1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/lemon/network_simplex.h Tue Feb 24 09:46:02 2009 +0100
1.3 @@ -0,0 +1,1191 @@
1.4 +/* -*- mode: C++; indent-tabs-mode: nil; -*-
1.5 + *
1.6 + * This file is a part of LEMON, a generic C++ optimization library.
1.7 + *
1.8 + * Copyright (C) 2003-2009
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_NETWORK_SIMPLEX_H
1.23 +#define LEMON_NETWORK_SIMPLEX_H
1.24 +
1.25 +/// \ingroup min_cost_flow
1.26 +///
1.27 +/// \file
1.28 +/// \brief Network simplex algorithm for finding a minimum cost flow.
1.29 +
1.30 +#include <vector>
1.31 +#include <limits>
1.32 +#include <algorithm>
1.33 +
1.34 +#include <lemon/math.h>
1.35 +
1.36 +namespace lemon {
1.37 +
1.38 + /// \addtogroup min_cost_flow
1.39 + /// @{
1.40 +
1.41 + /// \brief Implementation of the primal network simplex algorithm
1.42 + /// for finding a \ref min_cost_flow "minimum cost flow".
1.43 + ///
1.44 + /// \ref NetworkSimplex implements the primal network simplex algorithm
1.45 + /// for finding a \ref min_cost_flow "minimum cost flow".
1.46 + ///
1.47 + /// \tparam Digraph The digraph type the algorithm runs on.
1.48 + /// \tparam LowerMap The type of the lower bound map.
1.49 + /// \tparam CapacityMap The type of the capacity (upper bound) map.
1.50 + /// \tparam CostMap The type of the cost (length) map.
1.51 + /// \tparam SupplyMap The type of the supply map.
1.52 + ///
1.53 + /// \warning
1.54 + /// - Arc capacities and costs should be \e non-negative \e integers.
1.55 + /// - Supply values should be \e signed \e integers.
1.56 + /// - The value types of the maps should be convertible to each other.
1.57 + /// - \c CostMap::Value must be signed type.
1.58 + ///
1.59 + /// \note \ref NetworkSimplex provides five different pivot rule
1.60 + /// implementations that significantly affect the efficiency of the
1.61 + /// algorithm.
1.62 + /// By default "Block Search" pivot rule is used, which proved to be
1.63 + /// by far the most efficient according to our benchmark tests.
1.64 + /// However another pivot rule can be selected using \ref run()
1.65 + /// function with the proper parameter.
1.66 +#ifdef DOXYGEN
1.67 + template < typename Digraph,
1.68 + typename LowerMap,
1.69 + typename CapacityMap,
1.70 + typename CostMap,
1.71 + typename SupplyMap >
1.72 +
1.73 +#else
1.74 + template < typename Digraph,
1.75 + typename LowerMap = typename Digraph::template ArcMap<int>,
1.76 + typename CapacityMap = typename Digraph::template ArcMap<int>,
1.77 + typename CostMap = typename Digraph::template ArcMap<int>,
1.78 + typename SupplyMap = typename Digraph::template NodeMap<int> >
1.79 +#endif
1.80 + class NetworkSimplex
1.81 + {
1.82 + TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
1.83 +
1.84 + typedef typename CapacityMap::Value Capacity;
1.85 + typedef typename CostMap::Value Cost;
1.86 + typedef typename SupplyMap::Value Supply;
1.87 +
1.88 + typedef std::vector<Arc> ArcVector;
1.89 + typedef std::vector<Node> NodeVector;
1.90 + typedef std::vector<int> IntVector;
1.91 + typedef std::vector<bool> BoolVector;
1.92 + typedef std::vector<Capacity> CapacityVector;
1.93 + typedef std::vector<Cost> CostVector;
1.94 + typedef std::vector<Supply> SupplyVector;
1.95 +
1.96 + public:
1.97 +
1.98 + /// The type of the flow map
1.99 + typedef typename Digraph::template ArcMap<Capacity> FlowMap;
1.100 + /// The type of the potential map
1.101 + typedef typename Digraph::template NodeMap<Cost> PotentialMap;
1.102 +
1.103 + public:
1.104 +
1.105 + /// Enum type for selecting the pivot rule used by \ref run()
1.106 + enum PivotRuleEnum {
1.107 + FIRST_ELIGIBLE_PIVOT,
1.108 + BEST_ELIGIBLE_PIVOT,
1.109 + BLOCK_SEARCH_PIVOT,
1.110 + CANDIDATE_LIST_PIVOT,
1.111 + ALTERING_LIST_PIVOT
1.112 + };
1.113 +
1.114 + private:
1.115 +
1.116 + // State constants for arcs
1.117 + enum ArcStateEnum {
1.118 + STATE_UPPER = -1,
1.119 + STATE_TREE = 0,
1.120 + STATE_LOWER = 1
1.121 + };
1.122 +
1.123 + private:
1.124 +
1.125 + // References for the original data
1.126 + const Digraph &_orig_graph;
1.127 + const LowerMap *_orig_lower;
1.128 + const CapacityMap &_orig_cap;
1.129 + const CostMap &_orig_cost;
1.130 + const SupplyMap *_orig_supply;
1.131 + Node _orig_source;
1.132 + Node _orig_target;
1.133 + Capacity _orig_flow_value;
1.134 +
1.135 + // Result maps
1.136 + FlowMap *_flow_result;
1.137 + PotentialMap *_potential_result;
1.138 + bool _local_flow;
1.139 + bool _local_potential;
1.140 +
1.141 + // Data structures for storing the graph
1.142 + ArcVector _arc;
1.143 + NodeVector _node;
1.144 + IntNodeMap _node_id;
1.145 + IntVector _source;
1.146 + IntVector _target;
1.147 +
1.148 + // The number of nodes and arcs in the original graph
1.149 + int _node_num;
1.150 + int _arc_num;
1.151 +
1.152 + // Node and arc maps
1.153 + CapacityVector _cap;
1.154 + CostVector _cost;
1.155 + CostVector _supply;
1.156 + CapacityVector _flow;
1.157 + CostVector _pi;
1.158 +
1.159 + // Node and arc maps for the spanning tree structure
1.160 + IntVector _depth;
1.161 + IntVector _parent;
1.162 + IntVector _pred;
1.163 + IntVector _thread;
1.164 + BoolVector _forward;
1.165 + IntVector _state;
1.166 +
1.167 + // The root node
1.168 + int _root;
1.169 +
1.170 + // The entering arc in the current pivot iteration
1.171 + int _in_arc;
1.172 +
1.173 + // Temporary data used in the current pivot iteration
1.174 + int join, u_in, v_in, u_out, v_out;
1.175 + int right, first, second, last;
1.176 + int stem, par_stem, new_stem;
1.177 + Capacity delta;
1.178 +
1.179 + private:
1.180 +
1.181 + /// \brief Implementation of the "First Eligible" pivot rule for the
1.182 + /// \ref NetworkSimplex "network simplex" algorithm.
