1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/lemon/cancel_and_tighten.h Fri Nov 13 00:09:35 2009 +0100
1.3 @@ -0,0 +1,797 @@
1.4 +/* -*- C++ -*-
1.5 + *
1.6 + * This file is a part of LEMON, a generic C++ optimization library
1.7 + *
1.8 + * Copyright (C) 2003-2008
1.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
1.11 + *
1.12 + * Permission to use, modify and distribute this software is granted
1.13 + * provided that this copyright notice appears in all copies. For
1.14 + * precise terms see the accompanying LICENSE file.
1.15 + *
1.16 + * This software is provided "AS IS" with no warranty of any kind,
1.17 + * express or implied, and with no claim as to its suitability for any
1.18 + * purpose.
1.19 + *
1.20 + */
1.21 +
1.22 +#ifndef LEMON_CANCEL_AND_TIGHTEN_H
1.23 +#define LEMON_CANCEL_AND_TIGHTEN_H
1.24 +
1.25 +/// \ingroup min_cost_flow
1.26 +///
1.27 +/// \file
1.28 +/// \brief Cancel and Tighten algorithm for finding a minimum cost flow.
1.29 +
1.30 +#include <vector>
1.31 +
1.32 +#include <lemon/circulation.h>
1.33 +#include <lemon/bellman_ford.h>
1.34 +#include <lemon/howard.h>
1.35 +#include <lemon/adaptors.h>
1.36 +#include <lemon/tolerance.h>
1.37 +#include <lemon/math.h>
1.38 +
1.39 +#include <lemon/static_graph.h>
1.40 +
1.41 +namespace lemon {
1.42 +
1.43 + /// \addtogroup min_cost_flow
1.44 + /// @{
1.45 +
1.46 + /// \brief Implementation of the Cancel and Tighten algorithm for
1.47 + /// finding a minimum cost flow.
1.48 + ///
1.49 + /// \ref CancelAndTighten implements the Cancel and Tighten algorithm for
1.50 + /// finding a minimum cost flow.
1.51 + ///
1.52 + /// \tparam Digraph The digraph type the algorithm runs on.
1.53 + /// \tparam LowerMap The type of the lower bound map.
1.54 + /// \tparam CapacityMap The type of the capacity (upper bound) map.
1.55 + /// \tparam CostMap The type of the cost (length) map.
1.56 + /// \tparam SupplyMap The type of the supply map.
1.57 + ///
1.58 + /// \warning
1.59 + /// - Arc capacities and costs should be \e non-negative \e integers.
1.60 + /// - Supply values should be \e signed \e integers.
1.61 + /// - The value types of the maps should be convertible to each other.
1.62 + /// - \c CostMap::Value must be signed type.
1.63 + ///
1.64 + /// \author Peter Kovacs
1.65 + template < typename Digraph,
1.66 + typename LowerMap = typename Digraph::template ArcMap<int>,
1.67 + typename CapacityMap = typename Digraph::template ArcMap<int>,
1.68 + typename CostMap = typename Digraph::template ArcMap<int>,
1.69 + typename SupplyMap = typename Digraph::template NodeMap<int> >
1.70 + class CancelAndTighten
1.71 + {
1.72 + TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
1.73 +
1.74 + typedef typename CapacityMap::Value Capacity;
1.75 + typedef typename CostMap::Value Cost;
1.76 + typedef typename SupplyMap::Value Supply;
1.77 + typedef typename Digraph::template ArcMap<Capacity> CapacityArcMap;
1.78 + typedef typename Digraph::template NodeMap<Supply> SupplyNodeMap;
1.79 +
1.80 + typedef ResidualDigraph< const Digraph,
1.81 + CapacityArcMap, CapacityArcMap > ResDigraph;
1.82 +
1.83 + public:
1.84 +
1.85 + /// The type of the flow map.
1.86 + typedef typename Digraph::template ArcMap<Capacity> FlowMap;
1.87 + /// The type of the potential map.
1.88 + typedef typename Digraph::template NodeMap<Cost> PotentialMap;
1.89 +
1.90 + private:
1.91 +
1.92 + /// \brief Map adaptor class for handling residual arc costs.
1.93 + ///
1.94 + /// Map adaptor class for handling residual arc costs.
