kpeter@601: /* -*- mode: C++; indent-tabs-mode: nil; -*- kpeter@601: * kpeter@601: * This file is a part of LEMON, a generic C++ optimization library. kpeter@601: * alpar@877: * Copyright (C) 2003-2010 kpeter@601: * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport kpeter@601: * (Egervary Research Group on Combinatorial Optimization, EGRES). kpeter@601: * kpeter@601: * Permission to use, modify and distribute this software is granted kpeter@601: * provided that this copyright notice appears in all copies. For kpeter@601: * precise terms see the accompanying LICENSE file. kpeter@601: * kpeter@601: * This software is provided "AS IS" with no warranty of any kind, kpeter@601: * express or implied, and with no claim as to its suitability for any kpeter@601: * purpose. kpeter@601: * kpeter@601: */ kpeter@601: kpeter@601: #ifndef LEMON_NETWORK_SIMPLEX_H kpeter@601: #define LEMON_NETWORK_SIMPLEX_H kpeter@601: kpeter@663: /// \ingroup min_cost_flow_algs kpeter@601: /// kpeter@601: /// \file kpeter@605: /// \brief Network Simplex algorithm for finding a minimum cost flow. kpeter@601: kpeter@601: #include kpeter@601: #include kpeter@601: #include kpeter@601: kpeter@603: #include kpeter@601: #include kpeter@601: kpeter@601: namespace lemon { kpeter@601: kpeter@663: /// \addtogroup min_cost_flow_algs kpeter@601: /// @{ kpeter@601: kpeter@605: /// \brief Implementation of the primal Network Simplex algorithm kpeter@601: /// for finding a \ref min_cost_flow "minimum cost flow". kpeter@601: /// kpeter@605: /// \ref NetworkSimplex implements the primal Network Simplex algorithm kpeter@755: /// for finding a \ref min_cost_flow "minimum cost flow" alpar@1053: /// \cite amo93networkflows, \cite dantzig63linearprog, alpar@1053: /// \cite kellyoneill91netsimplex. kpeter@812: /// This algorithm is a highly efficient specialized version of the kpeter@812: /// linear programming simplex method directly for the minimum cost kpeter@812: /// flow problem. kpeter@606: /// kpeter@919: /// In general, \ref NetworkSimplex and \ref CostScaling are the fastest kpeter@1003: /// implementations available in LEMON for solving this problem. kpeter@1003: /// (For more information, see \ref min_cost_flow_algs "the module page".) kpeter@919: /// Furthermore, this class supports both directions of the supply/demand kpeter@919: /// inequality constraints. For more information, see \ref SupplyType. kpeter@640: /// kpeter@640: /// Most of the parameters of the problem (except for the digraph) kpeter@640: /// can be given using separate functions, and the algorithm can be kpeter@640: /// executed using the \ref run() function. If some parameters are not kpeter@640: /// specified, then default values will be used. kpeter@601: /// kpeter@605: /// \tparam GR The digraph type the algorithm runs on. kpeter@812: /// \tparam V The number type used for flow amounts, capacity bounds kpeter@786: /// and supply values in the algorithm. By default, it is \c int. kpeter@812: /// \tparam C The number type used for costs and potentials in the kpeter@786: /// algorithm. By default, it is the same as \c V. kpeter@601: /// kpeter@921: /// \warning Both \c V and \c C must be signed number types. kpeter@921: /// \warning All input data (capacities, supply values, and costs) must kpeter@608: /// be integer. kpeter@601: /// kpeter@605: /// \note %NetworkSimplex provides five different pivot rule kpeter@609: /// implementations, from which the most efficient one is used kpeter@786: /// by default. For more information, see \ref PivotRule. kpeter@641: template kpeter@601: class NetworkSimplex kpeter@601: { kpeter@605: public: kpeter@601: kpeter@642: /// The type of the flow amounts, capacity bounds and supply values kpeter@641: typedef V Value; kpeter@642: /// The type of the arc costs kpeter@607: typedef C Cost; kpeter@605: kpeter@605: public: kpeter@605: kpeter@640: /// \brief Problem type constants for the \c run() function. kpeter@605: /// kpeter@640: /// Enum type containing the problem type constants that can be kpeter@640: /// returned by the \ref run() function of the algorithm. kpeter@640: enum ProblemType { kpeter@640: /// The problem has no feasible solution (flow). kpeter@640: INFEASIBLE, kpeter@640: /// The problem has optimal solution (i.e. it is feasible and kpeter@640: /// bounded), and the algorithm has found optimal flow and node kpeter@640: /// potentials (primal and dual solutions). kpeter@640: OPTIMAL, kpeter@640: /// The objective function of the problem is unbounded, i.e. kpeter@640: /// there is a directed cycle having negative total cost and kpeter@640: /// infinite upper bound. kpeter@640: UNBOUNDED kpeter@640: }; alpar@877: kpeter@640: /// \brief Constants for selecting the type of the supply constraints. kpeter@640: /// kpeter@640: /// Enum type containing constants for selecting the supply type, kpeter@640: /// i.e. the direction of the inequalities in the supply/demand kpeter@640: /// constraints of the \ref min_cost_flow "minimum cost flow problem". kpeter@640: /// kpeter@663: /// The default supply type is \c GEQ, the \c LEQ type can be kpeter@663: /// selected using \ref supplyType(). kpeter@663: /// The equality form is a special case of both supply types. kpeter@640: enum SupplyType { kpeter@640: /// This option means that there are "greater or equal" kpeter@663: /// supply/demand constraints in the definition of the problem. kpeter@640: GEQ, kpeter@640: /// This option means that there are "less or equal" kpeter@663: /// supply/demand constraints in the definition of the problem. kpeter@663: LEQ kpeter@640: }; alpar@877: kpeter@640: /// \brief Constants for selecting the pivot rule. kpeter@640: /// kpeter@640: /// Enum type containing constants for selecting the pivot rule for kpeter@640: /// the \ref run() function. kpeter@640: /// kpeter@984: /// \ref NetworkSimplex provides five different implementations for kpeter@984: /// the pivot strategy that significantly affects the running time kpeter@605: /// of the algorithm. kpeter@984: /// According to experimental tests conducted on various problem kpeter@984: /// instances, \ref BLOCK_SEARCH "Block Search" and kpeter@984: /// \ref ALTERING_LIST "Altering Candidate List" rules turned out kpeter@984: /// to be the most efficient. kpeter@984: /// Since \ref BLOCK_SEARCH "Block Search" is a simpler strategy that kpeter@984: /// seemed to be slightly more robust, it is used by default. kpeter@984: /// However, another pivot rule can easily be selected using the kpeter@984: /// \ref run() function with the proper parameter. kpeter@605: enum PivotRule { kpeter@605: kpeter@786: /// The \e First \e Eligible pivot rule. kpeter@605: /// The next eligible arc is selected in a wraparound fashion kpeter@605: /// in every iteration. kpeter@605: FIRST_ELIGIBLE, kpeter@605: kpeter@786: /// The \e Best \e Eligible pivot rule. kpeter@605: /// The best eligible arc is selected in every iteration. kpeter@605: BEST_ELIGIBLE, kpeter@605: kpeter@786: /// The \e Block \e Search pivot rule. kpeter@605: /// A specified number of arcs are examined in every iteration kpeter@605: /// in a wraparound fashion and the best eligible arc is selected kpeter@605: /// from this block. kpeter@605: BLOCK_SEARCH, kpeter@605: kpeter@786: /// The \e Candidate \e List pivot rule. kpeter@605: /// In a major iteration a candidate list is built from eligible arcs kpeter@605: /// in a wraparound fashion and in the following minor iterations kpeter@605: /// the best eligible arc is selected from this list. kpeter@605: CANDIDATE_LIST, kpeter@605: kpeter@786: /// The \e Altering \e Candidate \e List pivot rule. kpeter@605: /// It is a modified