1.183 + ///
1.184 + /// This class implements the "First Eligible" pivot rule
1.185 + /// for the \ref NetworkSimplex "network simplex" algorithm.
1.186 + ///
1.187 + /// For more information see \ref NetworkSimplex::run().
1.188 + class FirstEligiblePivotRule
1.189 + {
1.190 + private:
1.191 +
1.192 + // References to the NetworkSimplex class
1.193 + const ArcVector &_arc;
1.194 + const IntVector &_source;
1.195 + const IntVector &_target;
1.196 + const CostVector &_cost;
1.197 + const IntVector &_state;
1.198 + const CostVector &_pi;
1.199 + int &_in_arc;
1.200 + int _arc_num;
1.201 +
1.202 + // Pivot rule data
1.203 + int _next_arc;
1.204 +
1.205 + public:
1.206 +
1.207 + /// Constructor
1.208 + FirstEligiblePivotRule(NetworkSimplex &ns) :
1.209 + _arc(ns._arc), _source(ns._source), _target(ns._target),
1.210 + _cost(ns._cost), _state(ns._state), _pi(ns._pi),
1.211 + _in_arc(ns._in_arc), _arc_num(ns._arc_num), _next_arc(0)
1.212 + {}
1.213 +
1.214 + /// Find next entering arc
1.215 + bool findEnteringArc() {
1.216 + Cost c;
1.217 + for (int e = _next_arc; e < _arc_num; ++e) {
1.218 + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
1.219 + if (c < 0) {
1.220 + _in_arc = e;
1.221 + _next_arc = e + 1;
1.222 + return true;
1.223 + }
1.224 + }
1.225 + for (int e = 0; e < _next_arc; ++e) {
1.226 + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
1.227 + if (c < 0) {
1.228 + _in_arc = e;
1.229 + _next_arc = e + 1;
1.230 + return true;
1.231 + }
1.232 + }
1.233 + return false;
1.234 + }
1.235 +
1.236 + }; //class FirstEligiblePivotRule
1.237 +
1.238 +
1.239 + /// \brief Implementation of the "Best Eligible" pivot rule for the
1.240 + /// \ref NetworkSimplex "network simplex" algorithm.
1.241 + ///
1.242 + /// This class implements the "Best Eligible" pivot rule
1.243 + /// for the \ref NetworkSimplex "network simplex" algorithm.
1.244 + ///
1.245 + /// For more information see \ref NetworkSimplex::run().
1.246 + class BestEligiblePivotRule
1.247 + {
1.248 + private:
1.249 +
1.250 + // References to the NetworkSimplex class
1.251 + const ArcVector &_arc;
1.252 + const IntVector &_source;
1.253 + const IntVector &_target;
1.254 + const CostVector &_cost;
1.255 + const IntVector &_state;
1.256 + const CostVector &_pi;
1.257 + int &_in_arc;
1.258 + int _arc_num;
1.259 +
1.260 + public:
1.261 +
1.262 + /// Constructor
1.263 + BestEligiblePivotRule(NetworkSimplex &ns) :
1.264 + _arc(ns._arc), _source(ns._source), _target(ns._target),
1.265 + _cost(ns._cost), _state(ns._state), _pi(ns._pi),
1.266 + _in_arc(ns._in_arc), _arc_num(ns._arc_num)
1.267 + {}
1.268 +
1.269 + /// Find next entering arc
1.270 + bool findEnteringArc() {
1.271 + Cost c, min = 0;
1.272 + for (int e = 0; e < _arc_num; ++e) {
1.273 + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
1.274 + if (c < min) {
1.275 + min = c;
1.276 + _in_arc = e;
1.277 + }
1.278 + }
1.279 + return min < 0;
1.280 + }
1.281 +
1.282 + }; //class BestEligiblePivotRule
1.283 +
1.284 +
1.285 + /// \brief Implementation of the "Block Search" pivot rule for the
1.286 + /// \ref NetworkSimplex "network simplex" algorithm.
1.287 + ///
1.288 + /// This class implements the "Block Search" pivot rule
1.289 + /// for the \ref NetworkSimplex "network simplex" algorithm.
1.290 + ///
1.291 + /// For more information see \ref NetworkSimplex::run().