1.95 + class ResidualCostMap : public MapBase<typename ResDigraph::Arc, Cost>
1.96 + {
1.97 + typedef typename ResDigraph::Arc Arc;
1.98 +
1.99 + private:
1.100 +
1.101 + const CostMap &_cost_map;
1.102 +
1.103 + public:
1.104 +
1.105 + ///\e
1.106 + ResidualCostMap(const CostMap &cost_map) : _cost_map(cost_map) {}
1.107 +
1.108 + ///\e
1.109 + Cost operator[](const Arc &e) const {
1.110 + return ResDigraph::forward(e) ? _cost_map[e] : -_cost_map[e];
1.111 + }
1.112 +
1.113 + }; //class ResidualCostMap
1.114 +
1.115 + /// \brief Map adaptor class for handling reduced arc costs.
1.116 + ///
1.117 + /// Map adaptor class for handling reduced arc costs.
1.118 + class ReducedCostMap : public MapBase<Arc, Cost>
1.119 + {
1.120 + private:
1.121 +
1.122 + const Digraph &_gr;
1.123 + const CostMap &_cost_map;
1.124 + const PotentialMap &_pot_map;
1.125 +
1.126 + public:
1.127 +
1.128 + ///\e
1.129 + ReducedCostMap( const Digraph &gr,
1.130 + const CostMap &cost_map,
1.131 + const PotentialMap &pot_map ) :
1.132 + _gr(gr), _cost_map(cost_map), _pot_map(pot_map) {}
1.133 +
1.134 + ///\e
1.135 + inline Cost operator[](const Arc &e) const {
1.136 + return _cost_map[e] + _pot_map[_gr.source(e)]
1.137 + - _pot_map[_gr.target(e)];
1.138 + }
1.139 +
1.140 + }; //class ReducedCostMap
1.141 +
1.142 + struct BFOperationTraits {
1.143 + static double zero() { return 0; }
1.144 +
1.145 + static double infinity() {
1.146 + return std::numeric_limits<double>::infinity();
1.147 + }
1.148 +
1.149 + static double plus(const double& left, const double& right) {
1.150 + return left + right;
1.151 + }
1.152 +
1.153 + static bool less(const double& left, const double& right) {
1.154 + return left + 1e-6 < right;
1.155 + }
1.156 + }; // class BFOperationTraits
1.157 +
1.158 + private:
1.159 +
1.160 + // The digraph the algorithm runs on
1.161 + const Digraph &_graph;
1.162 + // The original lower bound map
1.163 + const LowerMap *_lower;
1.164 + // The modified capacity map
1.165 + CapacityArcMap _capacity;
1.166 + // The original cost map
1.167 + const CostMap &_cost;
1.168 + // The modified supply map
1.169 + SupplyNodeMap _supply;
1.170 + bool _valid_supply;
1.171 +
1.172 + // Arc map of the current flow
1.173 + FlowMap *_flow;
1.174 + bool _local_flow;
1.175 + // Node map of the current potentials
1.176 + PotentialMap *_potential;
1.177 + bool _local_potential;
1.178 +
1.179 + // The residual digraph
1.180 + ResDigraph *_res_graph;
1.181 + // The residual cost map
1.182 + ResidualCostMap _res_cost;
1.183 +
1.184 + public:
1.185 +
1.186 + /// \brief General constructor (with lower bounds).
1.187 + ///
1.188 + /// General constructor (with lower bounds).
1.189 + ///
1.190 + /// \param digraph The digraph the algorithm runs on.
1.191 + /// \param lower The lower bounds of the arcs.
1.192 + /// \param capacity The capacities (upper bounds) of the arcs.
1.193 + /// \param cost The cost (length) values of the arcs.
1.194 + /// \param supply The supply values of the nodes (signed).
1.195 + CancelAndTighten( const Digraph &digraph,
1.196 + const LowerMap &lower,
1.197 + const CapacityMap &capacity,
1.198 + const CostMap &cost,
1.199 + const SupplyMap &supply ) :
1.200 + _graph(digraph), _lower(&lower), _capacity(digraph), _cost(cost),
1.201 + _supply(digraph), _flow(NULL), _local_flow(false),
1.202 + _potential(NULL), _local_potential(false),
1.203 + _res_graph(NULL), _res_cost(_cost)
1.204 + {
1.205 + // Check the sum of supply values
1.206 + Supply sum = 0;
1.207 + for (NodeIt n(_graph); n != INVALID; ++n) {
1.208 + _supply[n] = supply[n];
1.209 + sum += _supply[n];
1.210 + }
1.211 + _valid_supply = sum == 0;
1.212 +
1.213 + // Remove non-zero lower bounds
1.214 + for (ArcIt e(_graph); e != INVALID; ++e) {
1.215 + _capacity[e] = capacity[e];
1.216 + if (lower[e] != 0) {
1.217 + _capacity[e] -= lower[e];
1.218 + _supply[_graph.source(e)] -= lower[e];
1.219 + _supply[_graph.target(e)] += lower[e];
1.220 + }
1.221 + }
1.222 + }
1.223 +/*
1.224 + /// \brief General constructor (without lower bounds).
