | _dt->addCost(n, _max_value); |
---|
| 576 | } |
---|
| 577 | |
---|
| 578 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 579 | _flow->set(e, flowMap[e]); |
---|
| 580 | } |
---|
| 581 | _flow_value = 0; |
---|
| 582 | for (OutEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
---|
| 583 | _flow_value += (*_flow)[jt]; |
---|
| 584 | } |
---|
| 585 | for (InEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
---|
| 586 | _flow_value -= (*_flow)[jt]; |
---|
| 587 | } |
---|
| 588 | } |
---|
| 589 | |
---|
| 590 | /// \brief Initializes the algorithm |
---|
| 591 | /// |
---|
| 592 | /// Initializes the flow to the \c flowMap. The \c flowMap should |
---|
| 593 | /// contain a feasible flow, ie. in each node excluding the source |
---|
| 594 | /// and the target the incoming flow should be equal to the |
---|
| 595 | /// outgoing flow. |
---|
| 596 | /// \return %False when the given flowMap does not contain |
---|
| 597 | /// feasible flow. |
---|
| 598 | template <typename FlowMap> |
---|
| 599 | bool checkedFlowInit(const FlowMap& flowMap) { |
---|
| 600 | createStructures(); |
---|
| 601 | |
---|
| 602 | _dt->clear(); |
---|
| 603 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 604 | _dt->makeTree(n); |
---|
| 605 | _dt->addCost(n, _max_value); |
---|
| 606 | } |
---|
| 607 | |
---|
| 608 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
| 609 | _flow->set(e, flowMap[e]); |
---|
| 610 | } |
---|
| 611 | for (NodeIt it(_graph); it != INVALID; ++it) { |
---|
| 612 | if (it == _source || it == _target) continue; |
---|
| 613 | Value outFlow = 0; |
---|
| 614 | for (OutEdgeIt jt(_graph, it); jt != INVALID; ++jt) { |
---|
| 615 | outFlow += (*_flow)[jt]; |
---|
| 616 | } |
---|
| 617 | Value inFlow = 0; |
---|
| 618 | for (InEdgeIt jt(_graph, it); jt != INVALID; ++jt) { |
---|
| 619 | inFlow += (*_flow)[jt]; |
---|
| 620 | } |
---|
| 621 | if (_tolerance.different(outFlow, inFlow)) { |
---|
| 622 | return false; |
---|
| 623 | } |
---|
| 624 | } |
---|
| 625 | for (EdgeIt it(_graph); it != INVALID; ++it) { |
---|
| 626 | if (_tolerance.less((*_flow)[it], 0)) return false; |
---|
| 627 | if (_tolerance.less((*_capacity)[it], (*_flow)[it])) return false; |
---|
| 628 | } |
---|
| 629 | _flow_value = 0; |
---|
| 630 | for (OutEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
---|
| 631 | _flow_value += (*_flow)[jt]; |
---|
| 632 | } |
---|
| 633 | for (InEdgeIt jt(_graph, _source); jt != INVALID; ++jt) { |
---|
| 634 | _flow_value -= (*_flow)[jt]; |
---|
| 635 | } |
---|
| 636 | return true; |
---|
| 637 | } |
---|
| 638 | |
---|
| 639 | /// \brief Executes the algorithm |
---|
| 640 | /// |
---|
| 641 | /// It runs augmenting phases by adding blocking flow until the |
---|
| 642 | /// optimal solution is reached. |
---|
| 643 | void start() { |
---|
| 644 | while (augment()); |
---|
| 645 | } |
---|
| 646 | |
---|
| 647 | /// \brief Augments the flow with a blocking flow on a layered |
---|
| 648 | /// graph. |
---|
| 649 | /// |
---|
| 650 | /// This function builds a layered graph and then find a blocking |
---|
| 651 | /// flow on this graph. The number of the levels in the layered |
---|
| 652 | /// graph is strictly increasing in each augmenting phase |
---|
| 653 | /// therefore the number of the augmentings is at most \f$ n-1 |
---|
| 654 | /// \f$. The length of each phase is at most \f$ O(m \log(n)) |
---|
| 655 | /// \f$, that the overall time complexity is \f$ O(nm \log(n)) \f$. |
---|
| 656 | /// \return %False when there is not residual path between the |