1.292 + class BlockSearchPivotRule
1.293 + {
1.294 + private:
1.295 +
1.296 + // References to the NetworkSimplex class
1.297 + const ArcVector &_arc;
1.298 + const IntVector &_source;
1.299 + const IntVector &_target;
1.300 + const CostVector &_cost;
1.301 + const IntVector &_state;
1.302 + const CostVector &_pi;
1.303 + int &_in_arc;
1.304 + int _arc_num;
1.305 +
1.306 + // Pivot rule data
1.307 + int _block_size;
1.308 + int _next_arc;
1.309 +
1.310 + public:
1.311 +
1.312 + /// Constructor
1.313 + BlockSearchPivotRule(NetworkSimplex &ns) :
1.314 + _arc(ns._arc), _source(ns._source), _target(ns._target),
1.315 + _cost(ns._cost), _state(ns._state), _pi(ns._pi),
1.316 + _in_arc(ns._in_arc), _arc_num(ns._arc_num), _next_arc(0)
1.317 + {
1.318 + // The main parameters of the pivot rule
1.319 + const double BLOCK_SIZE_FACTOR = 2.0;
1.320 + const int MIN_BLOCK_SIZE = 10;
1.321 +
1.322 + _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_arc_num)),
1.323 + MIN_BLOCK_SIZE );
1.324 + }
1.325 +
1.326 + /// Find next entering arc
1.327 + bool findEnteringArc() {
1.328 + Cost c, min = 0;
1.329 + int cnt = _block_size;
1.330 + int e, min_arc = _next_arc;
1.331 + for (e = _next_arc; e < _arc_num; ++e) {
1.332 + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
1.333 + if (c < min) {
1.334 + min = c;
1.335 + min_arc = e;
1.336 + }
1.337 + if (--cnt == 0) {
1.338 + if (min < 0) break;
1.339 + cnt = _block_size;
1.340 + }
1.341 + }
1.342 + if (min == 0 || cnt > 0) {
1.343 + for (e = 0; e < _next_arc; ++e) {
1.344 + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
1.345 + if (c < min) {
1.346 + min = c;
1.347 + min_arc = e;
1.348 + }
1.349 + if (--cnt == 0) {
1.350 + if (min < 0) break;
1.351 + cnt = _block_size;
1.352 + }
1.353 + }
1.354 + }
1.355 + if (min >= 0) return false;
1.356 + _in_arc = min_arc;
1.357 + _next_arc = e;
1.358 + return true;
1.359 + }
1.360 +
1.361 + }; //class BlockSearchPivotRule
1.362 +
1.363 +
1.364 + /// \brief Implementation of the "Candidate List" pivot rule for the
1.365 + /// \ref NetworkSimplex "network simplex" algorithm.
1.366 + ///
1.367 + /// This class implements the "Candidate List" pivot rule
1.368 + /// for the \ref NetworkSimplex "network simplex" algorithm.
1.369 + ///
1.370 + /// For more information see \ref NetworkSimplex::run().
1.371 + class CandidateListPivotRule
1.372 + {
1.373 + private:
1.374 +
1.375 + // References to the NetworkSimplex class
1.376 + const ArcVector &_arc;
1.377 + const IntVector &_source;
1.378 + const IntVector &_target;
1.379 + const CostVector &_cost;
1.380 + const IntVector &_state;
1.381 + const CostVector &_pi;
1.382 + int &_in_arc;
1.383 + int _arc_num;
1.384 +
1.385 + // Pivot rule data
1.386 + IntVector _candidates;
1.387 + int _list_length, _minor_limit;
1.388 + int _curr_length, _minor_count;
1.389 + int _next_arc;
1.390 +
1.391 + public:
1.392 +
1.393 + /// Constructor
1.394 + CandidateListPivotRule(NetworkSimplex &ns) :
1.395 + _arc(ns._arc), _source(ns._source), _target(ns._target),
1.396 + _cost(ns._cost), _state(ns._state), _pi(ns._pi),
1.397 + _in_arc(ns._in_arc), _arc_num(ns._arc_num), _next_arc(0)
1.398 + {
1.399 + // The main parameters of the pivot rule
1.400 + const double LIST_LENGTH_FACTOR = 1.0;
1.401 + const int MIN_LIST_LENGTH = 10;
1.402 + const double MINOR_LIMIT_FACTOR = 0.1;
1.403 + const int MIN_MINOR_LIMIT = 3;
1.404 +
1.405 + _list_length = std::max( int(LIST_LENGTH_FACTOR * sqrt(_arc_num)),
1.406 + MIN_LIST_LENGTH );
1.407 + _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length),
1.408 + MIN_MINOR_LIMIT );
1.409 + _curr_length = _minor_count = 0;
1.410 + _candidates.resize(_list_length);
1.411 + }
1.412 +
1.413 + /// Find next entering arc
1.414 + bool findEnteringArc() {
1.415 + Cost min, c;
1.416 + int e, min_arc = _next_arc;
1.417 + if (_curr_length > 0 && _minor_count < _minor_limit) {
1.418 + // Minor iteration: select the best eligible arc from the
1.419 + // current candidate list
1.420 + ++_minor_count;
1.421 + min = 0;
1.422 + for (int i = 0; i < _curr_length; ++i) {
1.423 + e = _candidates[i];
1.424 + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
1.425 + if (c < min) {
1.426 + min = c;
1.427 + min_arc = e;
1.428 + }
1.429 + if (c >= 0) {
1.430 + _candidates[i--] = _candidates[--_curr_length];
1.431 + }
1.432 + }
1.433 + if (min < 0) {
1.434 + _in_arc = min_arc;
1.435 + return true;
1.436 + }
1.437 + }
1.438 +
1.439 + // Major iteration: build a new candidate list
1.440 + min = 0;
1.441 + _curr_length = 0;
1.442 + for (e = _next_arc; e < _arc_num; ++e) {
1.443 + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
1.444 + if (c < 0) {
1.445 + _candidates[_curr_length++] = e;
1.446 + if (c < min) {
1.447 + min = c;
1.448 + min_arc = e;
1.449 + }
1.450 + if (_curr_length == _list_length) break;
1.451 + }
1.452 + }
1.453 + if (_curr_length < _list_length) {
1.454 + for (e = 0; e < _next_arc; ++e) {
1.455 + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
1.456 + if (c < 0) {
1.457 + _candidates[_curr_length++] = e;
1.458 + if (c < min) {
1.459 + min = c;
1.460 + min_arc = e;
1.461 + }
1.462 + if (_curr_length == _list_length) break;
1.463 + }
1.464 + }
1.465 + }
1.466 + if (_curr_length == 0) return false;
1.467 + _minor_count = 1;
1.468 + _in_arc = min_arc;
1.469 + _next_arc = e;
1.470 + return true;
1.471 + }
1.472 +
1.473 + }; //class CandidateListPivotRule
1.474 +
1.475 +
1.476 + /// \brief Implementation of the "Altering Candidate List" pivot rule
1.477 + /// for the \ref NetworkSimplex "network simplex" algorithm.
1.478 + ///
1.479 + /// This class implements the "Altering Candidate List" pivot rule
1.480 + /// for the \ref NetworkSimplex "network simplex" algorithm.
