1.1 --- a/lemon/Makefile.am Mon Feb 23 18:01:14 2009 +0000
1.2 +++ b/lemon/Makefile.am Tue Feb 24 09:46:02 2009 +0100
1.3 @@ -85,6 +85,7 @@
1.4 lemon/max_matching.h \
1.5 lemon/min_cost_arborescence.h \
1.6 lemon/nauty_reader.h \
1.7 + lemon/network_simplex.h \
1.8 lemon/path.h \
1.9 lemon/preflow.h \
1.10 lemon/radix_sort.h \
2.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
2.2 +++ b/lemon/network_simplex.h Tue Feb 24 09:46:02 2009 +0100
2.3 @@ -0,0 +1,1191 @@
2.4 +/* -*- mode: C++; indent-tabs-mode: nil; -*-
2.5 + *
2.6 + * This file is a part of LEMON, a generic C++ optimization library.
2.7 + *
2.8 + * Copyright (C) 2003-2009
2.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
2.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
2.11 + *
2.12 + * Permission to use, modify and distribute this software is granted
2.13 + * provided that this copyright notice appears in all copies. For
2.14 + * precise terms see the accompanying LICENSE file.
2.15 + *
2.16 + * This software is provided "AS IS" with no warranty of any kind,
2.17 + * express or implied, and with no claim as to its suitability for any
2.18 + * purpose.
2.19 + *
2.20 + */
2.21 +
2.22 +#ifndef LEMON_NETWORK_SIMPLEX_H
2.23 +#define LEMON_NETWORK_SIMPLEX_H
2.24 +
2.25 +/// \ingroup min_cost_flow
2.26 +///
2.27 +/// \file
2.28 +/// \brief Network simplex algorithm for finding a minimum cost flow.
2.29 +
2.30 +#include <vector>
2.31 +#include <limits>
2.32 +#include <algorithm>
2.33 +
2.34 +#include <lemon/math.h>
2.35 +
2.36 +namespace lemon {
2.37 +
2.38 + /// \addtogroup min_cost_flow
2.39 + /// @{
2.40 +
2.41 + /// \brief Implementation of the primal network simplex algorithm
2.42 + /// for finding a \ref min_cost_flow "minimum cost flow".
2.43 + ///
2.44 + /// \ref NetworkSimplex implements the primal network simplex algorithm
2.45 + /// for finding a \ref min_cost_flow "minimum cost flow".
2.46 + ///
2.47 + /// \tparam Digraph The digraph type the algorithm runs on.
2.48 + /// \tparam LowerMap The type of the lower bound map.
2.49 + /// \tparam CapacityMap The type of the capacity (upper bound) map.
2.50 + /// \tparam CostMap The type of the cost (length) map.
2.51 + /// \tparam SupplyMap The type of the supply map.
2.52 + ///
2.53 + /// \warning
2.54 + /// - Arc capacities and costs should be \e non-negative \e integers.
2.55 + /// - Supply values should be \e signed \e integers.
2.56 + /// - The value types of the maps should be convertible to each other.
2.57 + /// - \c CostMap::Value must be signed type.
2.58 + ///
2.59 + /// \note \ref NetworkSimplex provides five different pivot rule
2.60 + /// implementations that significantly affect the efficiency of the
2.61 + /// algorithm.
2.62 + /// By default "Block Search" pivot rule is used, which proved to be
2.63 + /// by far the most efficient according to our benchmark tests.
2.64 + /// However another pivot rule can be selected using \ref run()
2.65 + /// function with the proper parameter.
2.66 +#ifdef DOXYGEN
2.67 + template < typename Digraph,
2.68 + typename LowerMap,
2.69 + typename CapacityMap,
2.70 + typename CostMap,
2.71 + typename SupplyMap >
2.72 +
2.73 +#else
2.74 + template < typename Digraph,
2.75 + typename LowerMap = typename Digraph::template ArcMap<int>,
2.76 + typename CapacityMap = typename Digraph::template ArcMap<int>,
2.77 + typename CostMap = typename Digraph::template ArcMap<int>,
2.78 + typename SupplyMap = typename Digraph::template NodeMap<int> >
2.79 +#endif
2.80 + class NetworkSimplex
2.81 + {
2.82 + TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
2.83 +
2.84 + typedef typename CapacityMap::Value Capacity;
2.85 + typedef typename CostMap::Value Cost;
2.86 + typedef typename SupplyMap::Value Supply;
2.87 +
2.88 + typedef std::vector<Arc> ArcVector;
2.89 + typedef std::vector<Node> NodeVector;
2.90 + typedef std::vector<int> IntVector;
2.91 + typedef std::vector<bool> BoolVector;
2.92 + typedef std::vector<Capacity> CapacityVector;
2.93 + typedef std::vector<Cost> CostVector;
2.94 + typedef std::vector<Supply> SupplyVector;
2.95 +
2.96 + public:
2.97 +
2.98 + /// The type of the flow map
2.99 + typedef typename Digraph::template ArcMap<Capacity> FlowMap;
2.100 + /// The type of the potential map
2.101 + typedef typename Digraph::template NodeMap<Cost> PotentialMap;
2.102 +
2.103 + public:
2.104 +
2.105 + /// Enum type for selecting the pivot rule used by \ref run()
2.106 + enum PivotRuleEnum {
2.107 + FIRST_ELIGIBLE_PIVOT,
2.108 + BEST_ELIGIBLE_PIVOT,
2.109 + BLOCK_SEARCH_PIVOT,
2.110 + CANDIDATE_LIST_PIVOT,
2.111 + ALTERING_LIST_PIVOT
2.112 + };
2.113 +
2.114 + private:
2.115 +
2.116 + // State constants for arcs
2.117 + enum ArcStateEnum {
2.118 + STATE_UPPER = -1,
2.119 + STATE_TREE = 0,
2.120 + STATE_LOWER = 1
2.121 + };
2.122 +
2.123 + private:
2.124 +
2.125 + // References for the original data
2.126 + const Digraph &_orig_graph;
2.127 + const LowerMap *_orig_lower;
2.128 + const CapacityMap &_orig_cap;
2.129 + const CostMap &_orig_cost;
2.130 + const SupplyMap *_orig_supply;
2.131 + Node _orig_source;
2.132 + Node _orig_target;
2.133 + Capacity _orig_flow_value;
2.134 +
2.135 + // Result maps
2.136 + FlowMap *_flow_result;
2.137 + PotentialMap *_potential_result;
2.138 + bool _local_flow;
2.139 + bool _local_potential;
2.140 +
2.141 + // Data structures for storing the graph
2.142 + ArcVector _arc;
2.143 + NodeVector _node;
2.144 + IntNodeMap _node_id;
2.145 + IntVector _source;
2.146 + IntVector _target;
2.147 +
2.148 + // The number of nodes and arcs in the original graph
2.149 + int _node_num;
2.150 + int _arc_num;
2.151 +
2.152 + // Node and arc maps
2.153 + CapacityVector _cap;
2.154 + CostVector _cost;
2.155 + CostVector _supply;
2.156 + CapacityVector _flow;
2.157 + CostVector _pi;
2.158 +
2.159 + // Node and arc maps for the spanning tree structure
2.160 + IntVector _depth;
2.161 + IntVector _parent;
2.162 + IntVector _pred;
2.163 + IntVector _thread;
2.164 + BoolVector _forward;
2.165 + IntVector _state;
2.166 +
2.167 + // The root node
2.168 + int _root;
2.169 +
2.170 + // The entering arc in the current pivot iteration
2.171 + int _in_arc;
2.172 +
2.173 + // Temporary data used in the current pivot iteration
2.174 + int join, u_in, v_in, u_out, v_out;
2.175 + int right, first, second, last;
2.176 + int stem, par_stem, new_stem;
2.177 + Capacity delta;
2.178 +
2.179 + private:
2.180 +
2.181 + /// \brief Implementation of the "First Eligible" pivot rule for the
2.182 + /// \ref NetworkSimplex "network simplex" algorithm.
2.183 + ///
2.184 + /// This class implements the "First Eligible" pivot rule
2.185 + /// for the \ref NetworkSimplex "network simplex" algorithm.
2.186 + ///
2.187 + /// For more information see \ref NetworkSimplex::run().
2.188 + class FirstEligiblePivotRule
2.189 + {
2.190 + private:
2.191 +
2.192 + // References to the NetworkSimplex class
2.193 + const ArcVector &_arc;
2.194 + const IntVector &_source;
2.195 + const IntVector &_target;
2.196 + const CostVector &_cost;
2.197 + const IntVector &_state;
2.198 + const CostVector &_pi;
2.199 + int &_in_arc;
2.200 + int _arc_num;
2.201 +
2.202 + // Pivot rule data
2.203 + int _next_arc;
2.204 +
2.205 + public:
2.206 +
2.207 + /// Constructor
2.208 + FirstEligiblePivotRule(NetworkSimplex &ns) :
2.209 + _arc(ns._arc), _source(ns._source), _target(ns._target),
2.210 + _cost(ns._cost), _state(ns._state), _pi(ns._pi),
2.211 + _in_arc(ns._in_arc), _arc_num(ns._arc_num), _next_arc(0)
2.212 + {}
2.213 +
2.214 + /// Find next entering arc
2.215 + bool findEnteringArc() {
2.216 + Cost c;
2.217 + for (int e = _next_arc; e < _arc_num; ++e) {
2.218 + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
2.219 + if (c < 0) {
2.220 + _in_arc = e;
2.221 + _next_arc = e + 1;
2.222 + return true;
2.223 + }
2.224 + }
2.225 + for (int e = 0; e < _next_arc; ++e) {
2.226 + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
2.227 + if (c < 0) {
2.228 + _in_arc = e;
2.229 + _next_arc = e + 1;
2.230 + return true;
2.231 + }
2.232 + }
2.233 + return false;
2.234 + }
2.235 +
2.236 + }; //class FirstEligiblePivotRule
2.237 +
2.238 +
2.239 + /// \brief Implementation of the "Best Eligible" pivot rule for the
2.240 + /// \ref NetworkSimplex "network simplex" algorithm.