---|
| 657 | /// source and the target so the current flow is a feasible and |
---|
| 658 | /// optimal solution. |
---|
| 659 | bool augment() { |
---|
| 660 | Node n; |
---|
| 661 | |
---|
| 662 | if (createLayeredGraph()) { |
---|
| 663 | |
---|
| 664 | Timer bf_timer; |
---|
| 665 | initEdges(); |
---|
| 666 | |
---|
| 667 | n = _dt->findRoot(_source); |
---|
| 668 | while (true) { |
---|
| 669 | Edge e; |
---|
| 670 | if (n == _target) { |
---|
| 671 | augmentPath(); |
---|
| 672 | } else if (!advance(n)) { |
---|
| 673 | if (n != _source) { |
---|
| 674 | retreat(n); |
---|
| 675 | } else { |
---|
| 676 | break; |
---|
| 677 | } |
---|
| 678 | } |
---|
| 679 | n = _dt->findRoot(_source); |
---|
| 680 | } |
---|
| 681 | extractTrees(); |
---|
| 682 | |
---|
| 683 | return true; |
---|
| 684 | } else { |
---|
| 685 | return false; |
---|
| 686 | } |
---|
| 687 | } |
---|
| 688 | |
---|
| 689 | /// \brief runs the algorithm. |
---|
| 690 | /// |
---|
| 691 | /// It is just a shorthand for: |
---|
| 692 | /// |
---|
| 693 | ///\code |
---|
| 694 | /// ek.init(); |
---|
| 695 | /// ek.start(); |
---|
| 696 | ///\endcode |
---|
| 697 | void run() { |
---|
| 698 | init(); |
---|
| 699 | start(); |
---|
| 700 | } |
---|
| 701 | |
---|
| 702 | /// @} |
---|
| 703 | |
---|
| 704 | /// \name Query Functions |
---|
| 705 | /// The result of the %Dijkstra algorithm can be obtained using these |
---|
| 706 | /// functions.\n |
---|
| 707 | /// Before the use of these functions, |
---|
| 708 | /// either run() or start() must be called. |
---|
| 709 | |
---|
| 710 | ///@{ |
---|
| 711 | |
---|
| 712 | /// \brief Returns the value of the maximum flow. |
---|
| 713 | /// |
---|
| 714 | /// Returns the value of the maximum flow by returning the excess |
---|
| 715 | /// of the target node \c t. This value equals to the value of |
---|
| 716 | /// the maximum flow already after the first phase. |
---|
| 717 | Value flowValue() const { |
---|
| 718 | return _flow_value; |
---|
| 719 | } |
---|
| 720 | |
---|
| 721 | |
---|
| 722 | /// \brief Returns the flow on the edge. |
---|
| 723 | /// |
---|
| 724 | /// Sets the \c flowMap to the flow on the edges. This method can |
---|
| 725 | /// be called after the second phase of algorithm. |
---|
| 726 | Value flow(const Edge& edge) const { |
---|
| 727 | return (*_flow)[edge]; |
---|
| 728 | } |
---|
| 729 | |
---|
| 730 | /// \brief Returns true when the node is on the source side of minimum cut. |
---|
| 731 | /// |
---|
| 732 | |
---|
| 733 | /// Returns true when the node is on the source side of minimum |
---|
| 734 | /// cut. This method can be called both after running \ref |
---|
| 735 | /// startFirstPhase() and \ref startSecondPhase(). |
---|
| 736 | bool minCut(const Node& node) const { |
---|
| 737 | return (*_level)[node] == -2; |
---|
| 738 | } |
---|
| 739 | |
---|
| 740 | /// \brief Returns a minimum value cut. |
---|
| 741 | /// |
---|
| 742 | /// Sets \c cut to the characteristic vector of a minimum value cut |
---|
| 743 | /// It simply calls the minMinCut member. |
---|
| 744 | /// \retval cut Write node bool map. |
---|
| 745 | template <typename CutMap> |
---|
| 746 | void minCutMap(CutMap& cutMap) const { |
---|
| 747 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 748 | cutMap.set(n, (*_level)[n] == -2); |
---|
| 749 | } |
---|
| 750 | cutMap.set(_source, true); |
---|
| 751 | } |
---|
| 752 | |
---|
| 753 | /// @} |
---|
| 754 | |
---|
| 755 | }; |
---|
| 756 | } |
---|
| 757 | |
---|
| 758 | #endif |
---|