1.481 + ///
1.482 + /// For more information see \ref NetworkSimplex::run().
1.483 + class AlteringListPivotRule
1.484 + {
1.485 + private:
1.486 +
1.487 + // References to the NetworkSimplex class
1.488 + const ArcVector &_arc;
1.489 + const IntVector &_source;
1.490 + const IntVector &_target;
1.491 + const CostVector &_cost;
1.492 + const IntVector &_state;
1.493 + const CostVector &_pi;
1.494 + int &_in_arc;
1.495 + int _arc_num;
1.496 +
1.497 + // Pivot rule data
1.498 + int _block_size, _head_length, _curr_length;
1.499 + int _next_arc;
1.500 + IntVector _candidates;
1.501 + CostVector _cand_cost;
1.502 +
1.503 + // Functor class to compare arcs during sort of the candidate list
1.504 + class SortFunc
1.505 + {
1.506 + private:
1.507 + const CostVector &_map;
1.508 + public:
1.509 + SortFunc(const CostVector &map) : _map(map) {}
1.510 + bool operator()(int left, int right) {
1.511 + return _map[left] > _map[right];
1.512 + }
1.513 + };
1.514 +
1.515 + SortFunc _sort_func;
1.516 +
1.517 + public:
1.518 +
1.519 + /// Constructor
1.520 + AlteringListPivotRule(NetworkSimplex &ns) :
1.521 + _arc(ns._arc), _source(ns._source), _target(ns._target),
1.522 + _cost(ns._cost), _state(ns._state), _pi(ns._pi),
1.523 + _in_arc(ns._in_arc), _arc_num(ns._arc_num),
1.524 + _next_arc(0), _cand_cost(ns._arc_num), _sort_func(_cand_cost)
1.525 + {
1.526 + // The main parameters of the pivot rule
1.527 + const double BLOCK_SIZE_FACTOR = 1.5;
1.528 + const int MIN_BLOCK_SIZE = 10;
1.529 + const double HEAD_LENGTH_FACTOR = 0.1;
1.530 + const int MIN_HEAD_LENGTH = 3;
1.531 +
1.532 + _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_arc_num)),
1.533 + MIN_BLOCK_SIZE );
1.534 + _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size),
1.535 + MIN_HEAD_LENGTH );
1.536 + _candidates.resize(_head_length + _block_size);
1.537 + _curr_length = 0;
1.538 + }
1.539 +
1.540 + /// Find next entering arc
1.541 + bool findEnteringArc() {
1.542 + // Check the current candidate list
1.543 + int e;
1.544 + for (int i = 0; i < _curr_length; ++i) {
1.545 + e = _candidates[i];
1.546 + _cand_cost[e] = _state[e] *
1.547 + (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
1.548 + if (_cand_cost[e] >= 0) {
1.549 + _candidates[i--] = _candidates[--_curr_length];
1.550 + }
1.551 + }
1.552 +
1.553 + // Extend the list
1.554 + int cnt = _block_size;
1.555 + int last_edge = 0;
1.556 + int limit = _head_length;
1.557 +
1.558 + for (int e = _next_arc; e < _arc_num; ++e) {
1.559 + _cand_cost[e] = _state[e] *
1.560 + (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
1.561 + if (_cand_cost[e] < 0) {
1.562 + _candidates[_curr_length++] = e;
1.563 + last_edge = e;
1.564 + }
1.565 + if (--cnt == 0) {
1.566 + if (_curr_length > limit) break;
1.567 + limit = 0;
1.568 + cnt = _block_size;
1.569 + }
1.570 + }
1.571 + if (_curr_length <= limit) {
1.572 + for (int e = 0; e < _next_arc; ++e) {
1.573 + _cand_cost[e] = _state[e] *
1.574 + (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
1.575 + if (_cand_cost[e] < 0) {
1.576 + _candidates[_curr_length++] = e;
1.577 + last_edge = e;
1.578 + }
1.579 + if (--cnt == 0) {
1.580 + if (_curr_length > limit) break;
1.581 + limit = 0;
1.582 + cnt = _block_size;
1.583 + }
1.584 + }
1.585 + }
1.586 + if (_curr_length == 0) return false;
1.587 + _next_arc = last_edge + 1;
1.588 +
1.589 + // Make heap of the candidate list (approximating a partial sort)
1.590 + make_heap( _candidates.begin(), _candidates.begin() + _curr_length,
1.591 + _sort_func );
1.592 +
1.593 + // Pop the first element of the heap
1.594 + _in_arc = _candidates[0];
1.595 + pop_heap( _candidates.begin(), _candidates.begin() + _curr_length,
1.596 + _sort_func );
1.597 + _curr_length = std::min(_head_length, _curr_length - 1);
1.598 + return true;
1.599 + }
1.600 +
1.601 + }; //class AlteringListPivotRule
1.602 +
1.603 + public:
1.604 +
1.605 + /// \brief General constructor (with lower bounds).
1.606 + ///
1.607 + /// General constructor (with lower bounds).
1.608 + ///
1.609 + /// \param digraph The digraph the algorithm runs on.
1.610 + /// \param lower The lower bounds of the arcs.
1.611 + /// \param capacity The capacities (upper bounds) of the arcs.
1.612 + /// \param cost The cost (length) values of the arcs.
1.613 + /// \param supply The supply values of the nodes (signed).
1.614 + NetworkSimplex( const Digraph &digraph,
1.615 + const LowerMap &lower,
1.616 + const CapacityMap &capacity,
1.617 + const CostMap &cost,
1.618 + const SupplyMap &supply ) :
1.619 + _orig_graph(digraph), _orig_lower(&lower), _orig_cap(capacity),
1.620 + _orig_cost(cost), _orig_supply(&supply),
1.621 + _flow_result(NULL), _potential_result(NULL),
1.622 + _local_flow(false), _local_potential(false),
1.623 + _node_id(digraph)
1.624 + {}
1.625 +
1.626 + /// \brief General constructor (without lower bounds).
1.627 + ///
1.628 + /// General constructor (without lower bounds).