2.241 + ///
2.242 + /// This class implements the "Best Eligible" pivot rule
2.243 + /// for the \ref NetworkSimplex "network simplex" algorithm.
2.244 + ///
2.245 + /// For more information see \ref NetworkSimplex::run().
2.246 + class BestEligiblePivotRule
2.247 + {
2.248 + private:
2.249 +
2.250 + // References to the NetworkSimplex class
2.251 + const ArcVector &_arc;
2.252 + const IntVector &_source;
2.253 + const IntVector &_target;
2.254 + const CostVector &_cost;
2.255 + const IntVector &_state;
2.256 + const CostVector &_pi;
2.257 + int &_in_arc;
2.258 + int _arc_num;
2.259 +
2.260 + public:
2.261 +
2.262 + /// Constructor
2.263 + BestEligiblePivotRule(NetworkSimplex &ns) :
2.264 + _arc(ns._arc), _source(ns._source), _target(ns._target),
2.265 + _cost(ns._cost), _state(ns._state), _pi(ns._pi),
2.266 + _in_arc(ns._in_arc), _arc_num(ns._arc_num)
2.267 + {}
2.268 +
2.269 + /// Find next entering arc
2.270 + bool findEnteringArc() {
2.271 + Cost c, min = 0;
2.272 + for (int e = 0; e < _arc_num; ++e) {
2.273 + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
2.274 + if (c < min) {
2.275 + min = c;
2.276 + _in_arc = e;
2.277 + }
2.278 + }
2.279 + return min < 0;
2.280 + }
2.281 +
2.282 + }; //class BestEligiblePivotRule
2.283 +
2.284 +
2.285 + /// \brief Implementation of the "Block Search" pivot rule for the
2.286 + /// \ref NetworkSimplex "network simplex" algorithm.
2.287 + ///
2.288 + /// This class implements the "Block Search" pivot rule
2.289 + /// for the \ref NetworkSimplex "network simplex" algorithm.
2.290 + ///
2.291 + /// For more information see \ref NetworkSimplex::run().
2.292 + class BlockSearchPivotRule
2.293 + {
2.294 + private:
2.295 +
2.296 + // References to the NetworkSimplex class
2.297 + const ArcVector &_arc;
2.298 + const IntVector &_source;
2.299 + const IntVector &_target;
2.300 + const CostVector &_cost;
2.301 + const IntVector &_state;
2.302 + const CostVector &_pi;
2.303 + int &_in_arc;
2.304 + int _arc_num;
2.305 +
2.306 + // Pivot rule data
2.307 + int _block_size;
2.308 + int _next_arc;
2.309 +
2.310 + public:
2.311 +
2.312 + /// Constructor
2.313 + BlockSearchPivotRule(NetworkSimplex &ns) :
2.314 + _arc(ns._arc), _source(ns._source), _target(ns._target),
2.315 + _cost(ns._cost), _state(ns._state), _pi(ns._pi),
2.316 + _in_arc(ns._in_arc), _arc_num(ns._arc_num), _next_arc(0)
2.317 + {
2.318 + // The main parameters of the pivot rule
2.319 + const double BLOCK_SIZE_FACTOR = 2.0;
2.320 + const int MIN_BLOCK_SIZE = 10;
2.321 +
2.322 + _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_arc_num)),
2.323 + MIN_BLOCK_SIZE );
2.324 + }
2.325 +
2.326 + /// Find next entering arc
2.327 + bool findEnteringArc() {
2.328 + Cost c, min = 0;
2.329 + int cnt = _block_size;
2.330 + int e, min_arc = _next_arc;
2.331 + for (e = _next_arc; e < _arc_num; ++e) {
2.332 + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
2.333 + if (c < min) {
2.334 + min = c;
2.335 + min_arc = e;
2.336 + }
2.337 + if (--cnt == 0) {
2.338 + if (min < 0) break;
2.339 + cnt = _block_size;
2.340 + }
2.341 + }
2.342 + if (min == 0 || cnt > 0) {
2.343 + for (e = 0; e < _next_arc; ++e) {
2.344 + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
2.345 + if (c < min) {
2.346 + min = c;
2.347 + min_arc = e;
2.348 + }
2.349 + if (--cnt == 0) {
2.350 + if (min < 0) break;
2.351 + cnt = _block_size;
2.352 + }
2.353 + }
2.354 + }
2.355 + if (min >= 0) return false;
2.356 + _in_arc = min_arc;
2.357 + _next_arc = e;
2.358 + return true;
2.359 + }
2.360 +
2.361 + }; //class BlockSearchPivotRule
2.362 +
2.363 +
2.364 + /// \brief Implementation of the "Candidate List" pivot rule for the
2.365 + /// \ref NetworkSimplex "network simplex" algorithm.
2.366 + ///
2.367 + /// This class implements the "Candidate List" pivot rule
2.368 + /// for the \ref NetworkSimplex "network simplex" algorithm.
2.369 + ///
2.370 + /// For more information see \ref NetworkSimplex::run().
2.371 + class CandidateListPivotRule
2.372 + {
2.373 + private:
2.374 +
2.375 + // References to the NetworkSimplex class
2.376 + const ArcVector &_arc;
2.377 + const IntVector &_source;
2.378 + const IntVector &_target;
2.379 + const CostVector &_cost;
2.380 + const IntVector &_state;
2.381 + const CostVector &_pi;
2.382 + int &_in_arc;
2.383 + int _arc_num;
2.384 +
2.385 + // Pivot rule data
2.386 + IntVector _candidates;
2.387 + int _list_length, _minor_limit;
2.388 + int _curr_length, _minor_count;
2.389 + int _next_arc;
2.390 +
2.391 + public:
2.392 +
2.393 + /// Constructor
2.394 + CandidateListPivotRule(NetworkSimplex &ns) :
2.395 + _arc(ns._arc), _source(ns._source), _target(ns._target),
2.396 + _cost(ns._cost), _state(ns._state), _pi(ns._pi),
2.397 + _in_arc(ns._in_arc), _arc_num(ns._arc_num), _next_arc(0)
2.398 + {
2.399 + // The main parameters of the pivot rule
2.400 + const double LIST_LENGTH_FACTOR = 1.0;
2.401 + const int MIN_LIST_LENGTH = 10;
2.402 + const double MINOR_LIMIT_FACTOR = 0.1;
2.403 + const int MIN_MINOR_LIMIT = 3;
2.404 +
2.405 + _list_length = std::max( int(LIST_LENGTH_FACTOR * sqrt(_arc_num)),
2.406 + MIN_LIST_LENGTH );
2.407 + _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length),
2.408 + MIN_MINOR_LIMIT );
2.409 + _curr_length = _minor_count = 0;
2.410 + _candidates.resize(_list_length);
2.411 + }
2.412 +
2.413 + /// Find next entering arc
2.414 + bool findEnteringArc() {
2.415 + Cost min, c;
2.416 + int e, min_arc = _next_arc;
2.417 + if (_curr_length > 0 && _minor_count < _minor_limit) {
2.418 + // Minor iteration: select the best eligible arc from the
2.419 + // current candidate list
2.420 + ++_minor_count;
2.421 + min = 0;
2.422 + for (int i = 0; i < _curr_length; ++i) {
2.423 + e = _candidates[i];
2.424 + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
2.425 + if (c < min) {
2.426 + min = c;
2.427 + min_arc = e;
2.428 + }
2.429 + if (c >= 0) {
2.430 + _candidates[i--] = _candidates[--_curr_length];
2.431 + }
2.432 + }
2.433 + if (min < 0) {
2.434 + _in_arc = min_arc;
2.435 + return true;
2.436 + }
2.437 + }
2.438 +
2.439 + // Major iteration: build a new candidate list
2.440 + min = 0;
2.441 + _curr_length = 0;
2.442 + for (e = _next_arc; e < _arc_num; ++e) {
2.443 + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
2.444 + if (c < 0) {
2.445 + _candidates[_curr_length++] = e;
2.446 + if (c < min) {
2.447 + min = c;
2.448 + min_arc = e;
2.449 + }
2.450 + if (_curr_length == _list_length) break;
2.451 + }
2.452 + }
2.453 + if (_curr_length < _list_length) {
2.454 + for (e = 0; e < _next_arc; ++e) {
2.455 + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
2.456 + if (c < 0) {
2.457 + _candidates[_curr_length++] = e;
2.458 + if (c < min) {
2.459 + min = c;
2.460 + min_arc = e;
2.461 + }
2.462 + if (_curr_length == _list_length) break;
2.463 + }
2.464 + }
2.465 + }
2.466 + if (_curr_length == 0) return false;
2.467 + _minor_count = 1;
2.468 + _in_arc = min_arc;
2.469 + _next_arc = e;
2.470 + return true;
2.471 + }
2.472 +
2.473 + }; //class CandidateListPivotRule
2.474 +
2.475 +
2.476 + /// \brief Implementation of the "Altering Candidate List" pivot rule
2.477 + /// for the \ref NetworkSimplex "network simplex" algorithm.
2.478 + ///
2.479 + /// This class implements the "Altering Candidate List" pivot rule
2.480 + /// for the \ref NetworkSimplex "network simplex" algorithm.
2.481 + ///
2.482 + /// For more information see \ref NetworkSimplex::run().