1.225 + ///
1.226 + /// General constructor (without lower bounds).
1.227 + ///
1.228 + /// \param digraph The digraph the algorithm runs on.
1.229 + /// \param capacity The capacities (upper bounds) of the arcs.
1.230 + /// \param cost The cost (length) values of the arcs.
1.231 + /// \param supply The supply values of the nodes (signed).
1.232 + CancelAndTighten( const Digraph &digraph,
1.233 + const CapacityMap &capacity,
1.234 + const CostMap &cost,
1.235 + const SupplyMap &supply ) :
1.236 + _graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost),
1.237 + _supply(supply), _flow(NULL), _local_flow(false),
1.238 + _potential(NULL), _local_potential(false),
1.239 + _res_graph(NULL), _res_cost(_cost)
1.240 + {
1.241 + // Check the sum of supply values
1.242 + Supply sum = 0;
1.243 + for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n];
1.244 + _valid_supply = sum == 0;
1.245 + }
1.246 +
1.247 + /// \brief Simple constructor (with lower bounds).
1.248 + ///
1.249 + /// Simple constructor (with lower bounds).
1.250 + ///
1.251 + /// \param digraph The digraph the algorithm runs on.
1.252 + /// \param lower The lower bounds of the arcs.
1.253 + /// \param capacity The capacities (upper bounds) of the arcs.
1.254 + /// \param cost The cost (length) values of the arcs.
1.255 + /// \param s The source node.
1.256 + /// \param t The target node.
1.257 + /// \param flow_value The required amount of flow from node \c s
1.258 + /// to node \c t (i.e. the supply of \c s and the demand of \c t).
1.259 + CancelAndTighten( const Digraph &digraph,
1.260 + const LowerMap &lower,
1.261 + const CapacityMap &capacity,
1.262 + const CostMap &cost,
1.263 + Node s, Node t,
1.264 + Supply flow_value ) :
1.265 + _graph(digraph), _lower(&lower), _capacity(capacity), _cost(cost),
1.266 + _supply(digraph, 0), _flow(NULL), _local_flow(false),
1.267 + _potential(NULL), _local_potential(false),
1.268 + _res_graph(NULL), _res_cost(_cost)
1.269 + {
1.270 + // Remove non-zero lower bounds
1.271 + _supply[s] = flow_value;
1.272 + _supply[t] = -flow_value;
1.273 + for (ArcIt e(_graph); e != INVALID; ++e) {
1.274 + if (lower[e] != 0) {
1.275 + _capacity[e] -= lower[e];
1.276 + _supply[_graph.source(e)] -= lower[e];
1.277 + _supply[_graph.target(e)] += lower[e];
1.278 + }
1.279 + }
1.280 + _valid_supply = true;
1.281 + }
1.282 +
1.283 + /// \brief Simple constructor (without lower bounds).
1.284 + ///
1.285 + /// Simple constructor (without lower bounds).
1.286 + ///
1.287 + /// \param digraph The digraph the algorithm runs on.
1.288 + /// \param capacity The capacities (upper bounds) of the arcs.
1.289 + /// \param cost The cost (length) values of the arcs.
1.290 + /// \param s The source node.
1.291 + /// \param t The target node.
1.292 + /// \param flow_value The required amount of flow from node \c s
1.293 + /// to node \c t (i.e. the supply of \c s and the demand of \c t).
1.294 + CancelAndTighten( const Digraph &digraph,
1.295 + const CapacityMap &capacity,
1.296 + const CostMap &cost,
1.297 + Node s, Node t,
1.298 + Supply flow_value ) :
1.299 + _graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost),
1.300 + _supply(digraph, 0), _flow(NULL), _local_flow(false),
1.301 + _potential(NULL), _local_potential(false),
1.302 + _res_graph(NULL), _res_cost(_cost)
1.303 + {
1.304 + _supply[s] = flow_value;
1.305 + _supply[t] = -flow_value;
1.306 + _valid_supply = true;
1.307 + }
1.308 +*/
1.309 + /// Destructor.