1.629 + ///
1.630 + /// \param digraph The digraph the algorithm runs on.
1.631 + /// \param capacity The capacities (upper bounds) of the arcs.
1.632 + /// \param cost The cost (length) values of the arcs.
1.633 + /// \param supply The supply values of the nodes (signed).
1.634 + NetworkSimplex( const Digraph &digraph,
1.635 + const CapacityMap &capacity,
1.636 + const CostMap &cost,
1.637 + const SupplyMap &supply ) :
1.638 + _orig_graph(digraph), _orig_lower(NULL), _orig_cap(capacity),
1.639 + _orig_cost(cost), _orig_supply(&supply),
1.640 + _flow_result(NULL), _potential_result(NULL),
1.641 + _local_flow(false), _local_potential(false),
1.642 + _node_id(digraph)
1.643 + {}
1.644 +
1.645 + /// \brief Simple constructor (with lower bounds).
1.646 + ///
1.647 + /// Simple constructor (with lower bounds).
1.648 + ///
1.649 + /// \param digraph The digraph the algorithm runs on.
1.650 + /// \param lower The lower bounds of the arcs.
1.651 + /// \param capacity The capacities (upper bounds) of the arcs.
1.652 + /// \param cost The cost (length) values of the arcs.
1.653 + /// \param s The source node.
1.654 + /// \param t The target node.
1.655 + /// \param flow_value The required amount of flow from node \c s
1.656 + /// to node \c t (i.e. the supply of \c s and the demand of \c t).
1.657 + NetworkSimplex( const Digraph &digraph,
1.658 + const LowerMap &lower,
1.659 + const CapacityMap &capacity,
1.660 + const CostMap &cost,
1.661 + Node s, Node t,
1.662 + Capacity flow_value ) :
1.663 + _orig_graph(digraph), _orig_lower(&lower), _orig_cap(capacity),
1.664 + _orig_cost(cost), _orig_supply(NULL),
1.665 + _orig_source(s), _orig_target(t), _orig_flow_value(flow_value),
1.666 + _flow_result(NULL), _potential_result(NULL),
1.667 + _local_flow(false), _local_potential(false),
1.668 + _node_id(digraph)
1.669 + {}
1.670 +
1.671 + /// \brief Simple constructor (without lower bounds).
1.672 + ///
1.673 + /// Simple constructor (without lower bounds).
1.674 + ///
1.675 + /// \param digraph The digraph the algorithm runs on.
1.676 + /// \param capacity The capacities (upper bounds) of the arcs.
1.677 + /// \param cost The cost (length) values of the arcs.
1.678 + /// \param s The source node.
1.679 + /// \param t The target node.
1.680 + /// \param flow_value The required amount of flow from node \c s
1.681 + /// to node \c t (i.e. the supply of \c s and the demand of \c t).
1.682 + NetworkSimplex( const Digraph &digraph,
1.683 + const CapacityMap &capacity,
1.684 + const CostMap &cost,
1.685 + Node s, Node t,
1.686 + Capacity flow_value ) :
1.687 + _orig_graph(digraph), _orig_lower(NULL), _orig_cap(capacity),
1.688 + _orig_cost(cost), _orig_supply(NULL),
1.689 + _orig_source(s), _orig_target(t), _orig_flow_value(flow_value),
1.690 + _flow_result(NULL), _potential_result(NULL),
1.691 + _local_flow(false), _local_potential(false),
1.692 + _node_id(digraph)
1.693 + {}
1.694 +
1.695 + /// Destructor.
1.696 + ~NetworkSimplex() {
1.697 + if (_local_flow) delete _flow_result;
1.698 + if (_local_potential) delete _potential_result;
1.699 + }
1.700 +
1.701 + /// \brief Set the flow map.
1.702 + ///
1.703 + /// This function sets the flow map.
1.704 + ///
1.705 + /// \return <tt>(*this)</tt>
1.706 + NetworkSimplex& flowMap(FlowMap &map) {
1.707 + if (_local_flow) {
1.708 + delete _flow_result;
1.709 + _local_flow = false;
1.710 + }
1.711 + _flow_result = ↦
1.712 + return *this;
1.713 + }
1.714 +
1.715 + /// \brief Set the potential map.
1.716 + ///
1.717 + /// This function sets the potential map.
1.718 + ///
1.719 + /// \return <tt>(*this)</tt>
1.720 + NetworkSimplex& potentialMap(PotentialMap &map) {
1.721 + if (_local_potential) {
1.722 + delete _potential_result;
1.723 + _local_potential = false;
1.724 + }
1.725 + _potential_result = ↦
1.726 + return *this;
1.727 + }
1.728 +
1.729 + /// \name Execution control
1.730 + /// The algorithm can be executed using the
1.731 + /// \ref lemon::NetworkSimplex::run() "run()" function.
1.732 + /// @{
1.733 +
1.734 + /// \brief Run the algorithm.
1.735 + ///
1.736 + /// This function runs the algorithm.
1.737 + ///
1.738 + /// \param pivot_rule The pivot rule that is used during the
1.739 + /// algorithm.
1.740 + ///
1.741 + /// The available pivot rules:
1.742 + ///
1.743 + /// - FIRST_ELIGIBLE_PIVOT The next eligible arc is selected in
1.744 + /// a wraparound fashion in every iteration
1.745 + /// (\ref FirstEligiblePivotRule).
1.746 + ///
1.747 + /// - BEST_ELIGIBLE_PIVOT The best eligible arc is selected in
1.748 + /// every iteration (\ref BestEligiblePivotRule).
1.749 + ///
1.750 + /// - BLOCK_SEARCH_PIVOT A specified number of arcs are examined in
1.751 + /// every iteration in a wraparound fashion and the best eligible
1.752 + /// arc is selected from this block (\ref BlockSearchPivotRule).
1.753 + ///
1.754 + /// - CANDIDATE_LIST_PIVOT In a major iteration a candidate list is
1.755 + /// built from eligible arcs in a wraparound fashion and in the
1.756 + /// following minor iterations the best eligible arc is selected
1.757 + /// from this list (\ref CandidateListPivotRule).