2.483 + class AlteringListPivotRule
2.484 + {
2.485 + private:
2.486 +
2.487 + // References to the NetworkSimplex class
2.488 + const ArcVector &_arc;
2.489 + const IntVector &_source;
2.490 + const IntVector &_target;
2.491 + const CostVector &_cost;
2.492 + const IntVector &_state;
2.493 + const CostVector &_pi;
2.494 + int &_in_arc;
2.495 + int _arc_num;
2.496 +
2.497 + // Pivot rule data
2.498 + int _block_size, _head_length, _curr_length;
2.499 + int _next_arc;
2.500 + IntVector _candidates;
2.501 + CostVector _cand_cost;
2.502 +
2.503 + // Functor class to compare arcs during sort of the candidate list
2.504 + class SortFunc
2.505 + {
2.506 + private:
2.507 + const CostVector &_map;
2.508 + public:
2.509 + SortFunc(const CostVector &map) : _map(map) {}
2.510 + bool operator()(int left, int right) {
2.511 + return _map[left] > _map[right];
2.512 + }
2.513 + };
2.514 +
2.515 + SortFunc _sort_func;
2.516 +
2.517 + public:
2.518 +
2.519 + /// Constructor
2.520 + AlteringListPivotRule(NetworkSimplex &ns) :
2.521 + _arc(ns._arc), _source(ns._source), _target(ns._target),
2.522 + _cost(ns._cost), _state(ns._state), _pi(ns._pi),
2.523 + _in_arc(ns._in_arc), _arc_num(ns._arc_num),
2.524 + _next_arc(0), _cand_cost(ns._arc_num), _sort_func(_cand_cost)
2.525 + {
2.526 + // The main parameters of the pivot rule
2.527 + const double BLOCK_SIZE_FACTOR = 1.5;
2.528 + const int MIN_BLOCK_SIZE = 10;
2.529 + const double HEAD_LENGTH_FACTOR = 0.1;
2.530 + const int MIN_HEAD_LENGTH = 3;
2.531 +
2.532 + _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_arc_num)),
2.533 + MIN_BLOCK_SIZE );
2.534 + _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size),
2.535 + MIN_HEAD_LENGTH );
2.536 + _candidates.resize(_head_length + _block_size);
2.537 + _curr_length = 0;
2.538 + }
2.539 +
2.540 + /// Find next entering arc
2.541 + bool findEnteringArc() {
2.542 + // Check the current candidate list
2.543 + int e;
2.544 + for (int i = 0; i < _curr_length; ++i) {
2.545 + e = _candidates[i];
2.546 + _cand_cost[e] = _state[e] *
2.547 + (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
2.548 + if (_cand_cost[e] >= 0) {
2.549 + _candidates[i--] = _candidates[--_curr_length];
2.550 + }
2.551 + }
2.552 +
2.553 + // Extend the list
2.554 + int cnt = _block_size;
2.555 + int last_edge = 0;
2.556 + int limit = _head_length;
2.557 +
2.558 + for (int e = _next_arc; e < _arc_num; ++e) {
2.559 + _cand_cost[e] = _state[e] *
2.560 + (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
2.561 + if (_cand_cost[e] < 0) {
2.562 + _candidates[_curr_length++] = e;
2.563 + last_edge = e;
2.564 + }
2.565 + if (--cnt == 0) {
2.566 + if (_curr_length > limit) break;
2.567 + limit = 0;
2.568 + cnt = _block_size;
2.569 + }
2.570 + }
2.571 + if (_curr_length <= limit) {
2.572 + for (int e = 0; e < _next_arc; ++e) {
2.573 + _cand_cost[e] = _state[e] *
2.574 + (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
2.575 + if (_cand_cost[e] < 0) {
2.576 + _candidates[_curr_length++] = e;
2.577 + last_edge = e;
2.578 + }
2.579 + if (--cnt == 0) {
2.580 + if (_curr_length > limit) break;
2.581 + limit = 0;
2.582 + cnt = _block_size;
2.583 + }
2.584 + }
2.585 + }
2.586 + if (_curr_length == 0) return false;
2.587 + _next_arc = last_edge + 1;
2.588 +
2.589 + // Make heap of the candidate list (approximating a partial sort)
2.590 + make_heap( _candidates.begin(), _candidates.begin() + _curr_length,
2.591 + _sort_func );
2.592 +
2.593 + // Pop the first element of the heap
2.594 + _in_arc = _candidates[0];
2.595 + pop_heap( _candidates.begin(), _candidates.begin() + _curr_length,
2.596 + _sort_func );
2.597 + _curr_length = std::min(_head_length, _curr_length - 1);
2.598 + return true;
2.599 + }
2.600 +
2.601 + }; //class AlteringListPivotRule
2.602 +
2.603 + public:
2.604 +
2.605 + /// \brief General constructor (with lower bounds).
2.606 + ///
2.607 + /// General constructor (with lower bounds).
2.608 + ///
2.609 + /// \param digraph The digraph the algorithm runs on.
2.610 + /// \param lower The lower bounds of the arcs.
2.611 + /// \param capacity The capacities (upper bounds) of the arcs.
2.612 + /// \param cost The cost (length) values of the arcs.
2.613 + /// \param supply The supply values of the nodes (signed).
2.614 + NetworkSimplex( const Digraph &digraph,
2.615 + const LowerMap &lower,
2.616 + const CapacityMap &capacity,
2.617 + const CostMap &cost,
2.618 + const SupplyMap &supply ) :
2.619 + _orig_graph(digraph), _orig_lower(&lower), _orig_cap(capacity),
2.620 + _orig_cost(cost), _orig_supply(&supply),
2.621 + _flow_result(NULL), _potential_result(NULL),
2.622 + _local_flow(false), _local_potential(false),
2.623 + _node_id(digraph)
2.624 + {}
2.625 +
2.626 + /// \brief General constructor (without lower bounds).
2.627 + ///
2.628 + /// General constructor (without lower bounds).
2.629 + ///
2.630 + /// \param digraph The digraph the algorithm runs on.
2.631 + /// \param capacity The capacities (upper bounds) of the arcs.
2.632 + /// \param cost The cost (length) values of the arcs.
2.633 + /// \param supply The supply values of the nodes (signed).
2.634 + NetworkSimplex( const Digraph &digraph,
2.635 + const CapacityMap &capacity,
2.636 + const CostMap &cost,
2.637 + const SupplyMap &supply ) :
2.638 + _orig_graph(digraph), _orig_lower(NULL), _orig_cap(capacity),
2.639 + _orig_cost(cost), _orig_supply(&supply),
2.640 + _flow_result(NULL), _potential_result(NULL),
2.641 + _local_flow(false), _local_potential(false),
2.642 + _node_id(digraph)
2.643 + {}
2.644 +
2.645 + /// \brief Simple constructor (with lower bounds).
2.646 + ///
2.647 + /// Simple constructor (with lower bounds).
2.648 + ///
2.649 + /// \param digraph The digraph the algorithm runs on.
2.650 + /// \param lower The lower bounds of the arcs.
2.651 + /// \param capacity The capacities (upper bounds) of the arcs.
2.652 + /// \param cost The cost (length) values of the arcs.
2.653 + /// \param s The source node.
2.654 + /// \param t The target node.
2.655 + /// \param flow_value The required amount of flow from node \c s
2.656 + /// to node \c t (i.e. the supply of \c s and the demand of \c t).
2.657 + NetworkSimplex( const Digraph &digraph,
2.658 + const LowerMap &lower,
2.659 + const CapacityMap &capacity,
2.660 + const CostMap &cost,
2.661 + Node s, Node t,
2.662 + Capacity flow_value ) :
2.663 + _orig_graph(digraph), _orig_lower(&lower), _orig_cap(capacity),
2.664 + _orig_cost(cost), _orig_supply(NULL),
2.665 + _orig_source(s), _orig_target(t), _orig_flow_value(flow_value),
2.666 + _flow_result(NULL), _potential_result(NULL),
2.667 + _local_flow(false), _local_potential(false),
2.668 + _node_id(digraph)
2.669 + {}
2.670 +
2.671 + /// \brief Simple constructor (without lower bounds).
2.672 + ///
2.673 + /// Simple constructor (without lower bounds).
2.674 + ///
2.675 + /// \param digraph The digraph the algorithm runs on.
2.676 + /// \param capacity The capacities (upper bounds) of the arcs.
2.677 + /// \param cost The cost (length) values of the arcs.
2.678 + /// \param s The source node.
2.679 + /// \param t The target node.
2.680 + /// \param flow_value The required amount of flow from node \c s
2.681 + /// to node \c t (i.e. the supply of \c s and the demand of \c t).
2.682 + NetworkSimplex( const Digraph &digraph,
2.683 + const CapacityMap &capacity,
2.684 + const CostMap &cost,
2.685 + Node s, Node t,
2.686 + Capacity flow_value ) :
2.687 + _orig_graph(digraph), _orig_lower(NULL), _orig_cap(capacity),
2.688 + _orig_cost(cost), _orig_supply(NULL),
2.689 + _orig_source(s), _orig_target(t), _orig_flow_value(flow_value),
2.690 + _flow_result(NULL), _potential_result(NULL),
2.691 + _local_flow(false), _local_potential(false),
2.692 + _node_id(digraph)
2.693 + {}
2.694 +
2.695 + /// Destructor.
2.696 + ~NetworkSimplex() {
2.697 + if (_local_flow) delete _flow_result;
2.698 + if (_local_potential) delete _potential_result;
2.699 + }
2.700 +
2.701 + /// \brief Set the flow map.
2.702 + ///
2.703 + /// This function sets the flow map.
2.704 + ///
2.705 + /// \return <tt>(*this)</tt>
2.706 + NetworkSimplex& flowMap(FlowMap &map) {
2.707 + if (_local_flow) {
2.708 + delete _flow_result;
2.709 + _local_flow = false;
2.710 + }
2.711 + _flow_result = ↦
2.712 + return *this;
2.713 + }
2.714 +
2.715 + /// \brief Set the potential map.
