kpeter@593: /* -*- mode: C++; indent-tabs-mode: nil; -*- kpeter@593: * kpeter@593: * This file is a part of LEMON, a generic C++ optimization library. kpeter@593: * kpeter@593: * Copyright (C) 2003-2009 kpeter@593: * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport kpeter@593: * (Egervary Research Group on Combinatorial Optimization, EGRES). kpeter@593: * kpeter@593: * Permission to use, modify and distribute this software is granted kpeter@593: * provided that this copyright notice appears in all copies. For kpeter@593: * precise terms see the accompanying LICENSE file. kpeter@593: * kpeter@593: * This software is provided "AS IS" with no warranty of any kind, kpeter@593: * express or implied, and with no claim as to its suitability for any kpeter@593: * purpose. kpeter@593: * kpeter@593: */ kpeter@593: kpeter@593: #ifndef LEMON_NETWORK_SIMPLEX_H kpeter@593: #define LEMON_NETWORK_SIMPLEX_H kpeter@593: kpeter@661: /// \ingroup min_cost_flow_algs kpeter@593: /// kpeter@593: /// \file kpeter@597: /// \brief Network Simplex algorithm for finding a minimum cost flow. kpeter@593: kpeter@593: #include kpeter@593: #include kpeter@593: #include kpeter@593: kpeter@595: #include kpeter@593: #include kpeter@593: kpeter@593: namespace lemon { kpeter@593: kpeter@661: /// \addtogroup min_cost_flow_algs kpeter@593: /// @{ kpeter@593: kpeter@597: /// \brief Implementation of the primal Network Simplex algorithm kpeter@593: /// for finding a \ref min_cost_flow "minimum cost flow". kpeter@593: /// kpeter@597: /// \ref NetworkSimplex implements the primal Network Simplex algorithm kpeter@593: /// for finding a \ref min_cost_flow "minimum cost flow". kpeter@598: /// This algorithm is a specialized version of the linear programming kpeter@598: /// simplex method directly for the minimum cost flow problem. kpeter@598: /// It is one of the most efficient solution methods. kpeter@598: /// kpeter@598: /// In general this class is the fastest implementation available kpeter@598: /// in LEMON for the minimum cost flow problem. kpeter@636: /// Moreover it supports both directions of the supply/demand inequality kpeter@636: /// constraints. For more information see \ref SupplyType. kpeter@636: /// kpeter@636: /// Most of the parameters of the problem (except for the digraph) kpeter@636: /// can be given using separate functions, and the algorithm can be kpeter@636: /// executed using the \ref run() function. If some parameters are not kpeter@636: /// specified, then default values will be used. kpeter@593: /// kpeter@597: /// \tparam GR The digraph type the algorithm runs on. kpeter@637: /// \tparam V The value type used for flow amounts, capacity bounds kpeter@599: /// and supply values in the algorithm. By default it is \c int. kpeter@599: /// \tparam C The value type used for costs and potentials in the kpeter@637: /// algorithm. By default it is the same as \c V. kpeter@593: /// kpeter@600: /// \warning Both value types must be signed and all input data must kpeter@600: /// be integer. kpeter@593: /// kpeter@597: /// \note %NetworkSimplex provides five different pivot rule kpeter@601: /// implementations, from which the most efficient one is used kpeter@601: /// by default. For more information see \ref PivotRule. kpeter@637: template kpeter@593: class NetworkSimplex kpeter@593: { kpeter@597: public: kpeter@593: kpeter@638: /// The type of the flow amounts, capacity bounds and supply values kpeter@637: typedef V Value; kpeter@638: /// The type of the arc costs kpeter@599: typedef C Cost; kpeter@597: kpeter@597: public: kpeter@597: kpeter@636: /// \brief Problem type constants for the \c run() function. kpeter@597: /// kpeter@636: /// Enum type containing the problem type constants that can be kpeter@636: /// returned by the \ref run() function