version of the Candidate List method. kpeter@984: /// It keeps only a few of the best eligible arcs from the former kpeter@605: /// candidate list and extends this list in every iteration. kpeter@605: ALTERING_LIST kpeter@605: }; alpar@877: kpeter@605: private: kpeter@605: kpeter@605: TEMPLATE_DIGRAPH_TYPEDEFS(GR); kpeter@605: kpeter@601: typedef std::vector IntVector; kpeter@642: typedef std::vector ValueVector; kpeter@607: typedef std::vector CostVector; kpeter@895: typedef std::vector CharVector; kpeter@919: // Note: vector is used instead of vector and kpeter@895: // vector for efficiency reasons kpeter@601: kpeter@601: // State constants for arcs kpeter@862: enum ArcState { kpeter@601: STATE_UPPER = -1, kpeter@601: STATE_TREE = 0, kpeter@601: STATE_LOWER = 1 kpeter@601: }; kpeter@601: kpeter@895: // Direction constants for tree arcs kpeter@895: enum ArcDirection { kpeter@895: DIR_DOWN = -1, kpeter@895: DIR_UP = 1 kpeter@895: }; kpeter@862: kpeter@601: private: kpeter@601: kpeter@605: // Data related to the underlying digraph kpeter@605: const GR &_graph; kpeter@605: int _node_num; kpeter@605: int _arc_num; kpeter@663: int _all_arc_num; kpeter@663: int _search_arc_num; kpeter@605: kpeter@605: // Parameters of the problem kpeter@642: bool _have_lower; kpeter@640: SupplyType _stype; kpeter@641: Value _sum_supply; kpeter@601: kpeter@605: // Data structures for storing the digraph kpeter@603: IntNodeMap _node_id; kpeter@642: IntArcMap _arc_id; kpeter@603: IntVector _source; kpeter@603: IntVector _target; kpeter@830: bool _arc_mixing; kpeter@603: kpeter@605: // Node and arc data kpeter@642: ValueVector _lower; kpeter@642: ValueVector _upper; kpeter@642: ValueVector _cap; kpeter@607: CostVector _cost; kpeter@642: ValueVector _supply; kpeter@642: ValueVector _flow; kpeter@607: CostVector _pi; kpeter@601: kpeter@603: // Data for storing the spanning tree structure kpeter@601: IntVector _parent; kpeter@601: IntVector _pred; kpeter@601: IntVector _thread; kpeter@604: IntVector _rev_thread; kpeter@604: IntVector _succ_num; kpeter@604: IntVector _last_succ; kpeter@895: CharVector _pred_dir; kpeter@895: CharVector _state; kpeter@604: IntVector _dirty_revs; kpeter@601: int _root; kpeter@601: kpeter@601: // Temporary data used in the current pivot iteration kpeter@603: int in_arc, join, u_in, v_in, u_out, v_out; kpeter@641: Value delta; kpeter@601: kpeter@811: const Value MAX; kpeter@663: kpeter@640: public: alpar@877: kpeter@640: /// \brief Constant for infinite upper bounds (capacities). kpeter@640: /// kpeter@640: /// Constant for infinite upper bounds (capacities). kpeter@641: /// It is \c std::numeric_limits::infinity() if available, kpeter@641: /// \c std::numeric_limits::max() otherwise. kpeter@641: const Value INF; kpeter@640: kpeter@601: private: kpeter@601: kpeter@605: // Implementation of the First Eligible pivot rule kpeter@601: class FirstEligiblePivotRule kpeter@601: { kpeter@601: private: kpeter@601: kpeter@601: // References to the NetworkSimplex class kpeter@601: const IntVector &_source; kpeter@601: const IntVector &_target; kpeter@607: const CostVector &_cost; kpeter@895: const CharVector &_state; kpeter@607: const CostVector &_pi; kpeter@601: int &_in_arc; kpeter@663: int _search_arc_num; kpeter@601: kpeter@601: // Pivot rule data kpeter@601: int _next_arc; kpeter@601: kpeter@601: public: kpeter@601: kpeter@605: // Constructor kpeter@601: FirstEligiblePivotRule(NetworkSimplex &ns) : kpeter@603: _source(ns._source), _target(ns._target), kpeter@601: _cost(ns._cost), _state(ns._state), _pi(ns._pi), kpeter@663: _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), kpeter@663: _next_arc(0) kpeter@601: {} kpeter@601: kpeter@605: // Find next entering arc kpeter@601: bool findEnteringArc() { kpeter@607: Cost c; kpeter@839: for (int e = _next_arc; e != _search_arc_num; ++e) { kpeter@601: c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@601: if (c < 0) { kpeter@601: _in_arc = e; kpeter@601: _next_arc = e + 1; kpeter@601: return true; kpeter@601: } kpeter@601: } kpeter@839: for (int e = 0; e != _next_arc; ++e) { kpeter@601: c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@601: if (c < 0) { kpeter@601: _in_arc = e; kpeter@601: _next_arc = e + 1; kpeter@601: return true; kpeter@601: } kpeter@601: } kpeter@601: return false; kpeter@601: } kpeter@601: kpeter@601: }; //class FirstEligiblePivotRule kpeter@601: kpeter@601: kpeter@605: // Implementation of the Best Eligible pivot rule kpeter@601: class BestEligiblePivotRule kpeter@601: { kpeter@601: private: kpeter@601: kpeter@601: // References to the NetworkSimplex class kpeter@601: const IntVector &_source; kpeter@601: const IntVector &_target; kpeter@607: const CostVector &_cost; kpeter@895: const CharVector &_state; kpeter@607: const CostVector &_pi; kpeter@601: int &_in_arc; kpeter@663: int _search_arc_num; kpeter@601: kpeter@601: public: kpeter@601: kpeter@605: // Constructor kpeter@601: BestEligiblePivotRule(NetworkSimplex &ns) : kpeter@603: _source(ns._source), _target(ns._target), kpeter@601: _cost(ns._cost), _state(ns._state), _pi(ns._pi), kpeter@663: _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num) kpeter@601: {} kpeter@601: kpeter@605: // Find next entering arc kpeter@601: bool findEnteringArc() { kpeter@607: Cost c, min = 0; kpeter@839: for (int e = 0; e != _search_arc_num; ++e) { kpeter@601: c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@601: if (c < min) { kpeter@601: min = c; kpeter@601: _in_arc = e; kpeter@601: } kpeter@601: } kpeter@601: return min < 0; kpeter@601: } kpeter@601: kpeter@601: }; //class BestEligiblePivotRule kpeter@601: kpeter@601: kpeter@605: // Implementation of the Block Search pivot rule kpeter@601: class BlockSearchPivotRule kpeter@601: { kpeter@601: private: kpeter@601: kpeter@601: // References to the NetworkSimplex class kpeter@601: const IntVector &_source; kpeter@601: const IntVector &_target; kpeter@607: const CostVector &_cost; kpeter@895: const CharVector &_state; kpeter@607: const CostVector &_pi; kpeter@601: int &_in_arc; kpeter@663: int _search_arc_num; kpeter@601: kpeter@601: // Pivot rule data kpeter@601: int _block_size; kpeter@601: int _next_arc; kpeter@601: kpeter@601: public: kpeter@601: kpeter@605: // Constructor kpeter@601: BlockSearchPivotRule(NetworkSimplex &ns) : kpeter@603: _source(ns._source), _target(ns._target), kpeter@601: _cost(ns._cost), _state(ns._state), _pi(ns._pi), kpeter@663: _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), kpeter@663: _next_arc(0) kpeter@601: { kpeter@601: // The main parameters of the pivot rule kpeter@839: const double BLOCK_SIZE_FACTOR = 1.0; kpeter@601: const int MIN_BLOCK_SIZE = 10; kpeter@601: alpar@612: _block_size = std::max( int(BLOCK_SIZE_FACTOR * kpeter@663: std::sqrt(double(_search_arc_num))), kpeter@601: MIN_BLOCK_SIZE ); kpeter@601: } kpeter@601: kpeter@605: // Find next entering arc kpeter@601: bool findEnteringArc() { kpeter@607: Cost c, min = 0; kpeter@601: int cnt = _block_size; kpeter@727: int e; kpeter@839: for (e = _next_arc; e != _search_arc_num; ++e) { kpeter@601: c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@601: if (c < min) { kpeter@601: min = c; kpeter@727: _in_arc = e; kpeter@601: } kpeter@601: if (--cnt == 0) { kpeter@727: if (min < 0) goto search_end; kpeter@601: cnt = _block_size; kpeter@601: } kpeter@601: } kpeter@839: for (e = 0; e != _next_arc; ++e) { kpeter@727: c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@727: if (c < min) { kpeter@727: min = c; kpeter@727: _in_arc = e; kpeter@727: } kpeter@727: if (--cnt == 0) { kpeter@727: if (min < 0) goto search_end; kpeter@727: cnt = _block_size; kpeter@601: } kpeter@601: } kpeter@601: if (min >= 0) return false; kpeter@727: kpeter@727: search_end: kpeter@601: _next_arc = e; kpeter@601: return true; kpeter@601: } kpeter@601: kpeter@601: }; //class BlockSearchPivotRule kpeter@601: kpeter@601: kpeter@605: // Implementation of the Candidate List pivot rule kpeter@601: class CandidateListPivotRule kpeter@601: { kpeter@601: private: kpeter@601: kpeter@601: // References to the NetworkSimplex class kpeter@601: const IntVector &_source; kpeter@601: const IntVector &_target; kpeter@607: const CostVector &_cost; kpeter@895: const CharVector &_state; kpeter@607: const CostVector &_pi; kpeter@601: int &_in_arc; kpeter@663: int _search_arc_num; kpeter@601: kpeter@601: // Pivot rule data kpeter@601: IntVector _candidates; kpeter@601: int _list_length, _minor_limit; kpeter@601: int _curr_length, _minor_count; kpeter@601: int _next_arc; kpeter@601: kpeter@601: public: kpeter@601: kpeter@601: /// Constructor kpeter@601: CandidateListPivotRule(NetworkSimplex &ns) : kpeter@603: _source(ns._source), _target(ns._target), kpeter@601: _cost(ns._cost), _state(ns._state), _pi(ns._pi), kpeter@663: _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), kpeter@663: _next_arc(0) kpeter@601: { kpeter@601: // The main parameters of the pivot rule kpeter@727: const double LIST_LENGTH_FACTOR = 0.25; kpeter@601: const int MIN_LIST_LENGTH = 10; kpeter@601: const double MINOR_LIMIT_FACTOR = 0.1; kpeter@601: const int MIN_MINOR_LIMIT = 3; kpeter@601: alpar@612: _list_length = std::max( int(LIST_LENGTH_FACTOR * kpeter@663: std::sqrt(double(_search_arc_num))), kpeter@601: MIN_LIST_LENGTH ); kpeter@601: _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length), kpeter@601: MIN_MINOR_LIMIT ); kpeter@601: _curr_length = _minor_count = 0; kpeter@601: _candidates.resize(_list_length); kpeter@601: } kpeter@601: kpeter@601: /// Find next entering arc kpeter@601: bool findEnteringArc() { kpeter@607: Cost min, c; kpeter@727: int e; kpeter@601: if (_curr_length > 0 && _minor_count < _minor_limit) { kpeter@601: // Minor iteration: select the best eligible arc from the kpeter@601: // current candidate list kpeter@601: ++_minor_count; kpeter@601: min = 0; kpeter@601: for (int i = 0; i < _curr_length; ++i) { kpeter@601: e = _candidates[i]; kpeter@601: c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@601: if (c < min) { kpeter@601: min = c; kpeter@727: _in_arc = e; kpeter@601: } kpeter@727: else if (c >= 0) { kpeter@601: _candidates[i--] = _candidates[--_curr_length]; kpeter@601: } kpeter@601: } kpeter@727: if (min < 0) return true; kpeter@601: } kpeter@601: kpeter@601: // Major iteration: build a new candidate list kpeter@601: min = 0; kpeter@601: _curr_length = 0; kpeter@839: for (e = _next_arc; e != _search_arc_num; ++e) { kpeter@601: c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@601: if (c < 0) { kpeter@601: _candidates[_curr_length++] = e; kpeter@601: if (c < min) { kpeter@601: min = c; kpeter@727: _in_arc = e; kpeter@601: } kpeter@727: if (_curr_length == _list_length) goto search_end; kpeter@601: } kpeter@601: } kpeter@839: for (e = 0; e != _next_arc; ++e) { kpeter@727: c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@727: if (c < 0) { kpeter@727: _candidates[_curr_length++] = e; kpeter@727: if (c < min) { kpeter@727: min = c; kpeter@727: _in_arc = e; kpeter@601: } kpeter@727: if (_curr_length == _list_length) goto search_end; kpeter@601: } kpeter@601: } kpeter@601: if (_curr_length == 0) return false; alpar@877: alpar@877: search_end: kpeter@601: _minor_count = 1; kpeter@601: _next_arc = e; kpeter@601: return true; kpeter@601: } kpeter@601: kpeter@601: }; //class CandidateListPivotRule kpeter@601: kpeter@601: kpeter@605: // Implementation of the Altering Candidate List pivot rule kpeter@601: class AlteringListPivotRule kpeter@601: { kpeter@601: private: kpeter@601: kpeter@601: // References to the NetworkSimplex class kpeter@601: const IntVector &_source; kpeter@601: const IntVector &_target; kpeter@607: const CostVector &_cost; kpeter@895: const CharVector &_state; kpeter@607: const CostVector &_pi; kpeter@601: int &_in_arc; kpeter@663: int _search_arc_num; kpeter@601: kpeter@601: // Pivot rule data kpeter@601: int _block_size, _head_length, _curr_length; kpeter@601: int _next_arc; kpeter@601: IntVector _candidates; kpeter@607: CostVector _cand_cost; kpeter@601: kpeter@601: // Functor class to compare arcs during sort of the candidate list kpeter@601: class SortFunc kpeter@601: { kpeter@601: private: kpeter@607: const CostVector &_map; kpeter@601: public: kpeter@607: SortFunc(const CostVector &map) : _map(map) {} kpeter@601: bool operator()(int left, int right) { kpeter@984: return _map[left] < _map[right]; kpeter@601: } kpeter@601: }; kpeter@601: kpeter@601: SortFunc _sort_func; kpeter@601: kpeter@601: public: kpeter@601: kpeter@605: // Constructor kpeter@601: AlteringListPivotRule(NetworkSimplex &ns) : kpeter@603: _source(ns._source), _target(ns._target), kpeter@601: _cost(ns._cost), _state(ns._state), _pi(ns._pi), kpeter@663: _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), kpeter@663: _next_arc(0), _cand_cost(ns._search_arc_num), _sort_func(_cand_cost) kpeter@601: { kpeter@601: // The main parameters of the pivot rule kpeter@727: const double BLOCK_SIZE_FACTOR = 1.0; kpeter@601: const int MIN_BLOCK_SIZE = 10; kpeter@984: const double HEAD_LENGTH_FACTOR = 0.01; kpeter@601: const int MIN_HEAD_LENGTH = 3; kpeter@601: alpar@612: _block_size = std::max( int(BLOCK_SIZE_FACTOR * kpeter@663: std::sqrt(double(_search_arc_num))), kpeter@601: MIN_BLOCK_SIZE ); kpeter@601: _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size), kpeter@601: MIN_HEAD_LENGTH ); kpeter@601: _candidates.resize(_head_length + _block_size); kpeter@601: _curr_length = 0; kpeter@601: } kpeter@601: kpeter@605: // Find next entering arc kpeter@601: bool findEnteringArc() { kpeter@601: // Check the current candidate list kpeter@601: int e; kpeter@895: Cost c; kpeter@839: for (int i = 0; i != _curr_length; ++i) { kpeter@601: e = _candidates[i]; kpeter@895: c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@895: if (c < 0) { kpeter@895: _cand_cost[e] = c; kpeter@895: } else { kpeter@601: _candidates[i--] = _candidates[--_curr_length]; kpeter@601: } kpeter@601: } kpeter@601: kpeter@601: // Extend the list kpeter@601: int cnt = _block_size; kpeter@601: int limit = _head_length; kpeter@601: kpeter@839: for (e = _next_arc; e != _search_arc_num; ++e) { kpeter@895: c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@895: if (c < 0) { kpeter@895: _cand_cost[e] = c; kpeter@601: _candidates[_curr_length++] = e; kpeter@601: } kpeter@601: if (--cnt == 0) { kpeter@727: if (_curr_length > limit) goto search_end; kpeter@601: limit = 0; kpeter@601: cnt = _block_size; kpeter@601: } kpeter@601: } kpeter@839: for (e = 0; e != _next_arc; ++e) { kpeter@984: c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@984: if (c < 0) { kpeter@984: _cand_cost[e] = c; kpeter@727: _candidates[_curr_length++] = e; kpeter@727: } kpeter@727: if (--cnt == 0) { kpeter@727: if (_curr_length > limit) goto search_end; kpeter@727: limit = 0; kpeter@727: cnt = _block_size; kpeter@601: } kpeter@601: } kpeter@601: if (_curr_length == 0) return false; alpar@877: kpeter@727: search_end: kpeter@601: kpeter@984: // Perform partial sort operation on the candidate list kpeter@984: int new_length = std::min(_head_length + 1, _curr_length); kpeter@984: std::partial_sort(_candidates.begin(), _candidates.begin() + new_length, kpeter@984: _candidates.begin() + _curr_length, _sort_func); kpeter@601: kpeter@984: // Select the entering arc and remove it from the list