1.310 + ~CancelAndTighten() {
1.311 + if (_local_flow) delete _flow;
1.312 + if (_local_potential) delete _potential;
1.313 + delete _res_graph;
1.314 + }
1.315 +
1.316 + /// \brief Set the flow map.
1.317 + ///
1.318 + /// Set the flow map.
1.319 + ///
1.320 + /// \return \c (*this)
1.321 + CancelAndTighten& flowMap(FlowMap &map) {
1.322 + if (_local_flow) {
1.323 + delete _flow;
1.324 + _local_flow = false;
1.325 + }
1.326 + _flow = ↦
1.327 + return *this;
1.328 + }
1.329 +
1.330 + /// \brief Set the potential map.
1.331 + ///
1.332 + /// Set the potential map.
1.333 + ///
1.334 + /// \return \c (*this)
1.335 + CancelAndTighten& potentialMap(PotentialMap &map) {
1.336 + if (_local_potential) {
1.337 + delete _potential;
1.338 + _local_potential = false;
1.339 + }
1.340 + _potential = ↦
1.341 + return *this;
1.342 + }
1.343 +
1.344 + /// \name Execution control
1.345 +
1.346 + /// @{
1.347 +
1.348 + /// \brief Run the algorithm.
1.349 + ///
1.350 + /// Run the algorithm.
1.351 + ///
1.352 + /// \return \c true if a feasible flow can be found.
1.353 + bool run() {
1.354 + return init() && start();
1.355 + }
1.356 +
1.357 + /// @}
1.358 +
1.359 + /// \name Query Functions
1.360 + /// The result of the algorithm can be obtained using these
1.361 + /// functions.\n
1.362 + /// \ref lemon::CancelAndTighten::run() "run()" must be called before
1.363 + /// using them.
1.364 +
1.365 + /// @{
1.366 +
1.367 + /// \brief Return a const reference to the arc map storing the
1.368 + /// found flow.
1.369 + ///
1.370 + /// Return a const reference to the arc map storing the found flow.
1.371 + ///
1.372 + /// \pre \ref run() must be called before using this function.
1.373 + const FlowMap& flowMap() const {
1.374 + return *_flow;
1.375 + }
1.376 +
1.377 + /// \brief Return a const reference to the node map storing the
1.378 + /// found potentials (the dual solution).
1.379 + ///
1.380 + /// Return a const reference to the node map storing the found
1.381 + /// potentials (the dual solution).
1.382 + ///
1.383 + /// \pre \ref run() must be called before using this function.
1.384 + const PotentialMap& potentialMap() const {
1.385 + return *_potential;
1.386 + }
1.387 +
1.388 + /// \brief Return the flow on the given arc.
1.389 + ///
1.390 + /// Return the flow on the given arc.
1.391 + ///
1.392 + /// \pre \ref run() must be called before using this function.
1.393 + Capacity flow(const Arc& arc) const {
1.394 + return (*_flow)[arc];
1.395 + }
1.396 +
1.397 + /// \brief Return the potential of the given node.
1.398 + ///
1.399 + /// Return the potential of the given node.
1.400 + ///
1.401 + /// \pre \ref run() must be called before using this function.
1.402 + Cost potential(const Node& node) const {
1.403 + return (*_potential)[node];
1.404 + }
1.405 +
1.406 + /// \brief Return the total cost of the found flow.
1.407 + ///
1.408 + /// Return the total cost of the found flow. The complexity of the
1.409 + /// function is \f$ O(e) \f$.
1.410 + ///
1.411 + /// \pre \ref run() must be called before using this function.
1.412 + Cost totalCost() const {
1.413 + Cost c = 0;
1.414 + for (ArcIt e(_graph); e != INVALID; ++e)
1.415 + c += (*_flow)[e] * _cost[e];
1.416 + return c;
1.417 + }
1.418 +
1.419 + /// @}
1.420 +
1.421 + private:
1.422 +
1.423 + /// Initialize the algorithm.