2.716 + ///
2.717 + /// This function sets the potential map.
2.718 + ///
2.719 + /// \return <tt>(*this)</tt>
2.720 + NetworkSimplex& potentialMap(PotentialMap &map) {
2.721 + if (_local_potential) {
2.722 + delete _potential_result;
2.723 + _local_potential = false;
2.724 + }
2.725 + _potential_result = ↦
2.726 + return *this;
2.727 + }
2.728 +
2.729 + /// \name Execution control
2.730 + /// The algorithm can be executed using the
2.731 + /// \ref lemon::NetworkSimplex::run() "run()" function.
2.732 + /// @{
2.733 +
2.734 + /// \brief Run the algorithm.
2.735 + ///
2.736 + /// This function runs the algorithm.
2.737 + ///
2.738 + /// \param pivot_rule The pivot rule that is used during the
2.739 + /// algorithm.
2.740 + ///
2.741 + /// The available pivot rules:
2.742 + ///
2.743 + /// - FIRST_ELIGIBLE_PIVOT The next eligible arc is selected in
2.744 + /// a wraparound fashion in every iteration
2.745 + /// (\ref FirstEligiblePivotRule).
2.746 + ///
2.747 + /// - BEST_ELIGIBLE_PIVOT The best eligible arc is selected in
2.748 + /// every iteration (\ref BestEligiblePivotRule).
2.749 + ///
2.750 + /// - BLOCK_SEARCH_PIVOT A specified number of arcs are examined in
2.751 + /// every iteration in a wraparound fashion and the best eligible
2.752 + /// arc is selected from this block (\ref BlockSearchPivotRule).
2.753 + ///
2.754 + /// - CANDIDATE_LIST_PIVOT In a major iteration a candidate list is
2.755 + /// built from eligible arcs in a wraparound fashion and in the
2.756 + /// following minor iterations the best eligible arc is selected
2.757 + /// from this list (\ref CandidateListPivotRule).
2.758 + ///
2.759 + /// - ALTERING_LIST_PIVOT It is a modified version of the
2.760 + /// "Candidate List" pivot rule. It keeps only the several best
2.761 + /// eligible arcs from the former candidate list and extends this
2.762 + /// list in every iteration (\ref AlteringListPivotRule).
2.763 + ///
2.764 + /// According to our comprehensive benchmark tests the "Block Search"
2.765 + /// pivot rule proved to be the fastest and the most robust on
2.766 + /// various test inputs. Thus it is the default option.
2.767 + ///
2.768 + /// \return \c true if a feasible flow can be found.
2.769 + bool run(PivotRuleEnum pivot_rule = BLOCK_SEARCH_PIVOT) {
2.770 + return init() && start(pivot_rule);
2.771 + }
2.772 +
2.773 + /// @}
2.774 +
2.775 + /// \name Query Functions
2.776 + /// The results of the algorithm can be obtained using these
2.777 + /// functions.\n
2.778 + /// \ref lemon::NetworkSimplex::run() "run()" must be called before
2.779 + /// using them.
2.780 + /// @{
2.781 +
2.782 + /// \brief Return a const reference to the flow map.
2.783 + ///
2.784 + /// This function returns a const reference to an arc map storing
2.785 + /// the found flow.
2.786 + ///
2.787 + /// \pre \ref run() must be called before using this function.
2.788 + const FlowMap& flowMap() const {
2.789 + return *_flow_result;
2.790 + }
2.791 +
2.792 + /// \brief Return a const reference to the potential map
2.793 + /// (the dual solution).
2.794 + ///
2.795 + /// This function returns a const reference to a node map storing
2.796 + /// the found potentials (the dual solution).
2.797 + ///
2.798 + /// \pre \ref run() must be called before using this function.
2.799 + const PotentialMap& potentialMap() const {
2.800 + return *_potential_result;
2.801 + }
2.802 +
2.803 + /// \brief Return the flow on the given arc.
2.804 + ///
2.805 + /// This function returns the flow on the given arc.
2.806 + ///
2.807 + /// \pre \ref run() must be called before using this function.
2.808 + Capacity flow(const Arc& arc) const {
2.809 + return (*_flow_result)[arc];
2.810 + }
2.811 +
2.812 + /// \brief Return the potential of the given node.
2.813 + ///
2.814 + /// This function returns the potential of the given node.
2.815 + ///
2.816 + /// \pre \ref run() must be called before using this function.
2.817 + Cost potential(const Node& node) const {
2.818 + return (*_potential_result)[node];
2.819 + }
2.820 +
2.821 + /// \brief Return the total cost of the found flow.
2.822 + ///
2.823 + /// This function returns the total cost of the found flow.
2.824 + /// The complexity of the function is \f$ O(e) \f$.
2.825 + ///
2.826 + /// \pre \ref run() must be called before using this function.
2.827 + Cost totalCost() const {
2.828 + Cost c = 0;
2.829 + for (ArcIt e(_orig_graph); e != INVALID; ++e)
2.830 + c += (*_flow_result)[e] * _orig_cost[e];
2.831 + return c;
2.832 + }
2.833 +
2.834 + /// @}
2.835 +
2.836 + private:
2.837 +
2.838 + // Initialize internal data structures
2.839 + bool init() {
2.840 + // Initialize result maps
2.841 + if (!_flow_result) {
2.842 + _flow_result = new FlowMap(_orig_graph);
2.843 + _local_flow = true;
2.844 + }
2.845 + if (!_potential_result) {
2.846 + _potential_result = new PotentialMap(_orig_graph);
2.847 + _local_potential = true;
2.848 + }
2.849 +
2.850 + // Initialize vectors
2.851 + _node_num = countNodes(_orig_graph);
2.852 + _arc_num = countArcs(_orig_graph);
2.853 + int all_node_num = _node_num + 1;
2.854 + int all_edge_num = _arc_num + _node_num;
2.855 +
2.856 + _arc.resize(_arc_num);
2.857 + _node.reserve(_node_num);
2.858 + _source.resize(all_edge_num);
2.859 + _target.resize(all_edge_num);
2.860 +
2.861 + _cap.resize(all_edge_num);
2.862 + _cost.resize(all_edge_num);
2.863 + _supply.resize(all_node_num);
2.864 + _flow.resize(all_edge_num, 0);
2.865 + _pi.resize(all_node_num, 0);
2.866 +
2.867 + _depth.resize(all_node_num);
2.868 + _parent.resize(all_node_num);
2.869 + _pred.resize(all_node_num);
2.870 + _thread.resize(all_node_num);
2.871 + _forward.resize(all_node_num);
2.872 + _state.resize(all_edge_num, STATE_LOWER);
2.873 +
2.874 + // Initialize node related data
2.875 + bool valid_supply = true;
2.876 + if (_orig_supply) {
2.877 + Supply sum = 0;
2.878 + int i = 0;
2.879 + for (NodeIt n(_orig_graph); n != INVALID; ++n, ++i) {
2.880 + _node.push_back(n);
2.881 + _node_id[n] = i;
2.882 + _supply[i] = (*_orig_supply)[n];
2.883 + sum += _supply[i];
2.884 + }
2.885 + valid_supply = (sum == 0);
2.886 + } else {
2.887 + int i = 0;
2.888 + for (NodeIt n(_orig_graph); n != INVALID; ++n, ++i) {
2.889 + _node.push_back(n);
2.890 + _node_id[n] = i;
2.891 + _supply[i] = 0;
2.892 + }
2.893 + _supply[_node_id[_orig_source]] = _orig_flow_value;
2.894 + _supply[_node_id[_orig_target]] = -_orig_flow_value;
2.895 + }
2.896 + if (!valid_supply) return false;
2.897 +
2.898 + // Set data for the artificial root node
2.899 + _root = _node_num;
2.900 + _depth[_root] = 0;
2.901 + _parent[_root] = -1;
2.902 + _pred[_root] = -1;
2.903 + _thread[_root] = 0;
2.904 + _supply[_root] = 0;
2.905 + _pi[_root] = 0;
2.906 +
2.907 + // Store the arcs in a mixed order
2.908 + int k = std::max(int(sqrt(_arc_num)), 10);
2.909 + int i = 0;
2.910 + for (ArcIt e(_orig_graph); e != INVALID; ++e) {
2.911 + _arc[i] = e;
2.912 + if ((i += k) >= _arc_num) i = (i % k) + 1;
2.913 + }
2.914 +
2.915 + // Initialize arc maps
2.916 + for (int i = 0; i != _arc_num; ++i) {
2.917 + Arc e = _arc[i];
2.918 + _source[i] = _node_id[_orig_graph.source(e)];
2.919 + _target[i] = _node_id[_orig_graph.target(e)];
2.920 + _cost[i] = _orig_cost[e];
2.921 + _cap[i] = _orig_cap[e];
2.922 + }
2.923 +
2.924 + // Remove non-zero lower bounds
2.925 + if (_orig_lower) {
2.926 + for (int i = 0; i != _arc_num; ++i) {
2.927 + Capacity c = (*_orig_lower)[_arc[i]];
2.928 + if (c != 0) {
2.929 + _cap[i] -= c;
2.930 + _supply[_source[i]] -= c;
2.931 + _supply[_target[i]] += c;
2.932 + }
2.933 + }
2.934 + }
2.935 +
2.936 + // Add artificial arcs and initialize the spanning tree data structure
2.937 + Cost max_cost = std::numeric_limits<Cost>::max() / 4;
2.938 + Capacity max_cap = std::numeric_limits<Capacity>::max();
2.939 + for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
2.940 + _thread[u] = u + 1;
2.941 + _depth[u] = 1;
2.942 + _parent[u] = _root;
2.943 + _pred[u] = e;
2.944 + if (_supply[u] >= 0) {
2.945 + _flow[e] = _supply[u];
2.946 + _forward[u] = true;
2.947 + _pi[u] = -max_cost;
2.948 + } else {
2.949 + _flow[e] = -_supply[u];
2.950 + _forward[u] = false;
2.951 + _pi[u] = max_cost;
2.952 + }
2.953 + _cost[e] = max_cost;
2.954 + _cap[e] = max_cap;
2.955 + _state[e] = STATE_TREE;
2.956 + }
2.957 +
2.958 + return true;
2.959 + }
2.960 +
2.961 + // Find the join node
2.962 + void findJoinNode() {
2.963 + int u = _source[_in_arc];
2.964 + int v = _target[_in_arc];
2.965 + while (_depth[u] > _depth[v]) u = _parent[u];
2.966 + while (_depth[v] > _depth[u]) v = _parent[v];
2.967 + while (u != v) {
2.968 + u = _parent[u];