1.758 + ///
1.759 + /// - ALTERING_LIST_PIVOT It is a modified version of the
1.760 + /// "Candidate List" pivot rule. It keeps only the several best
1.761 + /// eligible arcs from the former candidate list and extends this
1.762 + /// list in every iteration (\ref AlteringListPivotRule).
1.763 + ///
1.764 + /// According to our comprehensive benchmark tests the "Block Search"
1.765 + /// pivot rule proved to be the fastest and the most robust on
1.766 + /// various test inputs. Thus it is the default option.
1.767 + ///
1.768 + /// \return \c true if a feasible flow can be found.
1.769 + bool run(PivotRuleEnum pivot_rule = BLOCK_SEARCH_PIVOT) {
1.770 + return init() && start(pivot_rule);
1.771 + }
1.772 +
1.773 + /// @}
1.774 +
1.775 + /// \name Query Functions
1.776 + /// The results of the algorithm can be obtained using these
1.777 + /// functions.\n
1.778 + /// \ref lemon::NetworkSimplex::run() "run()" must be called before
1.779 + /// using them.
1.780 + /// @{
1.781 +
1.782 + /// \brief Return a const reference to the flow map.
1.783 + ///
1.784 + /// This function returns a const reference to an arc map storing
1.785 + /// the found flow.
1.786 + ///
1.787 + /// \pre \ref run() must be called before using this function.
1.788 + const FlowMap& flowMap() const {
1.789 + return *_flow_result;
1.790 + }
1.791 +
1.792 + /// \brief Return a const reference to the potential map
1.793 + /// (the dual solution).
1.794 + ///
1.795 + /// This function returns a const reference to a node map storing
1.796 + /// the found potentials (the dual solution).
1.797 + ///
1.798 + /// \pre \ref run() must be called before using this function.
1.799 + const PotentialMap& potentialMap() const {
1.800 + return *_potential_result;
1.801 + }
1.802 +
1.803 + /// \brief Return the flow on the given arc.
1.804 + ///
1.805 + /// This function returns the flow on the given arc.
1.806 + ///
1.807 + /// \pre \ref run() must be called before using this function.
1.808 + Capacity flow(const Arc& arc) const {
1.809 + return (*_flow_result)[arc];
1.810 + }
1.811 +
1.812 + /// \brief Return the potential of the given node.
1.813 + ///
1.814 + /// This function returns the potential of the given node.
1.815 + ///
1.816 + /// \pre \ref run() must be called before using this function.
1.817 + Cost potential(const Node& node) const {
1.818 + return (*_potential_result)[node];
1.819 + }
1.820 +
1.821 + /// \brief Return the total cost of the found flow.
1.822 + ///
1.823 + /// This function returns the total cost of the found flow.
1.824 + /// The complexity of the function is \f$ O(e) \f$.
1.825 + ///
1.826 + /// \pre \ref run() must be called before using this function.
1.827 + Cost totalCost() const {
1.828 + Cost c = 0;
1.829 + for (ArcIt e(_orig_graph); e != INVALID; ++e)
1.830 + c += (*_flow_result)[e] * _orig_cost[e];
1.831 + return c;
1.832 + }
1.833 +
1.834 + /// @}
1.835 +
1.836 + private:
1.837 +
1.838 + // Initialize internal data structures
1.839 + bool init() {
1.840 + // Initialize result maps
1.841 + if (!_flow_result) {
1.842 + _flow_result = new FlowMap(_orig_graph);
1.843 + _local_flow = true;
1.844 + }
1.845 + if (!_potential_result) {
1.846 + _potential_result = new PotentialMap(_orig_graph);
1.847 + _local_potential = true;
1.848 + }
1.849 +
1.850 + // Initialize vectors
1.851 + _node_num = countNodes(_orig_graph);
1.852 + _arc_num = countArcs(_orig_graph);
1.853 + int all_node_num = _node_num + 1;
1.854 + int all_edge_num = _arc_num + _node_num;
1.855 +
1.856 + _arc.resize(_arc_num);
1.857 + _node.reserve(_node_num);
1.858 + _source.resize(all_edge_num);
1.859 + _target.resize(all_edge_num);
1.860 +
1.861 + _cap.resize(all_edge_num);
1.862 + _cost.resize(all_edge_num);
1.863 + _supply.resize(all_node_num);
1.864 + _flow.resize(all_edge_num, 0);
1.865 + _pi.resize(all_node_num, 0);
1.866 +
1.867 + _depth.resize(all_node_num);
1.868 + _parent.resize(all_node_num);
1.869 + _pred.resize(all_node_num);
1.870 + _thread.resize(all_node_num);
1.871 + _forward.resize(all_node_num);
1.872 + _state.resize(all_edge_num, STATE_LOWER);
1.873 +
1.874 + // Initialize node related data
1.875 + bool valid_supply = true;
1.876 + if (_orig_supply) {
1.877 + Supply sum = 0;
1.878 + int i = 0;
1.879 + for (NodeIt n(_orig_graph); n != INVALID; ++n, ++i) {
1.880 + _node.push_back(n);
1.881 + _node_id[n] = i;
1.882 + _supply[i] = (*_orig_supply)[n];
1.883 + sum += _supply[i];
1.884 + }
1.885 + valid_supply = (sum == 0);
1.886 + } else {
1.887 + int i = 0;
1.888 + for (NodeIt n(_orig_graph); n != INVALID; ++n, ++i) {
1.889 + _node.push_back(n);
1.890 + _node_id[n] = i;
1.891 + _supply[i] = 0;
1.892 + }
1.893 + _supply[_node_id[_orig_source]] = _orig_flow_value;
1.894 + _supply[_node_id[_orig_target]] = -_orig_flow_value;