1.424 + bool init() {
1.425 + if (!_valid_supply) return false;
1.426 +
1.427 + // Initialize flow and potential maps
1.428 + if (!_flow) {
1.429 + _flow = new FlowMap(_graph);
1.430 + _local_flow = true;
1.431 + }
1.432 + if (!_potential) {
1.433 + _potential = new PotentialMap(_graph);
1.434 + _local_potential = true;
1.435 + }
1.436 +
1.437 + _res_graph = new ResDigraph(_graph, _capacity, *_flow);
1.438 +
1.439 + // Find a feasible flow using Circulation
1.440 + Circulation< Digraph, ConstMap<Arc, Capacity>,
1.441 + CapacityArcMap, SupplyMap >
1.442 + circulation( _graph, constMap<Arc>(Capacity(0)),
1.443 + _capacity, _supply );
1.444 + return circulation.flowMap(*_flow).run();
1.445 + }
1.446 +
1.447 + bool start() {
1.448 + const double LIMIT_FACTOR = 0.01;
1.449 + const int MIN_LIMIT = 3;
1.450 +
1.451 + typedef typename Digraph::template NodeMap<double> FloatPotentialMap;
1.452 + typedef typename Digraph::template NodeMap<int> LevelMap;
1.453 + typedef typename Digraph::template NodeMap<bool> BoolNodeMap;
1.454 + typedef typename Digraph::template NodeMap<Node> PredNodeMap;
1.455 + typedef typename Digraph::template NodeMap<Arc> PredArcMap;
1.456 + typedef typename ResDigraph::template ArcMap<double> ResShiftCostMap;
1.457 + FloatPotentialMap pi(_graph);
1.458 + LevelMap level(_graph);
1.459 + BoolNodeMap reached(_graph);
1.460 + BoolNodeMap processed(_graph);
1.461 + PredNodeMap pred_node(_graph);
1.462 + PredArcMap pred_arc(_graph);
1.463 + int node_num = countNodes(_graph);
1.464 + typedef std::pair<Arc, bool> pair;
1.465 + std::vector<pair> stack(node_num);
1.466 + std::vector<Node> proc_vector(node_num);
1.467 + ResShiftCostMap shift_cost(*_res_graph);
1.468 +
1.469 + Tolerance<double> tol;
1.470 + tol.epsilon(1e-6);
1.471 +
1.472 + Timer t1, t2, t3;
1.473 + t1.reset();
1.474 + t2.reset();
1.475 + t3.reset();
1.476 +
1.477 + // Initialize epsilon and the node potentials
1.478 + double epsilon = 0;
1.479 + for (ArcIt e(_graph); e != INVALID; ++e) {
1.480 + if (_capacity[e] - (*_flow)[e] > 0 && _cost[e] < -epsilon)
1.481 + epsilon = -_cost[e];
1.482 + else if ((*_flow)[e] > 0 && _cost[e] > epsilon)
1.483 + epsilon = _cost[e];
1.484 + }
1.485 + for (NodeIt v(_graph); v != INVALID; ++v) {
1.486 + pi[v] = 0;
1.487 + }
1.488 +
1.489 + // Start phases
1.490 + int limit = int(LIMIT_FACTOR * node_num);
1.491 + if (limit < MIN_LIMIT) limit = MIN_LIMIT;
1.492 + int iter = limit;
1.493 + while (epsilon * node_num >= 1) {
1.494 + t1.start();
1.495 + // Find and cancel cycles in the admissible digraph using DFS
1.496 + for (NodeIt n(_graph); n != INVALID; ++n) {
1.497 + reached[n] = false;
1.498 + processed[n] = false;
1.499 + }
1.500 + int stack_head = -1;
1.501 + int proc_head = -1;
1.502 +
1.503 + for (NodeIt start(_graph); start != INVALID; ++start) {
1.504 + if (reached[start]) continue;
1.505 +
1.506 + // New start node
1.507 + reached[start] = true;
1.508 + pred_arc[start] = INVALID;
1.509 + pred_node[start] = INVALID;
1.510 +
1.511 + // Find the first admissible residual outgoing arc
1.512 + double p = pi[start];
1.513 + Arc e;
1.514 + _graph.firstOut(e, start);
1.515 + while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 ||
1.516 + !tol.negative(_cost[e] + p - pi[_graph.target(e)])) )
1.517 + _graph.nextOut(e);
1.518 + if (e != INVALID) {
1.519 + stack[++stack_head] = pair(e, true);
1.520 + goto next_step_1;
1.521 + }
1.522 + _graph.firstIn(e, start);
1.523 + while ( e != INVALID && ((*_flow)[e] == 0 ||
1.524 + !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) )
1.525 + _graph.nextIn(e);
1.526 + if (e != INVALID) {
1.527 + stack[++stack_head] = pair(e, false);
1.528 + goto next_step_1;
1.529 + }
1.530 + processed[start] = true;
1.531 + proc_vector[++proc_head] = start;