kpeter@601: _in_arc = _candidates[0]; kpeter@727: _next_arc = e; kpeter@984: _candidates[0] = _candidates[new_length - 1]; kpeter@984: _curr_length = new_length - 1; kpeter@601: return true; kpeter@601: } kpeter@601: kpeter@601: }; //class AlteringListPivotRule kpeter@601: kpeter@601: public: kpeter@601: kpeter@605: /// \brief Constructor. kpeter@601: /// kpeter@609: /// The constructor of the class. kpeter@601: /// kpeter@603: /// \param graph The digraph the algorithm runs on. kpeter@896: /// \param arc_mixing Indicate if the arcs will be stored in a alpar@877: /// mixed order in the internal data structure. kpeter@896: /// In general, it leads to similar performance as using the original kpeter@896: /// arc order, but it makes the algorithm more robust and in special kpeter@896: /// cases, even significantly faster. Therefore, it is enabled by default. kpeter@896: NetworkSimplex(const GR& graph, bool arc_mixing = true) : kpeter@642: _graph(graph), _node_id(graph), _arc_id(graph), kpeter@830: _arc_mixing(arc_mixing), kpeter@811: MAX(std::numeric_limits::max()), kpeter@641: INF(std::numeric_limits::has_infinity ? kpeter@811: std::numeric_limits::infinity() : MAX) kpeter@605: { kpeter@812: // Check the number types kpeter@641: LEMON_ASSERT(std::numeric_limits::is_signed, kpeter@640: "The flow type of NetworkSimplex must be signed"); kpeter@640: LEMON_ASSERT(std::numeric_limits::is_signed, kpeter@640: "The cost type of NetworkSimplex must be signed"); kpeter@601: kpeter@830: // Reset data structures kpeter@729: reset(); kpeter@601: } kpeter@601: kpeter@609: /// \name Parameters kpeter@609: /// The parameters of the algorithm can be specified using these kpeter@609: /// functions. kpeter@609: kpeter@609: /// @{ kpeter@609: kpeter@605: /// \brief Set the lower bounds on the arcs. kpeter@605: /// kpeter@605: /// This function sets the lower bounds on the arcs. kpeter@640: /// If it is not used before calling \ref run(), the lower bounds kpeter@640: /// will be set to zero on all arcs. kpeter@605: /// kpeter@605: /// \param map An arc map storing the lower bounds. kpeter@641: /// Its \c Value type must be convertible to the \c Value type kpeter@605: /// of the algorithm. kpeter@605: /// kpeter@605: /// \return (*this) kpeter@640: template kpeter@640: NetworkSimplex& lowerMap(const LowerMap& map) { kpeter@642: _have_lower = true; kpeter@605: for (ArcIt a(_graph); a != INVALID; ++a) { kpeter@642: _lower[_arc_id[a]] = map[a]; kpeter@605: } kpeter@605: return *this; kpeter@605: } kpeter@605: kpeter@605: /// \brief Set the upper bounds (capacities) on the arcs. kpeter@605: /// kpeter@605: /// This function sets the upper bounds (capacities) on the arcs. kpeter@640: /// If it is not used before calling \ref run(), the upper bounds kpeter@640: /// will be set to \ref INF on all arcs (i.e. the flow value will be kpeter@812: /// unbounded from above). kpeter@605: /// kpeter@605: /// \param map An arc map storing the upper bounds. kpeter@641: /// Its \c Value type must be convertible to the \c Value type kpeter@605: /// of the algorithm. kpeter@605: /// kpeter@605: /// \return (*this) kpeter@640: template kpeter@640: NetworkSimplex& upperMap(const UpperMap& map) { kpeter@605: for (ArcIt a(_graph); a != INVALID; ++a) { kpeter@642: _upper[_arc_id[a]] = map[a]; kpeter@605: } kpeter@605: return *this; kpeter@605: } kpeter@605: kpeter@605: /// \brief Set the costs of the arcs. kpeter@605: /// kpeter@605: /// This function sets the costs of the arcs. kpeter@605: /// If it is not used before calling \ref run(), the costs kpeter@605: /// will be set to \c 1 on all arcs. kpeter@605: /// kpeter@605: /// \param map An arc map storing the costs. kpeter@607: /// Its \c Value type must be convertible to the \c Cost type kpeter@605: /// of the algorithm. kpeter@605: /// kpeter@605: /// \return (*this) kpeter@640: template kpeter@640: NetworkSimplex& costMap(const CostMap& map) { kpeter@605: for (ArcIt a(_graph); a != INVALID; ++a) { kpeter@642: _cost[_arc_id[a]] = map[a]; kpeter@605: } kpeter@605: return *this; kpeter@605: } kpeter@605: kpeter@605: /// \brief Set the supply values of the nodes. kpeter@605: /// kpeter@605: /// This function sets the supply values of the nodes. kpeter@605: /// If neither this function nor \ref stSupply() is used before kpeter@605: /// calling \ref run(), the supply of each node will be set to zero. kpeter@605: /// kpeter@605: /// \param map A node map storing the supply values. kpeter@641: /// Its \c Value type must be convertible to the \c Value type kpeter@605: /// of the algorithm. kpeter@605: /// kpeter@605: /// \return (*this) kpeter@919: /// kpeter@919: /// \sa supplyType() kpeter@640: template kpeter@640: NetworkSimplex& supplyMap(const SupplyMap& map) { kpeter@605: for (NodeIt n(_graph); n != INVALID; ++n) { kpeter@642: _supply[_node_id[n]] = map[n]; kpeter@605: } kpeter@605: return *this; kpeter@605: } kpeter@605: kpeter@605: /// \brief Set single source and target nodes and a supply value. kpeter@605: /// kpeter@605: /// This function sets a single source node and a single target node kpeter@605: /// and the required flow value. kpeter@605: /// If neither this function nor \ref supplyMap() is used before kpeter@605: /// calling \ref run(), the supply of each node will be set to zero. kpeter@605: /// kpeter@640: /// Using this function has the same effect as using \ref supplyMap() kpeter@919: /// with a map in which \c k is assigned to \c s, \c -k is kpeter@640: /// assigned to \c t and all other nodes have zero supply value. kpeter@640: /// kpeter@605: /// \param s The source node. kpeter@605: /// \param t The target node. kpeter@605: /// \param k The required amount of flow from node \c s to node \c t kpeter@605: /// (i.e. the supply of \c s and the demand of \c t). kpeter@605: /// kpeter@605: /// \return (*this) kpeter@641: NetworkSimplex& stSupply(const Node& s, const Node& t, Value k) { kpeter@642: for (int i = 0; i != _node_num; ++i) { kpeter@642: _supply[i] = 0; kpeter@642: } kpeter@642: _supply[_node_id[s]] = k; kpeter@642: _supply[_node_id[t]] = -k; kpeter@605: return *this; kpeter@605: } alpar@877: kpeter@640: /// \brief Set the type of the supply constraints. kpeter@609: /// kpeter@640: /// This function sets the type of the supply/demand constraints. kpeter@640: /// If it is not used before calling \ref run(), the \ref GEQ supply kpeter@609: /// type will be used. kpeter@609: /// kpeter@786: /// For more information, see \ref SupplyType. kpeter@609: /// kpeter@609: /// \return (*this) kpeter@640: NetworkSimplex& supplyType(SupplyType supply_type) { kpeter@640: _stype = supply_type; kpeter@609: return *this; kpeter@609: } kpeter@605: kpeter@609: /// @} kpeter@601: kpeter@605: /// \name Execution Control kpeter@605: /// The algorithm can be executed using \ref run(). kpeter@605: kpeter@601: /// @{ kpeter@601: kpeter@601: /// \brief Run the algorithm. kpeter@601: /// kpeter@601: /// This function runs the algorithm. kpeter@609: /// The paramters can be specified using functions \ref lowerMap(), alpar@877: /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(), kpeter@642: /// \ref supplyType(). kpeter@609: /// For example, kpeter@605: /// \code kpeter@605: /// NetworkSimplex ns(graph); kpeter@640: /// ns.lowerMap(lower).upperMap(upper).costMap(cost) kpeter@605: /// .supplyMap(sup).run(); kpeter@605: /// \endcode kpeter@601: /// kpeter@830: /// This function can be called more than once. All the given parameters kpeter@830: /// are kept for the next call, unless \ref resetParams() or \ref reset() kpeter@830: /// is used, thus only the modified parameters have to be set again. kpeter@830: /// If the