1.895 + }
1.896 + if (!valid_supply) return false;
1.897 +
1.898 + // Set data for the artificial root node
1.899 + _root = _node_num;
1.900 + _depth[_root] = 0;
1.901 + _parent[_root] = -1;
1.902 + _pred[_root] = -1;
1.903 + _thread[_root] = 0;
1.904 + _supply[_root] = 0;
1.905 + _pi[_root] = 0;
1.906 +
1.907 + // Store the arcs in a mixed order
1.908 + int k = std::max(int(sqrt(_arc_num)), 10);
1.909 + int i = 0;
1.910 + for (ArcIt e(_orig_graph); e != INVALID; ++e) {
1.911 + _arc[i] = e;
1.912 + if ((i += k) >= _arc_num) i = (i % k) + 1;
1.913 + }
1.914 +
1.915 + // Initialize arc maps
1.916 + for (int i = 0; i != _arc_num; ++i) {
1.917 + Arc e = _arc[i];
1.918 + _source[i] = _node_id[_orig_graph.source(e)];
1.919 + _target[i] = _node_id[_orig_graph.target(e)];
1.920 + _cost[i] = _orig_cost[e];
1.921 + _cap[i] = _orig_cap[e];
1.922 + }
1.923 +
1.924 + // Remove non-zero lower bounds
1.925 + if (_orig_lower) {
1.926 + for (int i = 0; i != _arc_num; ++i) {
1.927 + Capacity c = (*_orig_lower)[_arc[i]];
1.928 + if (c != 0) {
1.929 + _cap[i] -= c;
1.930 + _supply[_source[i]] -= c;
1.931 + _supply[_target[i]] += c;
1.932 + }
1.933 + }
1.934 + }
1.935 +
1.936 + // Add artificial arcs and initialize the spanning tree data structure
1.937 + Cost max_cost = std::numeric_limits<Cost>::max() / 4;
1.938 + Capacity max_cap = std::numeric_limits<Capacity>::max();
1.939 + for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
1.940 + _thread[u] = u + 1;
1.941 + _depth[u] = 1;
1.942 + _parent[u] = _root;
1.943 + _pred[u] = e;
1.944 + if (_supply[u] >= 0) {
1.945 + _flow[e] = _supply[u];
1.946 + _forward[u] = true;
1.947 + _pi[u] = -max_cost;
1.948 + } else {
1.949 + _flow[e] = -_supply[u];
1.950 + _forward[u] = false;
1.951 + _pi[u] = max_cost;
1.952 + }
1.953 + _cost[e] = max_cost;
1.954 + _cap[e] = max_cap;
1.955 + _state[e] = STATE_TREE;
1.956 + }
1.957 +
1.958 + return true;
1.959 + }
1.960 +
1.961 + // Find the join node
1.962 + void findJoinNode() {
1.963 + int u = _source[_in_arc];
1.964 + int v = _target[_in_arc];
1.965 + while (_depth[u] > _depth[v]) u = _parent[u];
1.966 + while (_depth[v] > _depth[u]) v = _parent[v];
1.967 + while (u != v) {
1.968 + u = _parent[u];
1.969 + v = _parent[v];
1.970 + }
1.971 + join = u;
1.972 + }
1.973 +
1.974 + // Find the leaving arc of the cycle and returns true if the
1.975 + // leaving arc is not the same as the entering arc
1.976 + bool findLeavingArc() {
1.977 + // Initialize first and second nodes according to the direction
1.978 + // of the cycle
1.979 + if (_state[_in_arc] == STATE_LOWER) {
1.980 + first = _source[_in_arc];
1.981 + second = _target[_in_arc];
1.982 + } else {
1.983 + first = _target[_in_arc];
1.984 + second = _source[_in_arc];
1.985 + }
1.986 + delta = _cap[_in_arc];
1.987 + int result = 0;
1.988 + Capacity d;
1.989 + int e;
1.990 +
1.991 + // Search the cycle along the path form the first node to the root
1.992 + for (int u = first; u != join; u = _parent[u]) {
1.993 + e = _pred[u];
1.994 + d = _forward[u] ? _flow[e] : _cap[e] - _flow[e];
1.995 + if (d < delta) {
1.996 + delta = d;
1.997 + u_out = u;
1.998 + result = 1;
1.999 + }
1.1000 + }
1.1001 + // Search the cycle along the path form the second node to the root
1.1002 + for (int u = second; u != join; u = _parent[u]) {
1.1003 + e = _pred[u];
1.1004 + d = _forward[u] ? _cap[e] - _flow[e] : _flow[e];
1.1005 + if (d <= delta) {
1.1006 + delta = d;
1.1007 + u_out = u;
1.1008 + result = 2;
1.1009 + }
1.1010 + }
1.1011 +
1.1012 + if (result == 1) {
1.1013 + u_in = first;
1.1014 + v_in = second;
1.1015 + } else {
1.1016 + u_in = second;
1.1017 + v_in = first;
1.1018 + }
1.1019 + return result != 0;
1.1020 + }
1.1021 +
1.1022 + // Change _flow and _state vectors
1.1023 + void changeFlow(bool change) {
1.1024 + // Augment along the cycle
1.1025 + if (delta > 0) {
1.1026 + Capacity val = _state[_in_arc] * delta;
1.1027 + _flow[_in_arc] += val;
1.1028 + for (int u = _source[_in_arc]; u != join; u = _parent[u]) {
1.1029 + _flow[_pred[u]] += _forward[u] ? -val : val;
1.1030 + }
1.1031 + for (int u = _target[_in_arc]; u != join; u = _parent[u]) {
1.1032 + _flow[_pred[u]] += _forward[u] ? val : -val;
1.1033 + }
1.1034 + }
1.1035 + // Update the state of the entering and leaving arcs
1.1036 + if (change) {
1.1037 + _state[_in_arc] = STATE_TREE;
1.1038 + _state[_pred[u_out]] =
1.1039 + (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER;
1.1040 + } else {
1.1041 + _state[_in_arc] = -_state[_in_arc];
1.1042 + }
1.1043 + }
1.1044 +
1.1045 + // Update _thread and _parent vectors
1.1046 + void updateThreadParent() {
1.1047 + int u;
1.1048 + v_out = _parent[u_out];
1.1049 +
1.1050 + // Handle the case when join and v_out coincide
1.1051 + bool par_first = false;