1.532 + continue;
1.533 + next_step_1:
1.534 +
1.535 + while (stack_head >= 0) {
1.536 + Arc se = stack[stack_head].first;
1.537 + bool sf = stack[stack_head].second;
1.538 + Node u, v;
1.539 + if (sf) {
1.540 + u = _graph.source(se);
1.541 + v = _graph.target(se);
1.542 + } else {
1.543 + u = _graph.target(se);
1.544 + v = _graph.source(se);
1.545 + }
1.546 +
1.547 + if (!reached[v]) {
1.548 + // A new node is reached
1.549 + reached[v] = true;
1.550 + pred_node[v] = u;
1.551 + pred_arc[v] = se;
1.552 + // Find the first admissible residual outgoing arc
1.553 + double p = pi[v];
1.554 + Arc e;
1.555 + _graph.firstOut(e, v);
1.556 + while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 ||
1.557 + !tol.negative(_cost[e] + p - pi[_graph.target(e)])) )
1.558 + _graph.nextOut(e);
1.559 + if (e != INVALID) {
1.560 + stack[++stack_head] = pair(e, true);
1.561 + goto next_step_2;
1.562 + }
1.563 + _graph.firstIn(e, v);
1.564 + while ( e != INVALID && ((*_flow)[e] == 0 ||
1.565 + !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) )
1.566 + _graph.nextIn(e);
1.567 + stack[++stack_head] = pair(e, false);
1.568 + next_step_2: ;
1.569 + } else {
1.570 + if (!processed[v]) {
1.571 + // A cycle is found
1.572 + Node n, w = u;
1.573 + Capacity d, delta = sf ? _capacity[se] - (*_flow)[se] :
1.574 + (*_flow)[se];
1.575 + for (n = u; n != v; n = pred_node[n]) {
1.576 + d = _graph.target(pred_arc[n]) == n ?
1.577 + _capacity[pred_arc[n]] - (*_flow)[pred_arc[n]] :
1.578 + (*_flow)[pred_arc[n]];
1.579 + if (d <= delta) {
1.580 + delta = d;
1.581 + w = pred_node[n];
1.582 + }
1.583 + }
1.584 +
1.585 +/*
1.586 + std::cout << "CYCLE FOUND: ";
1.587 + if (sf)
1.588 + std::cout << _cost[se] + pi[_graph.source(se)] - pi[_graph.target(se)];
1.589 + else
1.590 + std::cout << _graph.id(se) << ":" << -(_cost[se] + pi[_graph.source(se)] - pi[_graph.target(se)]);
1.591 + for (n = u; n != v; n = pred_node[n]) {
1.592 + if (_graph.target(pred_arc[n]) == n)
1.593 + std::cout << " " << _cost[pred_arc[n]] + pi[_graph.source(pred_arc[n])] - pi[_graph.target(pred_arc[n])];
1.594 + else
1.595 + std::cout << " " << -(_cost[pred_arc[n]] + pi[_graph.source(pred_arc[n])] - pi[_graph.target(pred_arc[n])]);
1.596 + }
1.597 + std::cout << "\n";
1.598 +*/
1.599 + // Augment along the cycle
1.600 + (*_flow)[se] = sf ? (*_flow)[se] + delta :
1.601 + (*_flow)[se] - delta;
1.602 + for (n = u; n != v; n = pred_node[n]) {
1.603 + if (_graph.target(pred_arc[n]) == n)
1.604 + (*_flow)[pred_arc[n]] += delta;
1.605 + else
1.606 + (*_flow)[pred_arc[n]] -= delta;
1.607 + }
1.608 + for (n = u; stack_head > 0 && n != w; n = pred_node[n]) {
1.609 + --stack_head;
1.610 + reached[n] = false;
1.611 + }
1.612 + u = w;
1.613 + }
1.614 + v = u;
1.615 +
1.616 + // Find the next admissible residual outgoing arc
1.617 + double p = pi[v];
1.618 + Arc e = stack[stack_head].first;
1.619 + if (!stack[stack_head].second) {
1.620 + _graph.nextIn(e);
1.621 + goto in_arc_3;
1.622 + }
1.623 + _graph.nextOut(e);
1.624 + while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 ||
1.625 + !tol.negative(_cost[e] + p - pi[_graph.target(e)])) )
1.626 + _graph.nextOut(e);
1.627 + if (e != INVALID) {
1.628 + stack[stack_head] = pair(e, true);
1.629 + goto next_step_3;
1.630 + }
1.631 + _graph.firstIn(e, v);
1.632 + in_arc_3:
1.633 + while ( e != INVALID && ((*_flow)[e] == 0 ||
1.634 + !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) )
1.635 + _graph.nextIn(e);
1.636 + stack[stack_head] = pair(e, false);
1.637 + next_step_3: ;
1.638 + }
1.639 +
1.640 + while (stack_head >= 0 && stack[stack_head].first == INVALID) {
1.641 + processed[v] = true;
1.642 + proc_vector[++proc_head] = v;
1.643 + if (--stack_head >= 0) {
1.644 + v = stack[stack_head].second ?