underlying digraph was also modified after the construction kpeter@830: /// of the class (or the last \ref reset() call), then the \ref reset() kpeter@830: /// function must be called. kpeter@606: /// kpeter@605: /// \param pivot_rule The pivot rule that will be used during the kpeter@786: /// algorithm. For more information, see \ref PivotRule. kpeter@601: /// kpeter@640: /// \return \c INFEASIBLE if no feasible flow exists, kpeter@640: /// \n \c OPTIMAL if the problem has optimal solution kpeter@640: /// (i.e. it is feasible and bounded), and the algorithm has found kpeter@640: /// optimal flow and node potentials (primal and dual solutions), kpeter@640: /// \n \c UNBOUNDED if the objective function of the problem is kpeter@640: /// unbounded, i.e. there is a directed cycle having negative total kpeter@640: /// cost and infinite upper bound. kpeter@640: /// kpeter@640: /// \see ProblemType, PivotRule kpeter@830: /// \see resetParams(), reset() kpeter@640: ProblemType run(PivotRule pivot_rule = BLOCK_SEARCH) { kpeter@640: if (!init()) return INFEASIBLE; kpeter@640: return start(pivot_rule); kpeter@601: } kpeter@601: kpeter@606: /// \brief Reset all the parameters that have been given before. kpeter@606: /// kpeter@606: /// This function resets all the paramaters that have been given kpeter@609: /// before using functions \ref lowerMap(), \ref upperMap(), kpeter@642: /// \ref costMap(), \ref supplyMap(), \ref stSupply(), \ref supplyType(). kpeter@606: /// kpeter@830: /// It is useful for multiple \ref run() calls. Basically, all the given kpeter@830: /// parameters are kept for the next \ref run() call, unless kpeter@830: /// \ref resetParams() or \ref reset() is used. kpeter@830: /// If the underlying digraph was also modified after the construction kpeter@830: /// of the class or the last \ref reset() call, then the \ref reset() kpeter@830: /// function must be used, otherwise \ref resetParams() is sufficient. kpeter@606: /// kpeter@606: /// For example, kpeter@606: /// \code kpeter@606: /// NetworkSimplex ns(graph); kpeter@606: /// kpeter@606: /// // First run kpeter@640: /// ns.lowerMap(lower).upperMap(upper).costMap(cost) kpeter@606: /// .supplyMap(sup).run(); kpeter@606: /// kpeter@830: /// // Run again with modified cost map (resetParams() is not called, kpeter@606: /// // so only the cost map have to be set again) kpeter@606: /// cost[e] += 100; kpeter@606: /// ns.costMap(cost).run(); kpeter@606: /// kpeter@830: /// // Run again from scratch using resetParams() kpeter@606: /// // (the lower bounds will be set to zero on all arcs) kpeter@830: /// ns.resetParams(); kpeter@640: /// ns.upperMap(capacity).costMap(cost) kpeter@606: /// .supplyMap(sup).run(); kpeter@606: /// \endcode kpeter@606: /// kpeter@606: /// \return (*this) kpeter@830: /// kpeter@830: /// \see reset(), run() kpeter@830: NetworkSimplex& resetParams() { kpeter@642: for (int i = 0; i != _node_num; ++i) { kpeter@642: _supply[i] = 0; kpeter@642: } kpeter@642: for (int i = 0; i != _arc_num; ++i) { kpeter@642: _lower[i] = 0; kpeter@642: _upper[i] = INF; kpeter@642: _cost[i] = 1; kpeter@642: } kpeter@642: _have_lower = false; kpeter@640: _stype = GEQ; kpeter@606: return *this; kpeter@606: } kpeter@606: kpeter@830: /// \brief Reset the internal data structures and all the parameters kpeter@830: /// that have been given before. kpeter@830: /// kpeter@830: /// This function resets the internal data structures and all the kpeter@830: /// paramaters that have been given before using functions \ref lowerMap(), kpeter@830: /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(), kpeter@830: /// \ref supplyType(). kpeter@830: /// kpeter@830: /// It is useful for multiple \ref run() calls. Basically, all the given kpeter@830: /// parameters are kept for the next \ref run() call, unless kpeter@830: /// \ref resetParams() or \ref reset() is used. kpeter@830: /// If the underlying digraph was also modified after the construction kpeter@830: /// of the class or the last \ref reset() call, then the \ref reset() kpeter@830: /// function must be used, otherwise \ref resetParams() is sufficient. kpeter@830: /// kpeter@830: /// See \ref resetParams() for examples. kpeter@830: /// kpeter@830: /// \return (*this) kpeter@830: /// kpeter@830: /// \see resetParams(), run() kpeter@830: NetworkSimplex& reset() { kpeter@830: // Resize vectors kpeter@830: _node_num = countNodes(_graph); kpeter@830: _arc_num = countArcs(_graph); kpeter@830: int all_node_num = _node_num + 1; kpeter@830: int max_arc_num = _arc_num + 2 * _node_num; kpeter@830: kpeter@830: _source.resize(max_arc_num); kpeter@830: _target.resize(max_arc_num); kpeter@830: kpeter@830: _lower.resize(_arc_num); kpeter@830: _upper.resize(_arc_num); kpeter@830: _cap.resize(max_arc_num); kpeter@830: _cost.resize(max_arc_num); kpeter@830: _supply.resize(all_node_num); kpeter@830: _flow.resize(max_arc_num); kpeter@830: _pi.resize(all_node_num); kpeter@830: kpeter@830: _parent.resize(all_node_num); kpeter@830: _pred.resize(all_node_num); kpeter@895: _pred_dir.resize(all_node_num); kpeter@830: _thread.resize(all_node_num); kpeter@830: _rev_thread.resize(all_node_num); kpeter@830: _succ_num.resize(all_node_num); kpeter@830: _last_succ.resize(all_node_num); kpeter@830: _state.resize(max_arc_num); kpeter@830: kpeter@830: // Copy the graph kpeter@830: int i = 0; kpeter@830: for (NodeIt n(_graph); n != INVALID; ++n, ++i) { kpeter@830: _node_id[n] = i; kpeter@830: } kpeter@830: if (_arc_mixing) { kpeter@830: // Store the arcs in a mixed order kpeter@896: const int skip = std::max(_arc_num / _node_num, 3); kpeter@830: int i = 0, j = 0; kpeter@830: for (ArcIt a(_graph); a != INVALID; ++a) { kpeter@830: _arc_id[a] = i; kpeter@830: _source[i] = _node_id[_graph.source(a)]; kpeter@830: _target[i] = _node_id[_graph.target(a)]; kpeter@896: if ((i += skip) >= _arc_num) i = ++j; kpeter@830: } kpeter@830: } else { kpeter@830: // Store the arcs in the original order kpeter@830: int i = 0; kpeter@830: for (ArcIt a(_graph); a != INVALID; ++a, ++i) { kpeter@830: _arc_id[a] = i; kpeter@830: _source[i] = _node_id[_graph.source(a)]; kpeter@830: _target[i] = _node_id[_graph.target(a)]; kpeter@830: } kpeter@830: } alpar@877: kpeter@830: // Reset parameters kpeter@830: resetParams(); kpeter@830: return *this; kpeter@830: } alpar@877: kpeter@601: /// @} kpeter@601: kpeter@601: /// \name Query Functions kpeter@601: /// The results of the algorithm can be obtained using these kpeter@601: /// functions.\n kpeter@605: /// The \ref run() function must be called before using them. kpeter@605: kpeter@601: /// @{ kpeter@601: kpeter@605: /// \brief Return the total cost of the found flow. kpeter@605: /// kpeter@605: /// This function returns the total cost of the found flow. kpeter@1080: /// Its complexity is O(m). kpeter@605: /// kpeter@605: /// \note The return type of the function can be specified as a kpeter@605: /// template parameter. For example, kpeter@605: /// \code kpeter@605: /// ns.totalCost(); kpeter@605: /// \endcode kpeter@607: /// It is useful if the total cost cannot be stored in the \c Cost kpeter@605: /// type of the algorithm, which is the default return type of the kpeter@605: /// function. kpeter@605: /// kpeter@605: /// \pre \ref run() must be called before using this function. kpeter@642: template kpeter@642: Number totalCost() const { kpeter@642: Number c = 0; kpeter@642: for (ArcIt a(_graph); a != INVALID; ++a) { kpeter@642: int i = _arc_id[a]; kpeter@642: c += Number(_flow[i]) * Number(_cost[i]); kpeter@605: } kpeter@605: return c; kpeter@605: } kpeter@605: kpeter@605: #ifndef DOXYGEN kpeter@607: Cost totalCost() const { kpeter@607: return