of the algorithm. kpeter@636: enum ProblemType { kpeter@636: /// The problem has no feasible solution (flow). kpeter@636: INFEASIBLE, kpeter@636: /// The problem has optimal solution (i.e. it is feasible and kpeter@636: /// bounded), and the algorithm has found optimal flow and node kpeter@636: /// potentials (primal and dual solutions). kpeter@636: OPTIMAL, kpeter@636: /// The objective function of the problem is unbounded, i.e. kpeter@636: /// there is a directed cycle having negative total cost and kpeter@636: /// infinite upper bound. kpeter@636: UNBOUNDED kpeter@636: }; kpeter@636: kpeter@636: /// \brief Constants for selecting the type of the supply constraints. kpeter@636: /// kpeter@636: /// Enum type containing constants for selecting the supply type, kpeter@636: /// i.e. the direction of the inequalities in the supply/demand kpeter@636: /// constraints of the \ref min_cost_flow "minimum cost flow problem". kpeter@636: /// kpeter@661: /// The default supply type is \c GEQ, the \c LEQ type can be kpeter@661: /// selected using \ref supplyType(). kpeter@661: /// The equality form is a special case of both supply types. kpeter@636: enum SupplyType { kpeter@636: /// This option means that there are "greater or equal" kpeter@661: /// supply/demand constraints in the definition of the problem. kpeter@636: GEQ, kpeter@636: /// This option means that there are "less or equal" kpeter@661: /// supply/demand constraints in the definition of the problem. kpeter@661: LEQ kpeter@636: }; kpeter@636: kpeter@636: /// \brief Constants for selecting the pivot rule. kpeter@636: /// kpeter@636: /// Enum type containing constants for selecting the pivot rule for kpeter@636: /// the \ref run() function. kpeter@636: /// kpeter@597: /// \ref NetworkSimplex provides five different pivot rule kpeter@597: /// implementations that significantly affect the running time kpeter@597: /// of the algorithm. kpeter@597: /// By default \ref BLOCK_SEARCH "Block Search" is used, which kpeter@597: /// proved to be the most efficient and the most robust on various kpeter@597: /// test inputs according to our benchmark tests. kpeter@597: /// However another pivot rule can be selected using the \ref run() kpeter@597: /// function with the proper parameter. kpeter@597: enum PivotRule { kpeter@597: kpeter@597: /// The First Eligible pivot rule. kpeter@597: /// The next eligible arc is selected in a wraparound fashion kpeter@597: /// in every iteration. kpeter@597: FIRST_ELIGIBLE, kpeter@597: kpeter@597: /// The Best Eligible pivot rule. kpeter@597: /// The best eligible arc is selected in every iteration. kpeter@597: BEST_ELIGIBLE, kpeter@597: kpeter@597: /// The Block Search pivot rule. kpeter@597: /// A specified number of arcs are examined in every iteration kpeter@597: /// in a wraparound fashion and the best eligible arc is selected kpeter@597: /// from this block. kpeter@597: BLOCK_SEARCH, kpeter@597: kpeter@597: /// The Candidate List pivot rule. kpeter@597: /// In a major iteration a candidate list is built from eligible arcs kpeter@597: /// in a wraparound fashion and in the following minor iterations kpeter@597: /// the best eligible arc is selected from this list. kpeter@597: CANDIDATE_LIST, kpeter@597: kpeter@597: /// The Altering Candidate List pivot rule. kpeter@597: /// It is a modified version of the Candidate List method. kpeter@597: /// It keeps only the several best eligible arcs from the former kpeter@597: /// candidate list and extends this list in every iteration. kpeter@597: ALTERING_LIST kpeter@597: }; kpeter@601: kpeter@597: private: kpeter@597: kpeter@597: TEMPLATE_DIGRAPH_TYPEDEFS(GR); kpeter@597: kpeter@593: typedef std::vector ArcVector; kpeter@593: typedef std::vector NodeVector; kpeter@593: typedef std::vector IntVector; kpeter@593: typedef std::vector BoolVector; kpeter@638: typedef std::vector ValueVector; kpeter@599: typedef std::vector CostVector; kpeter@593: kpeter@593: // State constants for arcs kpeter@593: enum ArcStateEnum { kpeter@593: STATE_UPPER = -1, kpeter@593: STATE_TREE = 0, kpeter@593: STATE_LOWER = 1 kpeter@593: }; kpeter@593: kpeter@593: private: kpeter@593: kpeter@597: // Data related to the underlying digraph kpeter@597: const GR &_graph; kpeter@597: int _node_num; kpeter@597: int _arc_num; kpeter@661: int _all_arc_num; kpeter@661: int _search_arc_num; kpeter@597: kpeter@597: // Parameters of the problem kpeter@638: bool _have_lower; kpeter@636: SupplyType _stype; kpeter@637: Value _sum_supply; kpeter@593: kpeter@597: // Data structures for storing the digraph kpeter@595: IntNodeMap _node_id; kpeter@638: IntArcMap _arc_id; kpeter@595: IntVector _source; kpeter@595: IntVector _target; kpeter@595: kpeter@597: // Node and arc data kpeter@638: ValueVector _lower; kpeter@638: ValueVector _upper; kpeter@638: ValueVector _cap; kpeter@599: CostVector _cost; kpeter@638: ValueVector _supply; kpeter@638: ValueVector _flow; kpeter@599: CostVector _pi; kpeter@593: kpeter@595: // Data for storing the spanning tree structure kpeter@593: IntVector _parent; kpeter@593: IntVector _pred; kpeter@593: IntVector _thread; kpeter@596: IntVector _rev_thread; kpeter@596: IntVector _succ_num; kpeter@596: IntVector _last_succ; kpeter@596: IntVector _dirty_revs; kpeter@593: BoolVector _forward; kpeter@593: IntVector _state; kpeter@593: int _root; kpeter@593: kpeter@593: // Temporary data used in the current pivot iteration kpeter@595: int in_arc, join, u_in, v_in, u_out, v_out; kpeter@595: int first, second, right, last; kpeter@593: int stem, par_stem, new_stem; kpeter@637: Value delta; kpeter@593: kpeter@636: public: kpeter@636: kpeter@636: /// \brief Constant for infinite upper bounds (capacities). kpeter@636: /// kpeter@636: /// Constant for infinite upper bounds (capacities). kpeter@637: /// It is \c std::numeric_limits::infinity() if available, kpeter@637: /// \c std::numeric_limits::max() otherwise. kpeter@637: const Value INF; kpeter@636: kpeter@593: private: kpeter@593: kpeter@597: // Implementation of the First Eligible pivot rule kpeter@593: class FirstEligiblePivotRule kpeter@593: { kpeter@593: private: kpeter@593: kpeter@593: // References to the NetworkSimplex class kpeter@593: const IntVector &_source; kpeter@593: const IntVector &_target; kpeter@599: const CostVector &_cost; kpeter@593: const IntVector &_state; kpeter@599: const CostVector &_pi; kpeter@593: int &_in_arc; kpeter@661: int _search_arc_num; kpeter@593: kpeter@593: // Pivot rule data kpeter@593: int _next_arc; kpeter@593: kpeter@593: public: kpeter@593: kpeter@597: // Constructor kpeter@593: FirstEligiblePivotRule(NetworkSimplex &ns) : kpeter@595: _source(ns._source), _target(ns._target), kpeter@593: _cost(ns._cost), _state(ns._state), _pi(ns._pi), kpeter@661: _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), kpeter@661: _next_arc(0) kpeter@593: {} kpeter@593: kpeter@597: // Find next entering arc kpeter@593: bool findEnteringArc() { kpeter@599: Cost c; kpeter@661: for (int e = _next_arc; e < _search_arc_num; ++e) { kpeter@593: c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@593: if (c < 0) { kpeter@593: _in_arc = e; kpeter@593: _next_arc = e + 1; kpeter@593: return true; kpeter@593: } kpeter@593: } kpeter@593: for (int e = 0; e < _next_arc; ++e) { kpeter@593: c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@593: if (c < 0) { kpeter@593: _in_arc = e; kpeter@593: _next_arc = e + 1; kpeter@593: return true; kpeter@593: } kpeter@593: } kpeter@593: return false; kpeter@593: } kpeter@593: kpeter@593: }; //class FirstEligiblePivotRule kpeter@593: kpeter@593: kpeter@597: // Implementation of the Best Eligible pivot rule kpeter@593: class BestEligiblePivotRule kpeter@593: { kpeter@593: private: kpeter@593: kpeter@593: // References to the NetworkSimplex class kpeter@593: const IntVector &_source; kpeter@593: const IntVector &_target; kpeter@599: const CostVector &_cost; kpeter@593: const IntVector &_state; kpeter@599: const CostVector &_pi; kpeter@593: int &_in_arc; kpeter@661: int _search_arc_num; kpeter@593: kpeter@593: public: kpeter@593: kpeter@597: // Constructor kpeter@593: BestEligiblePivotRule(NetworkSimplex &ns) : kpeter@595: _source(ns._source), _target(ns._target), kpeter@593: _cost(ns._cost), _state(ns._state), _pi(ns._pi), kpeter@661: _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num) kpeter@593: {} kpeter@593: kpeter@597: // Find next entering arc kpeter@593: bool findEnteringArc() { kpeter@599: Cost c, min = 0; kpeter@661: for (int e = 0; e < _search_arc_num; ++e) { kpeter@593: c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@593: if (c < min) { kpeter@593: min = c; kpeter@593: _in_arc = e; kpeter@593: } kpeter@593: } kpeter@593: return min < 0; kpeter@593: } kpeter@593: kpeter@593: }; //class BestEligiblePivotRule kpeter@593: kpeter@593: kpeter@597: // Implementation of the Block Search pivot rule kpeter@593: class BlockSearchPivotRule kpeter@593: { kpeter@593: private: kpeter@593: kpeter@593: // References to the NetworkSimplex class kpeter@593: const IntVector &_source; kpeter@593: const IntVector &_target; kpeter@599: const CostVector &_cost; kpeter@593: const IntVector &_state; kpeter@599: const CostVector &_pi; kpeter@593: int &_in_arc; kpeter@661: int _search_arc_num; kpeter@593: kpeter@593: // Pivot rule data kpeter@593: int _block_size; kpeter@593: int _next_arc; kpeter@593: kpeter@593: public: kpeter@593: kpeter@597: // Constructor kpeter@593: BlockSearchPivotRule(NetworkSimplex &ns) : kpeter@595: _source(ns._source), _target(ns._target), kpeter@593: _cost(ns._cost), _state(ns._state), _pi(ns._pi), kpeter@661: _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), kpeter@661: _next_arc(0) kpeter@593: { kpeter@593: // The main parameters of the pivot rule kpeter@661: const double BLOCK_SIZE_FACTOR = 0.5; kpeter@593: const int MIN_BLOCK_SIZE = 10; kpeter@593: alpar@604: _block_size = std::max( int(BLOCK_SIZE_FACTOR * kpeter@661: std::sqrt(double(_search_arc_num))), kpeter@593: MIN_BLOCK_SIZE ); kpeter@593: } kpeter@593: kpeter@597: // Find next entering arc kpeter@593: bool findEnteringArc() { kpeter@599: Cost c, min = 0; kpeter@593: int cnt = _block_size; kpeter@593: int e, min_arc = _next_arc; kpeter@661: for (e = _next_arc; e < _search_arc_num; ++e) { kpeter@593: c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@593: if (c < min) { kpeter@593: min = c; kpeter@593: min_arc = e; kpeter@593: } kpeter@593: if (--cnt == 0) { kpeter@593: if (min < 0) break; kpeter@593: cnt = _block_size; kpeter@593: } kpeter@593: } kpeter@593: if (min == 0 || cnt > 0) { kpeter@593: for (e = 0; e < _next_arc; ++e) { kpeter@593: c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@593: if (c < min) { kpeter@593: min = c; kpeter@593: min_arc = e; kpeter@593: } kpeter@593: if (--cnt == 0) { kpeter@593: if (min < 0) break; kpeter@593: cnt = _block_size; kpeter@593: } kpeter@593: } kpeter@593: } kpeter@593: if (min >= 0) return false; kpeter@593: _in_arc = min_arc; kpeter@593: _next_arc = e; kpeter@593: return true; kpeter@593: } kpeter@593: kpeter@593: }; //class BlockSearchPivotRule kpeter@593: kpeter@593: kpeter@597: // Implementation of the Candidate List pivot rule kpeter@593: class CandidateListPivotRule kpeter@593: { kpeter@593: private: kpeter@593: kpeter@593: // References to the NetworkSimplex class kpeter@593: const IntVector &_source; kpeter@593: const