2.969 + v = _parent[v];
2.970 + }
2.971 + join = u;
2.972 + }
2.973 +
2.974 + // Find the leaving arc of the cycle and returns true if the
2.975 + // leaving arc is not the same as the entering arc
2.976 + bool findLeavingArc() {
2.977 + // Initialize first and second nodes according to the direction
2.978 + // of the cycle
2.979 + if (_state[_in_arc] == STATE_LOWER) {
2.980 + first = _source[_in_arc];
2.981 + second = _target[_in_arc];
2.982 + } else {
2.983 + first = _target[_in_arc];
2.984 + second = _source[_in_arc];
2.985 + }
2.986 + delta = _cap[_in_arc];
2.987 + int result = 0;
2.988 + Capacity d;
2.989 + int e;
2.990 +
2.991 + // Search the cycle along the path form the first node to the root
2.992 + for (int u = first; u != join; u = _parent[u]) {
2.993 + e = _pred[u];
2.994 + d = _forward[u] ? _flow[e] : _cap[e] - _flow[e];
2.995 + if (d < delta) {
2.996 + delta = d;
2.997 + u_out = u;
2.998 + result = 1;
2.999 + }
2.1000 + }
2.1001 + // Search the cycle along the path form the second node to the root
2.1002 + for (int u = second; u != join; u = _parent[u]) {
2.1003 + e = _pred[u];
2.1004 + d = _forward[u] ? _cap[e] - _flow[e] : _flow[e];
2.1005 + if (d <= delta) {
2.1006 + delta = d;
2.1007 + u_out = u;
2.1008 + result = 2;
2.1009 + }
2.1010 + }
2.1011 +
2.1012 + if (result == 1) {
2.1013 + u_in = first;
2.1014 + v_in = second;
2.1015 + } else {
2.1016 + u_in = second;
2.1017 + v_in = first;
2.1018 + }
2.1019 + return result != 0;
2.1020 + }
2.1021 +
2.1022 + // Change _flow and _state vectors
2.1023 + void changeFlow(bool change) {
2.1024 + // Augment along the cycle
2.1025 + if (delta > 0) {
2.1026 + Capacity val = _state[_in_arc] * delta;
2.1027 + _flow[_in_arc] += val;
2.1028 + for (int u = _source[_in_arc]; u != join; u = _parent[u]) {
2.1029 + _flow[_pred[u]] += _forward[u] ? -val : val;
2.1030 + }
2.1031 + for (int u = _target[_in_arc]; u != join; u = _parent[u]) {
2.1032 + _flow[_pred[u]] += _forward[u] ? val : -val;
2.1033 + }
2.1034 + }
2.1035 + // Update the state of the entering and leaving arcs
2.1036 + if (change) {
2.1037 + _state[_in_arc] = STATE_TREE;
2.1038 + _state[_pred[u_out]] =
2.1039 + (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER;
2.1040 + } else {
2.1041 + _state[_in_arc] = -_state[_in_arc];
2.1042 + }
2.1043 + }
2.1044 +
2.1045 + // Update _thread and _parent vectors
2.1046 + void updateThreadParent() {
2.1047 + int u;
2.1048 + v_out = _parent[u_out];
2.1049 +
2.1050 + // Handle the case when join and v_out coincide
2.1051 + bool par_first = false;
2.1052 + if (join == v_out) {
2.1053 + for (u = join; u != u_in && u != v_in; u = _thread[u]) ;
2.1054 + if (u == v_in) {
2.1055 + par_first = true;
2.1056 + while (_thread[u] != u_out) u = _thread[u];
2.1057 + first = u;
2.1058 + }
2.1059 + }
2.1060 +
2.1061 + // Find the last successor of u_in (u) and the node after it (right)
2.1062 + // according to the thread index
2.1063 + for (u = u_in; _depth[_thread[u]] > _depth[u_in]; u = _thread[u]) ;
2.1064 + right = _thread[u];
2.1065 + if (_thread[v_in] == u_out) {
2.1066 + for (last = u; _depth[last] > _depth[u_out]; last = _thread[last]) ;
2.1067 + if (last == u_out) last = _thread[last];
2.1068 + }
2.1069 + else last = _thread[v_in];
2.1070 +
2.1071 + // Update stem nodes
2.1072 + _thread[v_in] = stem = u_in;
2.1073 + par_stem = v_in;
2.1074 + while (stem != u_out) {
2.1075 + _thread[u] = new_stem = _parent[stem];
2.1076 +
2.1077 + // Find the node just before the stem node (u) according to
2.1078 + // the original thread index
2.1079 + for (u = new_stem; _thread[u] != stem; u = _thread[u]) ;
2.1080 + _thread[u] = right;
2.1081 +
2.1082 + // Change the parent node of stem and shift stem and par_stem nodes
2.1083 + _parent[stem] = par_stem;
2.1084 + par_stem = stem;
2.1085 + stem = new_stem;
2.1086 +
2.1087 + // Find the last successor of stem (u) and the node after it (right)
2.1088 + // according to the thread index
2.1089 + for (u = stem; _depth[_thread[u]] > _depth[stem]; u = _thread[u]) ;
2.1090 + right = _thread[u];
2.1091 + }
2.1092 + _parent[u_out] = par_stem;
2.1093 + _thread[u] = last;
2.1094 +
2.1095 + if (join == v_out && par_first) {
2.1096 + if (first != v_in) _thread[first] = right;
2.1097 + } else {
2.1098 + for (u = v_out; _thread[u] != u_out; u = _thread[u]) ;
2.1099 + _thread[u] = right;
2.1100 + }
2.1101 + }
2.1102 +
2.1103 + // Update _pred and _forward vectors
2.1104 + void updatePredArc() {
2.1105 + int u = u_out, v;
2.1106 + while (u != u_in) {
2.1107 + v = _parent[u];
2.1108 + _pred[u] = _pred[v];
2.1109 + _forward[u] = !_forward[v];
2.1110 + u = v;
2.1111 + }
2.1112 + _pred[u_in] = _in_arc;
2.1113 + _forward[u_in] = (u_in == _source[_in_arc]);
2.1114 + }
2.1115 +
2.1116 + // Update _depth and _potential vectors
2.1117 + void updateDepthPotential() {
2.1118 + _depth[u_in] = _depth[v_in] + 1;
2.1119 + Cost sigma = _forward[u_in] ?
2.1120 + _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] :
2.1121 + _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]];
2.1122 + _pi[u_in] += sigma;
2.1123 + for(int u = _thread[u_in]; _parent[u] != -1; u = _thread[u]) {
2.1124 + _depth[u] = _depth[_parent[u]] + 1;
2.1125 + if (_depth[u] <= _depth[u_in]) break;
2.1126 + _pi[u] += sigma;
2.1127 + }
2.1128 + }
2.1129 +
2.1130 + // Execute the algorithm
2.1131 + bool start(PivotRuleEnum pivot_rule) {
2.1132 + // Select the pivot rule implementation
2.1133 + switch (pivot_rule) {
2.1134 + case FIRST_ELIGIBLE_PIVOT:
2.1135 + return start<FirstEligiblePivotRule>();
2.1136 + case BEST_ELIGIBLE_PIVOT:
2.1137 + return start<BestEligiblePivotRule>();
2.1138 + case BLOCK_SEARCH_PIVOT:
2.1139 + return start<BlockSearchPivotRule>();
2.1140 + case CANDIDATE_LIST_PIVOT:
2.1141 + return start<CandidateListPivotRule>();
2.1142 + case ALTERING_LIST_PIVOT:
2.1143 + return start<AlteringListPivotRule>();
2.1144 + }
2.1145 + return false;
2.1146 + }
2.1147 +
2.1148 + template<class PivotRuleImplementation>
2.1149 + bool start() {
2.1150 + PivotRuleImplementation pivot(*this);
2.1151 +
2.1152 + // Execute the network simplex algorithm
2.1153 + while (pivot.findEnteringArc()) {
2.1154 + findJoinNode();
2.1155 + bool change = findLeavingArc();
2.1156 + changeFlow(change);
2.1157 + if (change) {
2.1158 + updateThreadParent();
2.1159 + updatePredArc();
2.1160 + updateDepthPotential();
2.1161 + }
2.1162 + }
2.1163 +
2.1164 + // Check if the flow amount equals zero on all the artificial arcs
2.1165 + for (int e = _arc_num; e != _arc_num + _node_num; ++e) {
2.1166 + if (_flow[e] > 0) return false;
2.1167 + }
2.1168 +
2.1169 + // Copy flow values to _flow_result
2.1170 + if (_orig_lower) {
2.1171 + for (int i = 0; i != _arc_num; ++i) {
2.1172 + Arc e = _arc[i];
2.1173 + (*_flow_result)[e] = (*_orig_lower)[e] + _flow[i];
2.1174 + }
2.1175 + } else {
2.1176 + for (int i = 0; i != _arc_num; ++i) {
2.1177 + (*_flow_result)[_arc[i]] = _flow[i];
2.1178 + }
2.1179 + }
2.1180 + // Copy potential values to _potential_result
2.1181 + for (int i = 0; i != _node_num; ++i) {
2.1182 + (*_potential_result)[_node[i]] = _pi[i];
2.1183 + }
2.1184 +
2.1185 + return true;
2.1186 + }
2.1187 +
2.1188 + }; //class NetworkSimplex
2.1189 +
2.1190 + ///@}
2.1191 +
2.1192 +} //namespace lemon
2.1193 +
2.1194 +#endif //LEMON_NETWORK_SIMPLEX_H
3.1 --- a/test/CMakeLists.txt Mon Feb 23 18:01:14 2009 +0000
3.2 +++ b/test/CMakeLists.txt Tue Feb 24 09:46:02 2009 +0100
3.3 @@ -30,6 +30,7 @@
3.4 maps_test
3.5 max_matching_test
3.6 min_cost_arborescence_test
3.7 + min_cost_flow_test
3.8 path_test
3.9 preflow_test
3.10 radix_sort_test
4.1 --- a/test/Makefile.am Mon Feb 23 18:01:14 2009 +0000
4.2 +++ b/test/Makefile.am Tue Feb 24 09:46:02 2009 +0100
4.3 @@ -26,6 +26,7 @@
4.4 test/maps_test \
4.5 test/max_matching_test \
4.6 test/min_cost_arborescence_test \
4.7 + test/min_cost_flow_test \
4.8 test/path_test \
4.9 test/preflow_test \
4.10 test/radix_sort_test \
4.11 @@ -68,6 +69,7 @@
4.12 test_mip_test_SOURCES = test/mip_test.cc
4.13 test_max_matching_test_SOURCES = test/max_matching_test.cc
4.14 test_min_cost_arborescence_test_SOURCES = test/min_cost_arborescence_test.cc
4.15 +test_min_cost_flow_test_SOURCES = test/min_cost_flow_test.cc
4.16 test_path_test_SOURCES = test/path_test.cc
4.17 test_preflow_test_SOURCES = test/preflow_test.cc
4.18 test_radix_sort_test_SOURCES = test/radix_sort_test.cc
5.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
5.2 +++ b/test/min_cost_flow_test.cc Tue Feb 24 09:46:02 2009 +0100
5.3 @@ -0,0 +1,455 @@
5.4 +/* -*- mode: C++; indent-tabs-mode: nil; -*-
5.5 + *
5.6 + * This file is a part of LEMON, a generic C++ optimization library.