totalCost(); kpeter@605: } kpeter@605: #endif kpeter@605: kpeter@605: /// \brief Return the flow on the given arc. kpeter@605: /// kpeter@605: /// This function returns the flow on the given arc. kpeter@605: /// kpeter@605: /// \pre \ref run() must be called before using this function. kpeter@641: Value flow(const Arc& a) const { kpeter@642: return _flow[_arc_id[a]]; kpeter@605: } kpeter@605: kpeter@1003: /// \brief Copy the flow values (the primal solution) into the kpeter@1003: /// given map. kpeter@601: /// kpeter@642: /// This function copies the flow value on each arc into the given kpeter@642: /// map. The \c Value type of the algorithm must be convertible to kpeter@642: /// the \c Value type of the map. kpeter@601: /// kpeter@601: /// \pre \ref run() must be called before using this function. kpeter@642: template kpeter@642: void flowMap(FlowMap &map) const { kpeter@642: for (ArcIt a(_graph); a != INVALID; ++a) { kpeter@642: map.set(a, _flow[_arc_id[a]]); kpeter@642: } kpeter@601: } kpeter@601: kpeter@605: /// \brief Return the potential (dual value) of the given node. kpeter@605: /// kpeter@605: /// This function returns the potential (dual value) of the kpeter@605: /// given node. kpeter@605: /// kpeter@605: /// \pre \ref run() must be called before using this function. kpeter@607: Cost potential(const Node& n) const { kpeter@642: return _pi[_node_id[n]]; kpeter@605: } kpeter@605: kpeter@1003: /// \brief Copy the potential values (the dual solution) into the kpeter@1003: /// given map. kpeter@601: /// kpeter@642: /// This function copies the potential (dual value) of each node kpeter@642: /// into the given map. kpeter@642: /// The \c Cost type of the algorithm must be convertible to the kpeter@642: /// \c Value type of the map. kpeter@601: /// kpeter@601: /// \pre \ref run() must be called before using this function. kpeter@642: template kpeter@642: void potentialMap(PotentialMap &map) const { kpeter@642: for (NodeIt n(_graph); n != INVALID; ++n) { kpeter@642: map.set(n, _pi[_node_id[n]]); kpeter@642: } kpeter@601: } kpeter@601: kpeter@601: /// @} kpeter@601: kpeter@601: private: kpeter@601: kpeter@601: // Initialize internal data structures kpeter@601: bool init() { kpeter@605: if (_node_num == 0) return false; kpeter@601: kpeter@642: // Check the sum of supply values kpeter@642: _sum_supply = 0; kpeter@642: for (int i = 0; i != _node_num; ++i) { kpeter@642: _sum_supply += _supply[i]; kpeter@642: } alpar@643: if ( !((_stype == GEQ && _sum_supply <= 0) || alpar@643: (_stype == LEQ && _sum_supply >= 0)) ) return false; kpeter@601: kpeter@1070: // Check lower and upper bounds kpeter@1070: LEMON_DEBUG(checkBoundMaps(), kpeter@1070: "Upper bounds must be greater or equal to the lower bounds"); kpeter@1070: kpeter@642: // Remove non-zero lower bounds kpeter@642: if (_have_lower) { kpeter@642: for (int i = 0; i != _arc_num; ++i) { kpeter@642: Value c = _lower[i]; kpeter@642: if (c >= 0) { kpeter@811: _cap[i] = _upper[i] < MAX ? _upper[i] - c : INF; kpeter@642: } else { kpeter@811: _cap[i] = _upper[i] < MAX + c ? _upper[i] - c : INF; kpeter@642: } kpeter@642: _supply[_source[i]] -= c; kpeter@642: _supply[_target[i]] += c; kpeter@642: } kpeter@642: } else { kpeter@642: for (int i = 0; i != _arc_num; ++i) { kpeter@642: _cap[i] = _upper[i]; kpeter@642: } kpeter@605: } kpeter@601: kpeter@609: // Initialize artifical cost kpeter@640: Cost ART_COST; kpeter@609: if (std::numeric_limits::is_exact) { kpeter@663: ART_COST = std::numeric_limits::max() / 2 + 1; kpeter@609: } else { kpeter@888: ART_COST = 0; kpeter@609: for (int i = 0; i != _arc_num; ++i) { kpeter@640: if (_cost[i] > ART_COST) ART_COST = _cost[i]; kpeter@609: } kpeter@640: ART_COST = (ART_COST + 1) * _node_num; kpeter@609: } kpeter@609: kpeter@642: // Initialize arc maps kpeter@642: for (int i = 0; i != _arc_num; ++i) { kpeter@642: _flow[i] = 0; kpeter@642: _state[i] = STATE_LOWER; kpeter@642: } alpar@877: kpeter@601: // Set data for the artificial root node kpeter@601: _root = _node_num; kpeter@601: _parent[_root] = -1; kpeter@601: _pred[_root] = -1; kpeter@601: _thread[_root] = 0; kpeter@604: _rev_thread[0] = _root; kpeter@642: _succ_num[_root] = _node_num + 1; kpeter@604: _last_succ[_root] = _root - 1; kpeter@640: _supply[_root] = -_sum_supply; kpeter@663: _pi[_root] = 0; kpeter@601: kpeter@601: // Add artificial arcs and initialize the spanning tree data structure kpeter@663: if (_sum_supply == 0) { kpeter@663: // EQ supply constraints kpeter@663: _search_arc_num = _arc_num; kpeter@663: _all_arc_num = _arc_num + _node_num; kpeter@663: for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { kpeter@663: _parent[u] = _root; kpeter@663: _pred[u] = e; kpeter@663: _thread[u] = u + 1; kpeter@663: _rev_thread[u + 1] = u; kpeter@663: _succ_num[u] = 1; kpeter@663: _last_succ[u] = u; kpeter@663: _cap[e] = INF; kpeter@663: _state[e] = STATE_TREE; kpeter@663: if (_supply[u] >= 0) { kpeter@895: _pred_dir[u] = DIR_UP; kpeter@663: _pi[u] = 0; kpeter@663: _source[e] = u; kpeter@663: _target[e] = _root; kpeter@663: _flow[e] = _supply[u]; kpeter@663: _cost[e] = 0; kpeter@663: } else { kpeter@895: _pred_dir[u] = DIR_DOWN; kpeter@663: _pi[u] = ART_COST; kpeter@663: _source[e] = _root; kpeter@663: _target[e] = u; kpeter@663: _flow[e] = -_supply[u]; kpeter@663: _cost[e] = ART_COST; kpeter@663: } kpeter@601: } kpeter@601: } kpeter@663: else if (_sum_supply > 0) { kpeter@663: // LEQ supply constraints kpeter@663: _search_arc_num = _arc_num + _node_num; kpeter@663: int f = _arc_num + _node_num; kpeter@663: for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { kpeter@663: _parent[u] = _root; kpeter@663: _thread[u] = u + 1; kpeter@663: _rev_thread[u + 1] = u; kpeter@663: _succ_num[u] = 1; kpeter@663: _last_succ[u] = u; kpeter@663: if (_supply[u] >= 0) { kpeter@895: _pred_dir[u] = DIR_UP; kpeter@663: _pi[u] = 0; kpeter@663: _pred[u] = e; kpeter@663: _source[e] = u; kpeter@663: _target[e] = _root; kpeter@663: _cap[e] = INF; kpeter@663: _flow[e] = _supply[u]; kpeter@663: _cost[e] = 0; kpeter@663: _state[e] = STATE_TREE; kpeter@663: } else { kpeter@895: _pred_dir[u] = DIR_DOWN; kpeter@663: _pi[u] = ART_COST; kpeter@663: _pred[u] = f; kpeter@663: _source[f] = _root; kpeter@663: _target[f] = u; kpeter@663: _cap[f] = INF; kpeter@663: _flow[f] = -_supply[u]; kpeter@663: _cost[f] = ART_COST; kpeter@663: _state[f] = STATE_TREE; kpeter@663: _source[e] = u; kpeter@663: _target[e] = _root; kpeter@663: _cap[e] = INF; kpeter@663: _flow[e] = 0; kpeter@663: _cost[e] = 0; kpeter@663: _state[e] = STATE_LOWER; kpeter@663: ++f; kpeter@663: } kpeter@663: } kpeter@663: _all_arc_num = f; kpeter@663: } kpeter@663: else { kpeter@663: // GEQ supply constraints kpeter@663: _search_arc_num = _arc_num + _node_num; kpeter@663: int f = _arc_num + _node_num; kpeter@663: for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { kpeter@663: _parent[u] = _root; kpeter@663: _thread[u] = u + 1; kpeter@663: _rev_thread[u + 1] = u; kpeter@663: _succ_num[u] = 1; kpeter@663: _last_succ[u] = u; kpeter@663: if (_supply[u] <= 0) { kpeter@895: _pred_dir[u] = DIR_DOWN; kpeter@663: _pi[u] = 0; kpeter@663: _pred[u] = e; kpeter@663: _source[e] = _root; kpeter@663: _target[e] = u; kpeter@663: _cap[e] = INF; kpeter@663: _flow[e] = -_supply[u]; kpeter@663: _cost[e] = 0; kpeter@663: _state[e] = STATE_TREE; kpeter@663: } else { kpeter@895: _pred_dir[u] = DIR_UP; kpeter@663: _pi[u] = -ART_COST; kpeter@663: _pred[u] = f; kpeter@663: _source[f] = u; kpeter@663: _target[f] = _root; kpeter@663: _cap[f] = INF; kpeter@663: _flow[f] = _supply[u]; kpeter@663: _state[f] = STATE_TREE; kpeter@663: _cost[f] = ART_COST; kpeter@663: _source[e] = _root; kpeter@663: _target[e] = u; kpeter@663: _cap[e] = INF; kpeter@663: _flow[e] = 0; kpeter@663: _cost[e] = 0; kpeter@663: _state[e] = STATE_LOWER; kpeter@663: ++f; kpeter@663: } kpeter@663: } kpeter@663: _all_arc_num = f; kpeter@663: } kpeter@601: kpeter@601: return true; kpeter@601: } kpeter@1070: kpeter@1070: // Check if the upper bound is greater or equal to the lower bound kpeter@1070: // on each arc. kpeter@1070: bool checkBoundMaps() { kpeter@1070: for (int j = 0; j != _arc_num; ++j) { kpeter@1070: if (_upper[j] < _lower[j]) return false; kpeter@1070: } kpeter@1070: return true; kpeter@1070: } kpeter@601: kpeter@601: // Find the join node kpeter@601: void findJoinNode() { kpeter@603: int u = _source[in_arc]; kpeter@603: int v = _target[in_arc]; kpeter@601: while (u != v) { kpeter@604: if (_succ_num[u] < _succ_num[v]) { kpeter@604: u = _parent[u]; kpeter@604: } else { kpeter@604: v = _parent[v]; kpeter@604: } kpeter@601: } kpeter@601: join = u; kpeter@601: } kpeter@601: kpeter@601: // Find the leaving arc of the cycle and returns true if the kpeter@601: // leaving arc is not the same as the entering arc kpeter@601: bool findLeavingArc() { kpeter@601: // Initialize first and second nodes according to the direction kpeter@601: // of the cycle kpeter@895: int first, second; kpeter@603: if (_state[in_arc] == STATE_LOWER) { kpeter@603: first = _source[in_arc]; kpeter@603: second = _target[in_arc]; kpeter@601: } else { kpeter@603: first = _target[in_arc]; kpeter@603: second = _source[in_arc]; kpeter@601: } kpeter@603: delta = _cap[in_arc]; kpeter@601: int result = 0; kpeter@895: Value c, d; kpeter@601: int e; kpeter@601: kpeter@895: // Search the cycle form the first node to the join node kpeter@601: for (int u = first; u != join; u = _parent[u]) { kpeter@601: e = _pred[u]; kpeter@895: d = _flow[e]; kpeter@895: if (_pred_dir[u] == DIR_DOWN) { kpeter@895: c = _cap[e]; kpeter@895: d = c >= MAX ? INF : c - d; kpeter@895: } kpeter@601: if (d < delta) { kpeter@601: delta = d; kpeter@601: u_out = u; kpeter@601: result = 1; kpeter@601: } kpeter@601: } kpeter@895: kpeter@895: // Search the cycle form the second node to the join node kpeter@601: for (int u = second; u != join; u = _parent[u]) { kpeter@601: e = _pred[u]; kpeter@895: d = _flow[e]; kpeter@895: if (_pred_dir[u] == DIR_UP) { kpeter@895: c = _cap[e]; kpeter@895: d = c >= MAX ? INF : c - d; kpeter@895: } kpeter@601: if (d <= delta) { kpeter@601: delta = d; kpeter@601: u_out = u; kpeter@601: result = 2; kpeter@601: } kpeter@601: } kpeter@601: kpeter@601: if (result == 1) { kpeter@601: u_in = first; kpeter@601: v_in = second; kpeter@601: } else { kpeter@601: u_in = second; kpeter@601: v_in = first; kpeter@601: } kpeter@601: return result != 0; kpeter@601: } kpeter@601: kpeter@601: // Change _flow and _state vectors kpeter@601: void changeFlow(bool change) { kpeter@601: // Augment along the cycle kpeter@601: if (delta > 0) { kpeter@641: Value val = _state[in_arc] * delta; kpeter@603: _flow[in_arc] += val; kpeter@603: for (int u = _source[in_arc]; u != join; u = _parent[u]) { kpeter@895: _flow[_pred[u]] -= _pred_dir[u] * val; kpeter@601: } kpeter@603: for (int u = _target[in_arc]; u != join; u = _parent[u]) { kpeter@895: _flow[_pred[u]] += _pred_dir[u] * val; kpeter@601: } kpeter@601: } kpeter@601: // Update the state of the entering and leaving arcs kpeter@601: if (change) { kpeter@603: _state[in_arc] = STATE_TREE; kpeter@601: _state[_pred[u_out]] = kpeter@601: (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER; kpeter@601: } else { kpeter@603: _state[in_arc] = -_state[in_arc]; kpeter@601: } kpeter@601: } kpeter@601: kpeter@604: // Update the tree structure kpeter@604: void updateTreeStructure() { kpeter@604: int old_rev_thread = _rev_thread[u_out]; kpeter@604: int old_succ_num = _succ_num[u_out]; kpeter@604: int old_last_succ = _last_succ[u_out]; kpeter@601: v_out = _parent[u_out]; kpeter@601: kpeter@895: // Check if u_in and u_out coincide kpeter@895: if (u_in == u_out) { kpeter@895: // Update _parent, _pred, _pred_dir kpeter@895: _parent[u_in] = v_in; kpeter@895: _pred[u_in] = in_arc; kpeter@895: _pred_dir[u_in] = u_in == _source[in_arc] ? DIR_UP : DIR_DOWN; kpeter@604: kpeter@895: // Update _thread and _rev_thread kpeter@895: if (_thread[v_in] != u_out) { kpeter@895: int after = _thread[old_last_succ]; kpeter@895: _thread[old_rev_thread] = after; kpeter@895: _rev_thread[after] = old_rev_thread; kpeter@895: after = _thread[v_in]; kpeter@895: _thread[v_in] = u_out; kpeter@895: _rev_thread[u_out] = v_in; kpeter@895: _thread[old_last_succ] = after; kpeter@895: _rev_thread[after] = old_last_succ; kpeter@895: } kpeter@604: } else { kpeter@895: // Handle the case when old_rev_thread equals to v_in kpeter@895: // (it also means that join and v_out coincide) kpeter@895: int thread_continue = old_rev_thread == v_in ? kpeter@895: _thread[old_last_succ] : _thread[v_in]; kpeter@601: kpeter@895: // Update _thread and _parent along the stem nodes (i.e. the nodes kpeter@895: // between u_in and u_out, whose parent have to be changed) kpeter@895: int stem = u_in; // the current stem node kpeter@895: int par_stem = v_in; // the new parent of stem kpeter@895: int next_stem; // the next stem node kpeter@895: int last = _last_succ[u_in]; // the last successor of stem kpeter@895: int before, after = _thread[last]; kpeter@895: _thread[v_in] = u_in; kpeter@895: _dirty_revs.clear(); kpeter@895: _dirty_revs.push_back(v_in); kpeter@895: while (stem != u_out) { kpeter@895: // Insert the next stem node into the thread list kpeter@895: next_stem = _parent[stem]; kpeter@895: _thread[last] = next_stem; kpeter@895: _dirty_revs.push_back(last); kpeter@601: kpeter@895: // Remove the subtree of stem from the thread list kpeter@895: before = _rev_thread[stem]; kpeter@895: _thread[before] = after; kpeter@895: _rev_thread[after] = before; kpeter@601: kpeter@895: // Change the parent node and shift stem nodes kpeter@895: _parent[stem] = par_stem; kpeter@895: par_stem = stem; kpeter@895: stem = next_stem; kpeter@601: kpeter@895: // Update last and after kpeter@895: last = _last_succ[stem] == _last_succ[par_stem] ? kpeter@895: _rev_thread[par_stem] : _last_succ[stem]; kpeter@895: after = _thread[last]; kpeter@895: } kpeter@895: _parent[u_out] = par_stem; kpeter@895: _thread[last] = thread_continue; kpeter@895: _rev_thread[thread_continue] = last; kpeter@895: _last_succ[u_out] = last; kpeter@601: kpeter@895: // Remove the subtree of u_out from the thread list except for kpeter@895: // the case when old_rev_thread equals to v_in kpeter@895: if (old_rev_thread != v_in) { kpeter@895: _thread[old_rev_thread] = after; kpeter@895: _rev_thread[after] = old_rev_thread; kpeter@895: } kpeter@604: kpeter@895: // Update _rev_thread using the new _thread values kpeter@895: for (int i = 0; i != int(_dirty_revs.size()); ++i) { kpeter@895: int u = _dirty_revs[i]; kpeter@895: _rev_thread[_thread[u]] = u; kpeter@895: } kpeter@604: kpeter@895: // Update _pred, _pred_dir, _last_succ and _succ_num for the kpeter@895: // stem nodes from u_out to u_in kpeter@895: int tmp_sc = 0, tmp_ls = _last_succ[u_out]; kpeter@895: for (int u = u_out, p = _parent[u]; u != u_in; u = p, p = _parent[u]) { kpeter@895: _pred[u] = _pred[p]; kpeter@895: _pred_dir[u] = -_pred_dir[p]; kpeter@895: tmp_sc += _succ_num[u] - _succ_num[p]; kpeter@895: _succ_num[u] = tmp_sc; kpeter@895: _last_succ[p] = tmp_ls; kpeter@895: } kpeter@895: _pred[u_in] = in_arc; kpeter@895: _pred_dir[u_in] = u_in == _source[in_arc] ? DIR_UP : DIR_DOWN; kpeter@895: _succ_num[u_in] = old_succ_num; kpeter@604: } kpeter@604: kpeter@604: // Update _last_succ from v_in towards the root