1.645 + _graph.source(stack[stack_head].first) :
1.646 + _graph.target(stack[stack_head].first);
1.647 + // Find the next admissible residual outgoing arc
1.648 + double p = pi[v];
1.649 + Arc e = stack[stack_head].first;
1.650 + if (!stack[stack_head].second) {
1.651 + _graph.nextIn(e);
1.652 + goto in_arc_4;
1.653 + }
1.654 + _graph.nextOut(e);
1.655 + while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 ||
1.656 + !tol.negative(_cost[e] + p - pi[_graph.target(e)])) )
1.657 + _graph.nextOut(e);
1.658 + if (e != INVALID) {
1.659 + stack[stack_head] = pair(e, true);
1.660 + goto next_step_4;
1.661 + }
1.662 + _graph.firstIn(e, v);
1.663 + in_arc_4:
1.664 + while ( e != INVALID && ((*_flow)[e] == 0 ||
1.665 + !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) )
1.666 + _graph.nextIn(e);
1.667 + stack[stack_head] = pair(e, false);
1.668 + next_step_4: ;
1.669 + }
1.670 + }
1.671 + }
1.672 + }
1.673 + t1.stop();
1.674 +
1.675 + // Tighten potentials and epsilon
1.676 + if (--iter > 0) {
1.677 + // Compute levels
1.678 + t2.start();
1.679 + for (int i = proc_head; i >= 0; --i) {
1.680 + Node v = proc_vector[i];
1.681 + double p = pi[v];
1.682 + int l = 0;
1.683 + for (InArcIt e(_graph, v); e != INVALID; ++e) {
1.684 + Node u = _graph.source(e);
1.685 + if ( _capacity[e] - (*_flow)[e] > 0 &&
1.686 + tol.negative(_cost[e] + pi[u] - p) &&
1.687 + level[u] + 1 > l ) l = level[u] + 1;
1.688 + }
1.689 + for (OutArcIt e(_graph, v); e != INVALID; ++e) {
1.690 + Node u = _graph.target(e);
1.691 + if ( (*_flow)[e] > 0 &&
1.692 + tol.negative(-_cost[e] + pi[u] - p) &&
1.693 + level[u] + 1 > l ) l = level[u] + 1;
1.694 + }
1.695 + level[v] = l;
1.696 + }
1.697 +
1.698 + // Modify potentials
1.699 + double p, q = -1;
1.700 + for (ArcIt e(_graph); e != INVALID; ++e) {
1.701 + Node u = _graph.source(e);
1.702 + Node v = _graph.target(e);
1.703 + if (_capacity[e] - (*_flow)[e] > 0 && level[u] - level[v] > 0) {
1.704 + p = (_cost[e] + pi[u] - pi[v] + epsilon) /
1.705 + (level[u] - level[v] + 1);
1.706 + if (q < 0 || p < q) q = p;
1.707 + }
1.708 + else if ((*_flow)[e] > 0 && level[v] - level[u] > 0) {
1.709 + p = (-_cost[e] - pi[u] + pi[v] + epsilon) /
1.710 + (level[v] - level[u] + 1);
1.711 + if (q < 0 || p < q) q = p;
1.712 + }
1.713 + }
1.714 + for (NodeIt v(_graph); v != INVALID; ++v) {
1.715 + pi[v] -= q * level[v];
1.716 + }
1.717 +
1.718 + // Modify epsilon
1.719 + epsilon = 0;
1.720 + for (ArcIt e(_graph); e != INVALID; ++e) {
1.721 + double curr = _cost[e] + pi[_graph.source(e)]
1.722 + - pi[_graph.target(e)];
1.723 + if (_capacity[e] - (*_flow)[e] > 0 && curr < -epsilon)
1.724 + epsilon = -curr;
1.725 + else if ((*_flow)[e] > 0 && curr > epsilon)