5.7 + *
5.8 + * Copyright (C) 2003-2009
5.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
5.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
5.11 + *
5.12 + * Permission to use, modify and distribute this software is granted
5.13 + * provided that this copyright notice appears in all copies. For
5.14 + * precise terms see the accompanying LICENSE file.
5.15 + *
5.16 + * This software is provided "AS IS" with no warranty of any kind,
5.17 + * express or implied, and with no claim as to its suitability for any
5.18 + * purpose.
5.19 + *
5.20 + */
5.21 +
5.22 +#include <iostream>
5.23 +#include <fstream>
5.24 +
5.25 +#include <lemon/list_graph.h>
5.26 +#include <lemon/smart_graph.h>
5.27 +#include <lemon/lgf_reader.h>
5.28 +
5.29 +//#include <lemon/cycle_canceling.h>
5.30 +//#include <lemon/capacity_scaling.h>
5.31 +//#include <lemon/cost_scaling.h>
5.32 +#include <lemon/network_simplex.h>
5.33 +//#include <lemon/min_cost_flow.h>
5.34 +//#include <lemon/min_cost_max_flow.h>
5.35 +
5.36 +#include <lemon/concepts/digraph.h>
5.37 +#include <lemon/concept_check.h>
5.38 +
5.39 +#include "test_tools.h"
5.40 +
5.41 +using namespace lemon;
5.42 +
5.43 +char test_lgf[] =
5.44 + "@nodes\n"
5.45 + "label sup1 sup2 sup3\n"
5.46 + " 1 20 27 0\n"
5.47 + " 2 -4 0 0\n"
5.48 + " 3 0 0 0\n"
5.49 + " 4 0 0 0\n"
5.50 + " 5 9 0 0\n"
5.51 + " 6 -6 0 0\n"
5.52 + " 7 0 0 0\n"
5.53 + " 8 0 0 0\n"
5.54 + " 9 3 0 0\n"
5.55 + " 10 -2 0 0\n"
5.56 + " 11 0 0 0\n"
5.57 + " 12 -20 -27 0\n"
5.58 + "\n"
5.59 + "@arcs\n"
5.60 + " cost cap low1 low2\n"
5.61 + " 1 2 70 11 0 8\n"
5.62 + " 1 3 150 3 0 1\n"
5.63 + " 1 4 80 15 0 2\n"
5.64 + " 2 8 80 12 0 0\n"
5.65 + " 3 5 140 5 0 3\n"
5.66 + " 4 6 60 10 0 1\n"
5.67 + " 4 7 80 2 0 0\n"
5.68 + " 4 8 110 3 0 0\n"
5.69 + " 5 7 60 14 0 0\n"
5.70 + " 5 11 120 12 0 0\n"
5.71 + " 6 3 0 3 0 0\n"
5.72 + " 6 9 140 4 0 0\n"
5.73 + " 6 10 90 8 0 0\n"
5.74 + " 7 1 30 5 0 0\n"
5.75 + " 8 12 60 16 0 4\n"
5.76 + " 9 12 50 6 0 0\n"
5.77 + "10 12 70 13 0 5\n"
5.78 + "10 2 100 7 0 0\n"
5.79 + "10 7 60 10 0 0\n"
5.80 + "11 10 20 14 0 6\n"
5.81 + "12 11 30 10 0 0\n"
5.82 + "\n"
5.83 + "@attributes\n"
5.84 + "source 1\n"
5.85 + "target 12\n";
5.86 +
5.87 +
5.88 +// Check the interface of an MCF algorithm
5.89 +template <typename GR, typename Value>
5.90 +class McfClassConcept
5.91 +{
5.92 +public:
5.93 +
5.94 + template <typename MCF>
5.95 + struct Constraints {
5.96 + void constraints() {
5.97 + checkConcept<concepts::Digraph, GR>();
5.98 +
5.99 + MCF mcf_test1(g, lower, upper, cost, sup);
5.100 + MCF mcf_test2(g, upper, cost, sup);
5.101 + MCF mcf_test3(g, lower, upper, cost, n, n, k);
5.102 + MCF mcf_test4(g, upper, cost, n, n, k);
5.103 +
5.104 + // TODO: This part should be enabled and the next part
5.105 + // should be removed if map copying is supported
5.106 +/*
5.107 + flow = mcf_test1.flowMap();
5.108 + mcf_test1.flowMap(flow);
5.109 +
5.110 + pot = mcf_test1.potentialMap();
5.111 + mcf_test1.potentialMap(pot);
5.112 +*/
5.113 +/**/
5.114 + const typename MCF::FlowMap &fm =
5.115 + mcf_test1.flowMap();
5.116 + mcf_test1.flowMap(flow);
5.117 + const typename MCF::PotentialMap &pm =
5.118 + mcf_test1.potentialMap();
5.119 + mcf_test1.potentialMap(pot);
5.120 + ignore_unused_variable_warning(fm);
5.121 + ignore_unused_variable_warning(pm);
5.122 +/**/
5.123 +
5.124 + mcf_test1.run();
5.125 +
5.126 + v = mcf_test1.totalCost();
5.127 + v = mcf_test1.flow(a);
5.128 + v = mcf_test1.potential(n);
5.129 + }
5.130 +
5.131 + typedef typename GR::Node Node;
5.132 + typedef typename GR::Arc Arc;
5.133 + typedef concepts::ReadMap<Node, Value> NM;
5.134 + typedef concepts::ReadMap<Arc, Value> AM;
5.135 +
5.136 + const GR &g;
5.137 + const AM &lower;
5.138 + const AM &upper;
5.139 + const AM &cost;
5.140 + const NM ⊃
5.141 + const Node &n;
5.142 + const Arc &a;
5.143 + const Value &k;
5.144 + Value v;
5.145 +
5.146 + typename MCF::FlowMap &flow;
5.147 + typename MCF::PotentialMap &pot;
5.148 + };
5.149 +
5.150 +};
5.151 +
5.152 +
5.153 +// Check the feasibility of the given flow (primal soluiton)
5.154 +template < typename GR, typename LM, typename UM,
5.155 + typename SM, typename FM >
5.156 +bool checkFlow( const GR& gr, const LM& lower, const UM& upper,
5.157 + const SM& supply, const FM& flow )
5.158 +{
5.159 + TEMPLATE_DIGRAPH_TYPEDEFS(GR);
5.160 +
5.161 + for (ArcIt e(gr); e != INVALID; ++e) {
5.162 + if (flow[e] < lower[e] || flow[e] > upper[e]) return false;
5.163 + }
5.164 +
5.165 + for (NodeIt n(gr); n != INVALID; ++n) {
5.166 + typename SM::Value sum = 0;
5.167 + for (OutArcIt e(gr, n); e != INVALID; ++e)
5.168 + sum += flow[e];
5.169 + for (InArcIt e(gr, n); e != INVALID; ++e)
5.170 + sum -= flow[e];
5.171 + if (sum != supply[n]) return false;
5.172 + }
5.173 +
5.174 + return true;
5.175 +}
5.176 +
5.177 +// Check the feasibility of the given potentials (dual soluiton)
5.178 +// using the Complementary Slackness optimality condition
5.179 +template < typename GR, typename LM, typename UM,
5.180 + typename CM, typename FM, typename PM >
5.181 +bool checkPotential( const GR& gr, const LM& lower, const UM& upper,
5.182 + const CM& cost, const FM& flow, const PM& pi )
5.183 +{
5.184 + TEMPLATE_DIGRAPH_TYPEDEFS(GR);
5.185 +
5.186 + bool opt = true;
5.187 + for (ArcIt e(gr); opt && e != INVALID; ++e) {
5.188 + typename CM::Value red_cost =
5.189 + cost[e] + pi[gr.source(e)] - pi[gr.target(e)];
5.190 + opt = red_cost == 0 ||
5.191 + (red_cost > 0 && flow[e] == lower[e]) ||
5.192 + (red_cost < 0 && flow[e] == upper[e]);
5.193 + }
5.194 + return opt;
5.195 +}
5.196 +
5.197 +// Run a minimum cost flow algorithm and check the results
5.198 +template < typename MCF, typename GR,
5.199 + typename LM, typename UM,
5.200 + typename CM, typename SM >
5.201 +void checkMcf( const MCF& mcf, bool mcf_result,
5.202 + const GR& gr, const LM& lower, const UM& upper,