1.1052 + if (join == v_out) {
1.1053 + for (u = join; u != u_in && u != v_in; u = _thread[u]) ;
1.1054 + if (u == v_in) {
1.1055 + par_first = true;
1.1056 + while (_thread[u] != u_out) u = _thread[u];
1.1057 + first = u;
1.1058 + }
1.1059 + }
1.1060 +
1.1061 + // Find the last successor of u_in (u) and the node after it (right)
1.1062 + // according to the thread index
1.1063 + for (u = u_in; _depth[_thread[u]] > _depth[u_in]; u = _thread[u]) ;
1.1064 + right = _thread[u];
1.1065 + if (_thread[v_in] == u_out) {
1.1066 + for (last = u; _depth[last] > _depth[u_out]; last = _thread[last]) ;
1.1067 + if (last == u_out) last = _thread[last];
1.1068 + }
1.1069 + else last = _thread[v_in];
1.1070 +
1.1071 + // Update stem nodes
1.1072 + _thread[v_in] = stem = u_in;
1.1073 + par_stem = v_in;
1.1074 + while (stem != u_out) {
1.1075 + _thread[u] = new_stem = _parent[stem];
1.1076 +
1.1077 + // Find the node just before the stem node (u) according to
1.1078 + // the original thread index
1.1079 + for (u = new_stem; _thread[u] != stem; u = _thread[u]) ;
1.1080 + _thread[u] = right;
1.1081 +
1.1082 + // Change the parent node of stem and shift stem and par_stem nodes
1.1083 + _parent[stem] = par_stem;
1.1084 + par_stem = stem;
1.1085 + stem = new_stem;
1.1086 +
1.1087 + // Find the last successor of stem (u) and the node after it (right)
1.1088 + // according to the thread index
1.1089 + for (u = stem; _depth[_thread[u]] > _depth[stem]; u = _thread[u]) ;
1.1090 + right = _thread[u];
1.1091 + }
1.1092 + _parent[u_out] = par_stem;
1.1093 + _thread[u] = last;
1.1094 +
1.1095 + if (join == v_out && par_first) {
1.1096 + if (first != v_in) _thread[first] = right;
1.1097 + } else {
1.1098 + for (u = v_out; _thread[u] != u_out; u = _thread[u]) ;
1.1099 + _thread[u] = right;
1.1100 + }
1.1101 + }
1.1102 +
1.1103 + // Update _pred and _forward vectors
1.1104 + void updatePredArc() {
1.1105 + int u = u_out, v;
1.1106 + while (u != u_in) {
1.1107 + v = _parent[u];
1.1108 + _pred[u] = _pred[v];
1.1109 + _forward[u] = !_forward[v];
1.1110 + u = v;
1.1111 + }
1.1112 + _pred[u_in] = _in_arc;
1.1113 + _forward[u_in] = (u_in == _source[_in_arc]);
1.1114 + }
1.1115 +
1.1116 + // Update _depth and _potential vectors
1.1117 + void updateDepthPotential() {
1.1118 + _depth[u_in] = _depth[v_in] + 1;
1.1119 + Cost sigma = _forward[u_in] ?
1.1120 + _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] :
1.1121 + _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]];
1.1122 + _pi[u_in] += sigma;
1.1123 + for(int u = _thread[u_in]; _parent[u] != -1; u = _thread[u]) {
1.1124 + _depth[u] = _depth[_parent[u]] + 1;
1.1125 + if (_depth[u] <= _depth[u_in]) break;
1.1126 + _pi[u] += sigma;
1.1127 + }
1.1128 + }
1.1129 +
1.1130 + // Execute the algorithm
1.1131 + bool start(PivotRuleEnum pivot_rule) {
1.1132 + // Select the pivot rule implementation
1.1133 + switch (pivot_rule) {
1.1134 + case FIRST_ELIGIBLE_PIVOT:
1.1135 + return start<FirstEligiblePivotRule>();
1.1136 + case BEST_ELIGIBLE_PIVOT:
1.1137 + return start<BestEligiblePivotRule>();
1.1138 + case BLOCK_SEARCH_PIVOT:
1.1139 + return start<BlockSearchPivotRule>();
1.1140 + case CANDIDATE_LIST_PIVOT:
1.1141 + return start<CandidateListPivotRule>();
1.1142 + case ALTERING_LIST_PIVOT:
1.1143 + return start<AlteringListPivotRule>();
1.1144 + }
1.1145 + return false;
1.1146 + }
1.1147 +
1.1148 + template<class PivotRuleImplementation>
1.1149 + bool start() {
1.1150 + PivotRuleImplementation pivot(*this);
1.1151 +
1.1152 + // Execute the network simplex algorithm
1.1153 + while (pivot.findEnteringArc()) {
1.1154 + findJoinNode();
1.1155 + bool change = findLeavingArc();
1.1156 + changeFlow(change);
1.1157 + if (change) {
1.1158 + updateThreadParent();
1.1159 + updatePredArc();
1.1160 + updateDepthPotential();
1.1161 + }
1.1162 + }
1.1163 +
1.1164 + // Check if the flow amount equals zero on all the artificial arcs
1.1165 + for (int e = _arc_num; e != _arc_num + _node_num; ++e) {
1.1166 + if (_flow[e] > 0) return false;
1.1167 + }
1.1168 +
1.1169 + // Copy flow values to _flow_result
1.1170 + if (_orig_lower) {
1.1171 + for (int i = 0; i != _arc_num; ++i) {
1.1172 + Arc e = _arc[i];
1.1173 + (*_flow_result)[e] = (*_orig_lower)[e] + _flow[i];
1.1174 + }
1.1175 + } else {
1.1176 + for (int i = 0; i != _arc_num; ++i) {
1.1177 + (*_flow_result)[_arc[i]] = _flow[i];
1.1178 + }
1.1179 + }
1.1180 + // Copy potential values to _potential_result
1.1181 + for (int i = 0; i != _node_num; ++i) {
1.1182 + (*_potential_result)[_node[i]] = _pi[i];
1.1183 + }
1.1184 +
1.1185 + return true;
1.1186 + }
1.1187 +
1.1188 + }; //class NetworkSimplex
1.1189 +
1.1190 + ///@}
1.1191 +
1.1192 +} //namespace lemon
1.1193 +
1.1194 +#endif //LEMON_NETWORK_SIMPLEX_H