1.726 + epsilon = curr;
1.727 + }
1.728 + t2.stop();
1.729 + } else {
1.730 + // Set epsilon to the minimum cycle mean
1.731 + t3.start();
1.732 +
1.733 +/**/
1.734 + StaticDigraph static_graph;
1.735 + typename ResDigraph::template NodeMap<typename StaticDigraph::Node> node_ref(*_res_graph);
1.736 + typename ResDigraph::template ArcMap<typename StaticDigraph::Arc> arc_ref(*_res_graph);
1.737 + static_graph.build(*_res_graph, node_ref, arc_ref);
1.738 + typename StaticDigraph::template NodeMap<double> static_pi(static_graph);
1.739 + typename StaticDigraph::template ArcMap<double> static_cost(static_graph);
1.740 +
1.741 + for (typename ResDigraph::ArcIt e(*_res_graph); e != INVALID; ++e)
1.742 + static_cost[arc_ref[e]] = _res_cost[e];
1.743 +
1.744 + Howard<StaticDigraph, typename StaticDigraph::template ArcMap<double> >
1.745 + mmc(static_graph, static_cost);
1.746 + mmc.findMinMean();
1.747 + epsilon = -mmc.cycleMean();
1.748 +/**/
1.749 +
1.750 +/*
1.751 + Howard<ResDigraph, ResidualCostMap> mmc(*_res_graph, _res_cost);
1.752 + mmc.findMinMean();
1.753 + epsilon = -mmc.cycleMean();
1.754 +*/
1.755 +
1.756 + // Compute feasible potentials for the current epsilon
1.757 + for (typename StaticDigraph::ArcIt e(static_graph); e != INVALID; ++e)
1.758 + static_cost[e] += epsilon;
1.759 + typename BellmanFord<StaticDigraph, typename StaticDigraph::template ArcMap<double> >::
1.760 + template SetDistMap<typename StaticDigraph::template NodeMap<double> >::
1.761 + template SetOperationTraits<BFOperationTraits>::Create
1.762 + bf(static_graph, static_cost);
1.763 + bf.distMap(static_pi).init(0);
1.764 + bf.start();
1.765 + for (NodeIt n(_graph); n != INVALID; ++n)
1.766 + pi[n] = static_pi[node_ref[n]];
1.767 +
1.768 +/*
1.769 + for (typename ResDigraph::ArcIt e(*_res_graph); e != INVALID; ++e)
1.770 + shift_cost[e] = _res_cost[e] + epsilon;
1.771 + typename BellmanFord<ResDigraph, ResShiftCostMap>::
1.772 + template SetDistMap<FloatPotentialMap>::
1.773 + template SetOperationTraits<BFOperationTraits>::Create
1.774 + bf(*_res_graph, shift_cost);
1.775 + bf.distMap(pi).init(0);
1.776 + bf.start();
1.777 +*/
1.778 +
1.779 + iter = limit;
1.780 + t3.stop();
1.781 + }
1.782 + }
1.783 +
1.784 +// std::cout << t1.realTime() << " " << t2.realTime() << " " << t3.realTime() << "\n";
1.785 +
1.786 + // Handle non-zero lower bounds
1.787 + if (_lower) {
1.788 + for (ArcIt e(_graph); e != INVALID; ++e)
1.789 + (*_flow)[e] += (*_lower)[e];
1.790 + }
1.791 + return true;
1.792 + }
1.793 +
1.794 + }; //class CancelAndTighten
1.795 +
1.796 + ///@}
1.797 +
1.798 +} //namespace lemon
1.799 +
1.800 +#endif //LEMON_CANCEL_AND_TIGHTEN_H