5.203 + const CM& cost, const SM& supply,
5.204 + bool result, typename CM::Value total,
5.205 + const std::string &test_id = "" )
5.206 +{
5.207 + check(mcf_result == result, "Wrong result " + test_id);
5.208 + if (result) {
5.209 + check(checkFlow(gr, lower, upper, supply, mcf.flowMap()),
5.210 + "The flow is not feasible " + test_id);
5.211 + check(mcf.totalCost() == total, "The flow is not optimal " + test_id);
5.212 + check(checkPotential(gr, lower, upper, cost, mcf.flowMap(),
5.213 + mcf.potentialMap()),
5.214 + "Wrong potentials " + test_id);
5.215 + }
5.216 +}
5.217 +
5.218 +int main()
5.219 +{
5.220 + // Check the interfaces
5.221 + {
5.222 + typedef int Value;
5.223 + // This typedef should be enabled if the standard maps are
5.224 + // reference maps in the graph concepts
5.225 + //typedef concepts::Digraph GR;
5.226 + typedef ListDigraph GR;
5.227 + typedef concepts::ReadMap<GR::Node, Value> NM;
5.228 + typedef concepts::ReadMap<GR::Arc, Value> AM;
5.229 +
5.230 + //checkConcept< McfClassConcept<GR, Value>,
5.231 + // CycleCanceling<GR, AM, AM, AM, NM> >();
5.232 + //checkConcept< McfClassConcept<GR, Value>,
5.233 + // CapacityScaling<GR, AM, AM, AM, NM> >();
5.234 + //checkConcept< McfClassConcept<GR, Value>,
5.235 + // CostScaling<GR, AM, AM, AM, NM> >();
5.236 + checkConcept< McfClassConcept<GR, Value>,
5.237 + NetworkSimplex<GR, AM, AM, AM, NM> >();
5.238 + //checkConcept< MinCostFlow<GR, Value>,
5.239 + // NetworkSimplex<GR, AM, AM, AM, NM> >();
5.240 + }
5.241 +
5.242 + // Run various MCF tests
5.243 + typedef ListDigraph Digraph;
5.244 + DIGRAPH_TYPEDEFS(ListDigraph);
5.245 +
5.246 + // Read the test digraph
5.247 + Digraph gr;
5.248 + Digraph::ArcMap<int> c(gr), l1(gr), l2(gr), u(gr);
5.249 + Digraph::NodeMap<int> s1(gr), s2(gr), s3(gr);
5.250 + Node v, w;
5.251 +
5.252 + std::istringstream input(test_lgf);
5.253 + DigraphReader<Digraph>(gr, input)
5.254 + .arcMap("cost", c)
5.255 + .arcMap("cap", u)
5.256 + .arcMap("low1", l1)
5.257 + .arcMap("low2", l2)
5.258 + .nodeMap("sup1", s1)
5.259 + .nodeMap("sup2", s2)
5.260 + .nodeMap("sup3", s3)
5.261 + .node("source", v)
5.262 + .node("target", w)
5.263 + .run();
5.264 +
5.265 +/*
5.266 + // A. Test CapacityScaling with scaling
5.267 + {
5.268 + CapacityScaling<Digraph> mcf1(gr, u, c, s1);
5.269 + CapacityScaling<Digraph> mcf2(gr, u, c, v, w, 27);
5.270 + CapacityScaling<Digraph> mcf3(gr, u, c, s3);
5.271 + CapacityScaling<Digraph> mcf4(gr, l2, u, c, s1);
5.272 + CapacityScaling<Digraph> mcf5(gr, l2, u, c, v, w, 27);
5.273 + CapacityScaling<Digraph> mcf6(gr, l2, u, c, s3);
5.274 +
5.275 + checkMcf(mcf1, mcf1.run(), gr, l1, u, c, s1, true, 5240, "#A1");
5.276 + checkMcf(mcf2, mcf2.run(), gr, l1, u, c, s2, true, 7620, "#A2");
5.277 + checkMcf(mcf3, mcf3.run(), gr, l1, u, c, s3, true, 0, "#A3");
5.278 + checkMcf(mcf4, mcf4.run(), gr, l2, u, c, s1, true, 5970, "#A4");
5.279 + checkMcf(mcf5, mcf5.run(), gr, l2, u, c, s2, true, 8010, "#A5");
5.280 + checkMcf(mcf6, mcf6.run(), gr, l2, u, c, s3, false, 0, "#A6");
5.281 + }
5.282 +
5.283 + // B. Test CapacityScaling without scaling
5.284 + {
5.285 + CapacityScaling<Digraph> mcf1(gr, u, c, s1);
5.286 + CapacityScaling<Digraph> mcf2(gr, u, c, v, w, 27);
5.287 + CapacityScaling<Digraph> mcf3(gr, u, c, s3);
5.288 + CapacityScaling<Digraph> mcf4(gr, l2, u, c, s1);
5.289 + CapacityScaling<Digraph> mcf5(gr, l2, u, c, v, w, 27);
5.290 + CapacityScaling<Digraph> mcf6(gr, l2, u, c, s3);
5.291 +
5.292 + checkMcf(mcf1, mcf1.run(false), gr, l1, u, c, s1, true, 5240, "#B1");
5.293 + checkMcf(mcf2, mcf2.run(false), gr, l1, u, c, s2, true, 7620, "#B2");
5.294 + checkMcf(mcf3, mcf3.run(false), gr, l1, u, c, s3, true, 0, "#B3");
5.295 + checkMcf(mcf4, mcf4.run(false), gr, l2, u, c, s1, true, 5970, "#B4");
5.296 + checkMcf(mcf5, mcf5.run(false), gr, l2, u, c, s2, true, 8010, "#B5");
5.297 + checkMcf(mcf6, mcf6.run(false), gr, l2, u, c, s3, false, 0, "#B6");
5.298 + }
5.299 +
5.300 + // C. Test CostScaling using partial augment-relabel method
5.301 + {
5.302 + CostScaling<Digraph> mcf1(gr, u, c, s1);
5.303 + CostScaling<Digraph> mcf2(gr, u, c, v, w, 27);
5.304 + CostScaling<Digraph> mcf3(gr, u, c, s3);
5.305 + CostScaling<Digraph> mcf4(gr, l2, u, c, s1);
5.306 + CostScaling<Digraph> mcf5(gr, l2, u, c, v, w, 27);
5.307 + CostScaling<Digraph> mcf6(gr, l2, u, c, s3);
5.308 +
5.309 + checkMcf(mcf1, mcf1.run(), gr, l1, u, c, s1, true, 5240, "#C1");
5.310 + checkMcf(mcf2, mcf2.run(), gr, l1, u, c, s2, true, 7620, "#C2");
5.311 + checkMcf(mcf3, mcf3.run(), gr, l1, u, c, s3, true, 0, "#C3");
5.312 + checkMcf(mcf4, mcf4.run(), gr, l2, u, c, s1, true, 5970, "#C4");
5.313 + checkMcf(mcf5, mcf5.run(), gr, l2, u, c, s2, true, 8010, "#C5");
5.314 + checkMcf(mcf6, mcf6.run(), gr, l2, u, c, s3, false, 0, "#C6");
5.315 + }
5.316 +
5.317 + // D. Test CostScaling using push-relabel method
5.318 + {
5.319 + CostScaling<Digraph> mcf1(gr, u, c, s1);
5.320 + CostScaling<Digraph> mcf2(gr, u, c, v, w, 27);
5.321 + CostScaling<Digraph> mcf3(gr, u, c, s3);
5.322 + CostScaling<Digraph> mcf4(gr, l2, u, c, s1);
5.323 + CostScaling<Digraph> mcf5(gr, l2, u, c, v, w, 27);
5.324 + CostScaling<Digraph> mcf6(gr, l2, u, c, s3);
5.325 +
5.326 + checkMcf(mcf1, mcf1.run(false), gr, l1, u, c, s1, true, 5240, "#D1");
5.327 + checkMcf(mcf2, mcf2.run(false), gr, l1, u, c, s2, true, 7620, "#D2");
5.328 + checkMcf(mcf3, mcf3.run(false), gr, l1, u, c, s3, true, 0, "#D3");
5.329 + checkMcf(mcf4, mcf4.run(false), gr, l2, u, c, s1, true, 5970, "#D4");
5.330 + checkMcf(mcf5, mcf5.run(false), gr, l2, u, c, s2, true, 8010, "#D5");
5.331 + checkMcf(mcf6, mcf6.run(false), gr, l2, u, c, s3, false, 0, "#D6");
5.332 + }
5.333 +*/
5.334 +
5.335 + // E. Test NetworkSimplex with FIRST_ELIGIBLE_PIVOT
5.336 + {
5.337 + NetworkSimplex<Digraph>::PivotRuleEnum pr =
5.338 + NetworkSimplex<Digraph>::FIRST_ELIGIBLE_PIVOT;