kpeter@895: int up_limit_out = _last_succ[join] == v_in ? join : -1; kpeter@895: int last_succ_out = _last_succ[u_out]; kpeter@895: for (int u = v_in; u != -1 && _last_succ[u] == v_in; u = _parent[u]) { kpeter@895: _last_succ[u] = last_succ_out; kpeter@604: } kpeter@895: kpeter@604: // Update _last_succ from v_out towards the root kpeter@604: if (join != old_rev_thread && v_in != old_rev_thread) { kpeter@895: for (int u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; kpeter@604: u = _parent[u]) { kpeter@604: _last_succ[u] = old_rev_thread; kpeter@604: } kpeter@895: } kpeter@895: else if (last_succ_out != old_last_succ) { kpeter@895: for (int u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; kpeter@604: u = _parent[u]) { kpeter@895: _last_succ[u] = last_succ_out; kpeter@604: } kpeter@604: } kpeter@604: kpeter@604: // Update _succ_num from v_in to join kpeter@895: for (int u = v_in; u != join; u = _parent[u]) { kpeter@604: _succ_num[u] += old_succ_num; kpeter@604: } kpeter@604: // Update _succ_num from v_out to join kpeter@895: for (int u = v_out; u != join; u = _parent[u]) { kpeter@604: _succ_num[u] -= old_succ_num; kpeter@601: } kpeter@601: } kpeter@601: kpeter@895: // Update potentials in the subtree that has been moved kpeter@604: void updatePotential() { kpeter@895: Cost sigma = _pi[v_in] - _pi[u_in] - kpeter@895: _pred_dir[u_in] * _cost[in_arc]; kpeter@608: int end = _thread[_last_succ[u_in]]; kpeter@608: for (int u = u_in; u != end; u = _thread[u]) { kpeter@608: _pi[u] += sigma; kpeter@601: } kpeter@601: } kpeter@601: kpeter@839: // Heuristic initial pivots kpeter@839: bool initialPivots() { kpeter@839: Value curr, total = 0; kpeter@839: std::vector supply_nodes, demand_nodes; kpeter@839: for (NodeIt u(_graph); u != INVALID; ++u) { kpeter@839: curr = _supply[_node_id[u]]; kpeter@839: if (curr > 0) { kpeter@839: total += curr; kpeter@839: supply_nodes.push_back(u); kpeter@839: } kpeter@839: else if (curr < 0) { kpeter@839: demand_nodes.push_back(u); kpeter@839: } kpeter@839: } kpeter@839: if (_sum_supply > 0) total -= _sum_supply; kpeter@839: if (total <= 0) return true; kpeter@839: kpeter@839: IntVector arc_vector; kpeter@839: if (_sum_supply >= 0) { kpeter@839: if (supply_nodes.size() == 1 && demand_nodes.size() == 1) { kpeter@839: // Perform a reverse graph search from the sink to the source kpeter@839: typename GR::template NodeMap reached(_graph, false); kpeter@839: Node s = supply_nodes[0], t = demand_nodes[0]; kpeter@839: std::vector stack; kpeter@839: reached[t] = true; kpeter@839: stack.push_back(t); kpeter@839: while (!stack.empty()) { kpeter@839: Node u, v = stack.back(); kpeter@839: stack.pop_back(); kpeter@839: if (v == s) break; kpeter@839: for (InArcIt a(_graph, v); a != INVALID; ++a) { kpeter@839: if (reached[u = _graph.source(a)]) continue; kpeter@839: int j = _arc_id[a]; kpeter@839: if (_cap[j] >= total) { kpeter@839: arc_vector.push_back(j); kpeter@839: reached[u] = true; kpeter@839: stack.push_back(u); kpeter@839: } kpeter@839: } kpeter@839: } kpeter@839: } else { kpeter@1049: // Find the min. cost incoming arc for each demand node kpeter@839: for (int i = 0; i != int(demand_nodes.size()); ++i) { kpeter@839: Node v = demand_nodes[i]; kpeter@839: Cost c, min_cost = std::numeric_limits::max(); kpeter@839: Arc min_arc = INVALID; kpeter@839: for (InArcIt a(_graph, v); a != INVALID; ++a) { kpeter@839: c = _cost[_arc_id[a]]; kpeter@839: if (c < min_cost) { kpeter@839: min_cost = c; kpeter@839: min_arc = a; kpeter@839: } kpeter@839: } kpeter@839: if (min_arc != INVALID) { kpeter@839: arc_vector.push_back(_arc_id[min_arc]); kpeter@839: } kpeter@839: } kpeter@839: } kpeter@839: } else { kpeter@839: // Find the min. cost outgoing arc for each supply node kpeter@839: for (int i = 0; i != int(supply_nodes.size()); ++i) { kpeter@839: Node u = supply_nodes[i]; kpeter@839: Cost c, min_cost = std::numeric_limits::max(); kpeter@839: Arc min_arc = INVALID; kpeter@839: for (OutArcIt a(_graph, u); a != INVALID; ++a) { kpeter@839: c = _cost[_arc_id[a]]; kpeter@839: if (c < min_cost) { kpeter@839: min_cost = c; kpeter@839: min_arc = a; kpeter@839: } kpeter@839: } kpeter@839: if (min_arc != INVALID) { kpeter@839: arc_vector.push_back(_arc_id[min_arc]); kpeter@839: } kpeter@839: } kpeter@839: } kpeter@839: kpeter@839: // Perform heuristic initial pivots kpeter@839: for (int i = 0; i != int(arc_vector.size()); ++i) { kpeter@839: in_arc = arc_vector[i]; kpeter@839: if (_state[in_arc] * (_cost[in_arc] + _pi[_source[in_arc]] - kpeter@839: _pi[_target[in_arc]]) >= 0) continue; kpeter@839: findJoinNode(); kpeter@839: bool change = findLeavingArc(); kpeter@839: if (delta >= MAX) return false; kpeter@839: changeFlow(change); kpeter@839: if (change) { kpeter@839: updateTreeStructure(); kpeter@839: updatePotential(); kpeter@839: } kpeter@839: } kpeter@839: return true; kpeter@839: } kpeter@839: kpeter@601: // Execute the algorithm kpeter@640: ProblemType start(PivotRule pivot_rule) { kpeter@601: // Select the pivot rule implementation kpeter@601: switch (pivot_rule) { kpeter@605: case FIRST_ELIGIBLE: kpeter@601: return start(); kpeter@605: case BEST_ELIGIBLE: kpeter@601: return start(); kpeter@605: case BLOCK_SEARCH: kpeter@601: return start(); kpeter@605: case CANDIDATE_LIST: kpeter@601: return start(); kpeter@605: case ALTERING_LIST: kpeter@601: return start(); kpeter@601: } kpeter@640: return INFEASIBLE; // avoid warning kpeter@601: } kpeter@601: kpeter@605: template kpeter@640: ProblemType start() { kpeter@605: PivotRuleImpl pivot(*this); kpeter@601: kpeter@839: // Perform heuristic initial pivots kpeter@839: if (!initialPivots()) return UNBOUNDED; kpeter@839: kpeter@605: // Execute the Network Simplex algorithm kpeter@601: while (pivot.findEnteringArc()) { kpeter@601: findJoinNode(); kpeter@601: bool change = findLeavingArc(); kpeter@811: if (delta >= MAX) return UNBOUNDED; kpeter@601: changeFlow(change); kpeter@601: if (change) { kpeter@604: updateTreeStructure(); kpeter@604: updatePotential(); kpeter@601: } kpeter@601: } alpar@877: kpeter@640: // Check feasibility kpeter@663: for (int e = _search_arc_num; e != _all_arc_num; ++e) { kpeter@663: if (_flow[e] != 0) return INFEASIBLE; kpeter@640: } kpeter@601: kpeter@642: // Transform the solution and the supply map to the original form kpeter@642: if (_have_lower) { kpeter@601: for (int i = 0; i != _arc_num; ++i) { kpeter@642: Value c = _lower[i]; kpeter@642: if (c != 0) { kpeter@642: _flow[i] += c; kpeter@642: _supply[_source[i]] += c; kpeter@642: _supply[_target[i]] -= c; kpeter@642: } kpeter@601: } kpeter@601: } alpar@877: kpeter@663: // Shift potentials to meet the requirements of the GEQ/LEQ type kpeter@663: // optimality conditions kpeter@663: if (_sum_supply == 0) { kpeter@663: if (_stype == GEQ) { kpeter@888: Cost max_pot = -std::numeric_limits::max(); kpeter@663: for (int i = 0; i != _node_num; ++i) { kpeter@663: if (_pi[i] > max_pot) max_pot = _pi[i]; kpeter@663: } kpeter@663: if (max_pot > 0) { kpeter@663: for (int i = 0; i != _node_num; ++i) kpeter@663: _pi[i] -= max_pot; kpeter@663: } kpeter@663: } else { kpeter@663: Cost min_pot = std::numeric_limits::max(); kpeter@663: for (int i = 0; i != _node_num; ++i) { kpeter@663: if (_pi[i] < min_pot) min_pot = _pi[i]; kpeter@663: } kpeter@663: if (min_pot < 0) { kpeter@663: for (int i = 0; i != _node_num; ++i) kpeter@663: _pi[i] -= min_pot; kpeter@663: } kpeter@663: } kpeter@663: } kpeter@601: kpeter@640: return OPTIMAL; kpeter@601: } kpeter@601: kpeter@601: }; //class NetworkSimplex kpeter@601: kpeter@601: ///@} kpeter@601: kpeter@601: } //namespace lemon kpeter@601: kpeter@601: #endif //LEMON_NETWORK_SIMPLEX_H