5.339 + NetworkSimplex<Digraph> mcf1(gr, u, c, s1);
5.340 + NetworkSimplex<Digraph> mcf2(gr, u, c, v, w, 27);
5.341 + NetworkSimplex<Digraph> mcf3(gr, u, c, s3);
5.342 + NetworkSimplex<Digraph> mcf4(gr, l2, u, c, s1);
5.343 + NetworkSimplex<Digraph> mcf5(gr, l2, u, c, v, w, 27);
5.344 + NetworkSimplex<Digraph> mcf6(gr, l2, u, c, s3);
5.345 +
5.346 + checkMcf(mcf1, mcf1.run(pr), gr, l1, u, c, s1, true, 5240, "#E1");
5.347 + checkMcf(mcf2, mcf2.run(pr), gr, l1, u, c, s2, true, 7620, "#E2");
5.348 + checkMcf(mcf3, mcf3.run(pr), gr, l1, u, c, s3, true, 0, "#E3");
5.349 + checkMcf(mcf4, mcf4.run(pr), gr, l2, u, c, s1, true, 5970, "#E4");
5.350 + checkMcf(mcf5, mcf5.run(pr), gr, l2, u, c, s2, true, 8010, "#E5");
5.351 + checkMcf(mcf6, mcf6.run(pr), gr, l2, u, c, s3, false, 0, "#E6");
5.352 + }
5.353 +
5.354 + // F. Test NetworkSimplex with BEST_ELIGIBLE_PIVOT
5.355 + {
5.356 + NetworkSimplex<Digraph>::PivotRuleEnum pr =
5.357 + NetworkSimplex<Digraph>::BEST_ELIGIBLE_PIVOT;
5.358 + NetworkSimplex<Digraph> mcf1(gr, u, c, s1);
5.359 + NetworkSimplex<Digraph> mcf2(gr, u, c, v, w, 27);
5.360 + NetworkSimplex<Digraph> mcf3(gr, u, c, s3);
5.361 + NetworkSimplex<Digraph> mcf4(gr, l2, u, c, s1);
5.362 + NetworkSimplex<Digraph> mcf5(gr, l2, u, c, v, w, 27);
5.363 + NetworkSimplex<Digraph> mcf6(gr, l2, u, c, s3);
5.364 +
5.365 + checkMcf(mcf1, mcf1.run(pr), gr, l1, u, c, s1, true, 5240, "#F1");
5.366 + checkMcf(mcf2, mcf2.run(pr), gr, l1, u, c, s2, true, 7620, "#F2");
5.367 + checkMcf(mcf3, mcf3.run(pr), gr, l1, u, c, s3, true, 0, "#F3");
5.368 + checkMcf(mcf4, mcf4.run(pr), gr, l2, u, c, s1, true, 5970, "#F4");
5.369 + checkMcf(mcf5, mcf5.run(pr), gr, l2, u, c, s2, true, 8010, "#F5");
5.370 + checkMcf(mcf6, mcf6.run(pr), gr, l2, u, c, s3, false, 0, "#F6");
5.371 + }
5.372 +
5.373 + // G. Test NetworkSimplex with BLOCK_SEARCH_PIVOT
5.374 + {
5.375 + NetworkSimplex<Digraph>::PivotRuleEnum pr =
5.376 + NetworkSimplex<Digraph>::BLOCK_SEARCH_PIVOT;
5.377 + NetworkSimplex<Digraph> mcf1(gr, u, c, s1);
5.378 + NetworkSimplex<Digraph> mcf2(gr, u, c, v, w, 27);
5.379 + NetworkSimplex<Digraph> mcf3(gr, u, c, s3);
5.380 + NetworkSimplex<Digraph> mcf4(gr, l2, u, c, s1);
5.381 + NetworkSimplex<Digraph> mcf5(gr, l2, u, c, v, w, 27);
5.382 + NetworkSimplex<Digraph> mcf6(gr, l2, u, c, s3);
5.383 +
5.384 + checkMcf(mcf1, mcf1.run(pr), gr, l1, u, c, s1, true, 5240, "#G1");
5.385 + checkMcf(mcf2, mcf2.run(pr), gr, l1, u, c, s2, true, 7620, "#G2");
5.386 + checkMcf(mcf3, mcf3.run(pr), gr, l1, u, c, s3, true, 0, "#G3");
5.387 + checkMcf(mcf4, mcf4.run(pr), gr, l2, u, c, s1, true, 5970, "#G4");
5.388 + checkMcf(mcf5, mcf5.run(pr), gr, l2, u, c, s2, true, 8010, "#G5");
5.389 + checkMcf(mcf6, mcf6.run(pr), gr, l2, u, c, s3, false, 0, "#G6");
5.390 + }
5.391 +
5.392 + // H. Test NetworkSimplex with CANDIDATE_LIST_PIVOT
5.393 + {
5.394 + NetworkSimplex<Digraph>::PivotRuleEnum pr =
5.395 + NetworkSimplex<Digraph>::CANDIDATE_LIST_PIVOT;
5.396 + NetworkSimplex<Digraph> mcf1(gr, u, c, s1);
5.397 + NetworkSimplex<Digraph> mcf2(gr, u, c, v, w, 27);
5.398 + NetworkSimplex<Digraph> mcf3(gr, u, c, s3);
5.399 + NetworkSimplex<Digraph> mcf4(gr, l2, u, c, s1);
5.400 + NetworkSimplex<Digraph> mcf5(gr, l2, u, c, v, w, 27);
5.401 + NetworkSimplex<Digraph> mcf6(gr, l2, u, c, s3);
5.402 +
5.403 + checkMcf(mcf1, mcf1.run(pr), gr, l1, u, c, s1, true, 5240, "#H1");
5.404 + checkMcf(mcf2, mcf2.run(pr), gr, l1, u, c, s2, true, 7620, "#H2");
5.405 + checkMcf(mcf3, mcf3.run(pr), gr, l1, u, c, s3, true, 0, "#H3");
5.406 + checkMcf(mcf4, mcf4.run(pr), gr, l2, u, c, s1, true, 5970, "#H4");
5.407 + checkMcf(mcf5, mcf5.run(pr), gr, l2, u, c, s2, true, 8010, "#H5");
5.408 + checkMcf(mcf6, mcf6.run(pr), gr, l2, u, c, s3, false, 0, "#H6");
5.409 + }
5.410 +
5.411 + // I. Test NetworkSimplex with ALTERING_LIST_PIVOT
5.412 + {
5.413 + NetworkSimplex<Digraph>::PivotRuleEnum pr =
5.414 + NetworkSimplex<Digraph>::ALTERING_LIST_PIVOT;
5.415 + NetworkSimplex<Digraph> mcf1(gr, u, c, s1);
5.416 + NetworkSimplex<Digraph> mcf2(gr, u, c, v, w, 27);
5.417 + NetworkSimplex<Digraph> mcf3(gr, u, c, s3);
5.418 + NetworkSimplex<Digraph> mcf4(gr, l2, u, c, s1);
5.419 + NetworkSimplex<Digraph> mcf5(gr, l2, u, c, v, w, 27);
5.420 + NetworkSimplex<Digraph> mcf6(gr, l2, u, c, s3);
5.421 +
5.422 + checkMcf(mcf1, mcf1.run(pr), gr, l1, u, c, s1, true, 5240, "#I1");
5.423 + checkMcf(mcf2, mcf2.run(pr), gr, l1, u, c, s2, true, 7620, "#I2");
5.424 + checkMcf(mcf3, mcf3.run(pr), gr, l1, u, c, s3, true, 0, "#I3");
5.425 + checkMcf(mcf4, mcf4.run(pr), gr, l2, u, c, s1, true, 5970, "#I4");
5.426 + checkMcf(mcf5, mcf5.run(pr), gr, l2, u, c, s2, true, 8010, "#I5");
5.427 + checkMcf(mcf6, mcf6.run(pr), gr, l2, u, c, s3, false, 0, "#I6");
5.428 + }
5.429 +
5.430 +/*
5.431 + // J. Test MinCostFlow
5.432 + {
5.433 + MinCostFlow<Digraph> mcf1(gr, u, c, s1);
5.434 + MinCostFlow<Digraph> mcf2(gr, u, c, v, w, 27);
5.435 + MinCostFlow<Digraph> mcf3(gr, u, c, s3);
5.436 + MinCostFlow<Digraph> mcf4(gr, l2, u, c, s1);
5.437 + MinCostFlow<Digraph> mcf5(gr, l2, u, c, v, w, 27);
5.438 + MinCostFlow<Digraph> mcf6(gr, l2, u, c, s3);
5.439 +
5.440 + checkMcf(mcf1, mcf1.run(), gr, l1, u, c, s1, true, 5240, "#J1");
5.441 + checkMcf(mcf2, mcf2.run(), gr, l1, u, c, s2, true, 7620, "#J2");
5.442 + checkMcf(mcf3, mcf3.run(), gr, l1, u, c, s3, true, 0, "#J3");
5.443 + checkMcf(mcf4, mcf4.run(), gr, l2, u, c, s1, true, 5970, "#J4");
5.444 + checkMcf(mcf5, mcf5.run(), gr, l2, u, c, s2, true, 8010, "#J5");
5.445 + checkMcf(mcf6, mcf6.run(), gr, l2, u, c, s3, false, 0, "#J6");
5.446 + }
5.447 +*/
5.448 +/*
5.449 + // K. Test MinCostMaxFlow
5.450 + {
5.451 + MinCostMaxFlow<Digraph> mcmf(gr, u, c, v, w);
5.452 + mcmf.run();
5.453 + checkMcf(mcmf, true, gr, l1, u, c, s3, true, 7620, "#K1");
5.454 + }
5.455 +*/
5.456 +
5.457 + return 0;
5.458 +}