IntVector &_target; kpeter@599: const CostVector &_cost; kpeter@593: const IntVector &_state; kpeter@599: const CostVector &_pi; kpeter@593: int &_in_arc; kpeter@661: int _search_arc_num; kpeter@593: kpeter@593: // Pivot rule data kpeter@593: IntVector _candidates; kpeter@593: int _list_length, _minor_limit; kpeter@593: int _curr_length, _minor_count; kpeter@593: int _next_arc; kpeter@593: kpeter@593: public: kpeter@593: kpeter@593: /// Constructor kpeter@593: CandidateListPivotRule(NetworkSimplex &ns) : kpeter@595: _source(ns._source), _target(ns._target), kpeter@593: _cost(ns._cost), _state(ns._state), _pi(ns._pi), kpeter@661: _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), kpeter@661: _next_arc(0) kpeter@593: { kpeter@593: // The main parameters of the pivot rule kpeter@593: const double LIST_LENGTH_FACTOR = 1.0; kpeter@593: const int MIN_LIST_LENGTH = 10; kpeter@593: const double MINOR_LIMIT_FACTOR = 0.1; kpeter@593: const int MIN_MINOR_LIMIT = 3; kpeter@593: alpar@604: _list_length = std::max( int(LIST_LENGTH_FACTOR * kpeter@661: std::sqrt(double(_search_arc_num))), kpeter@593: MIN_LIST_LENGTH ); kpeter@593: _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length), kpeter@593: MIN_MINOR_LIMIT ); kpeter@593: _curr_length = _minor_count = 0; kpeter@593: _candidates.resize(_list_length); kpeter@593: } kpeter@593: kpeter@593: /// Find next entering arc kpeter@593: bool findEnteringArc() { kpeter@599: Cost min, c; kpeter@593: int e, min_arc = _next_arc; kpeter@593: if (_curr_length > 0 && _minor_count < _minor_limit) { kpeter@593: // Minor iteration: select the best eligible arc from the kpeter@593: // current candidate list kpeter@593: ++_minor_count; kpeter@593: min = 0; kpeter@593: for (int i = 0; i < _curr_length; ++i) { kpeter@593: e = _candidates[i]; kpeter@593: c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@593: if (c < min) { kpeter@593: min = c; kpeter@593: min_arc = e; kpeter@593: } kpeter@593: if (c >= 0) { kpeter@593: _candidates[i--] = _candidates[--_curr_length]; kpeter@593: } kpeter@593: } kpeter@593: if (min < 0) { kpeter@593: _in_arc = min_arc; kpeter@593: return true; kpeter@593: } kpeter@593: } kpeter@593: kpeter@593: // Major iteration: build a new candidate list kpeter@593: min = 0; kpeter@593: _curr_length = 0; kpeter@661: for (e = _next_arc; e < _search_arc_num; ++e) { kpeter@593: c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@593: if (c < 0) { kpeter@593: _candidates[_curr_length++] = e; kpeter@593: if (c < min) { kpeter@593: min = c; kpeter@593: min_arc = e; kpeter@593: } kpeter@593: if (_curr_length == _list_length) break; kpeter@593: } kpeter@593: } kpeter@593: if (_curr_length < _list_length) { kpeter@593: for (e = 0; e < _next_arc; ++e) { kpeter@593: c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@593: if (c < 0) { kpeter@593: _candidates[_curr_length++] = e; kpeter@593: if (c < min) { kpeter@593: min = c; kpeter@593: min_arc = e; kpeter@593: } kpeter@593: if (_curr_length == _list_length) break; kpeter@593: } kpeter@593: } kpeter@593: } kpeter@593: if (_curr_length == 0) return false; kpeter@593: _minor_count = 1; kpeter@593: _in_arc = min_arc; kpeter@593: _next_arc = e; kpeter@593: return true; kpeter@593: } kpeter@593: kpeter@593: }; //class CandidateListPivotRule kpeter@593: kpeter@593: kpeter@597: // Implementation of the Altering Candidate List pivot rule kpeter@593: class AlteringListPivotRule kpeter@593: { kpeter@593: private: kpeter@593: kpeter@593: // References to the NetworkSimplex class kpeter@593: const IntVector &_source; kpeter@593: const IntVector &_target; kpeter@599: const CostVector &_cost; kpeter@593: const IntVector &_state; kpeter@599: const CostVector &_pi; kpeter@593: int &_in_arc; kpeter@661: int _search_arc_num; kpeter@593: kpeter@593: // Pivot rule data kpeter@593: int _block_size, _head_length, _curr_length; kpeter@593: int _next_arc; kpeter@593: IntVector _candidates; kpeter@599: CostVector _cand_cost; kpeter@593: kpeter@593: // Functor class to compare arcs during sort of the candidate list kpeter@593: class SortFunc kpeter@593: { kpeter@593: private: kpeter@599: const CostVector &_map; kpeter@593: public: kpeter@599: SortFunc(const CostVector &map) : _map(map) {} kpeter@593: bool operator()(int left, int right) { kpeter@593: return _map[left] > _map[right]; kpeter@593: } kpeter@593: }; kpeter@593: kpeter@593: SortFunc _sort_func; kpeter@593: kpeter@593: public: kpeter@593: kpeter@597: // Constructor kpeter@593: AlteringListPivotRule(NetworkSimplex &ns) : kpeter@595: _source(ns._source), _target(ns._target), kpeter@593: _cost(ns._cost), _state(ns._state), _pi(ns._pi), kpeter@661: _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), kpeter@661: _next_arc(0), _cand_cost(ns._search_arc_num), _sort_func(_cand_cost) kpeter@593: { kpeter@593: // The main parameters of the pivot rule kpeter@593: const double BLOCK_SIZE_FACTOR = 1.5; kpeter@593: const int MIN_BLOCK_SIZE = 10; kpeter@593: const double HEAD_LENGTH_FACTOR = 0.1; kpeter@593: const int MIN_HEAD_LENGTH = 3; kpeter@593: alpar@604: _block_size = std::max( int(BLOCK_SIZE_FACTOR * kpeter@661: std::sqrt(double(_search_arc_num))), kpeter@593: MIN_BLOCK_SIZE ); kpeter@593: _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size), kpeter@593: MIN_HEAD_LENGTH ); kpeter@593: _candidates.resize(_head_length + _block_size); kpeter@593: _curr_length = 0; kpeter@593: } kpeter@593: kpeter@597: // Find next entering arc kpeter@593: bool findEnteringArc() { kpeter@593: // Check the current candidate list kpeter@593: int e; kpeter@593: for (int i = 0; i < _curr_length; ++i) { kpeter@593: e = _candidates[i]; kpeter@593: _cand_cost[e] = _state[e] * kpeter@593: (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@593: if (_cand_cost[e] >= 0) { kpeter@593: _candidates[i--] = _candidates[--_curr_length]; kpeter@593: } kpeter@593: } kpeter@593: kpeter@593: // Extend the list kpeter@593: int cnt = _block_size; kpeter@595: int last_arc = 0; kpeter@593: int limit = _head_length; kpeter@593: kpeter@661: for (int e = _next_arc; e < _search_arc_num; ++e) { kpeter@593: _cand_cost[e] = _state[e] * kpeter@593: (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@593: if (_cand_cost[e] < 0) { kpeter@593: _candidates[_curr_length++] = e; kpeter@595: last_arc = e; kpeter@593: } kpeter@593: if (--cnt == 0) { kpeter@593: if (_curr_length > limit) break; kpeter@593: limit = 0; kpeter@593: cnt = _block_size; kpeter@593: } kpeter@593: } kpeter@593: if (_curr_length <= limit) { kpeter@593: for (int e = 0; e < _next_arc; ++e) { kpeter@593: _cand_cost[e] = _state[e] * kpeter@593: (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@593: if (_cand_cost[e] < 0) { kpeter@593: _candidates[_curr_length++] = e; kpeter@595: last_arc = e; kpeter@593: } kpeter@593: if (--cnt == 0) { kpeter@593: if (_curr_length > limit) break; kpeter@593: limit = 0; kpeter@593: cnt = _block_size; kpeter@593: } kpeter@593: } kpeter@593: } kpeter@593: if (_curr_length == 0) return false; kpeter@595: _next_arc = last_arc + 1; kpeter@593: kpeter@593: // Make heap of the candidate list (approximating a partial sort) kpeter@593: make_heap( _candidates.begin(), _candidates.begin() + _curr_length, kpeter@593: _sort_func ); kpeter@593: kpeter@593: // Pop the first element of the heap kpeter@593: _in_arc = _candidates[0]; kpeter@593: pop_heap( _candidates.begin(), _candidates.begin() + _curr_length, kpeter@593: _sort_func ); kpeter@593: _curr_length = std::min(_head_length, _curr_length - 1); kpeter@593: return true; kpeter@593: } kpeter@593: kpeter@593: }; //class AlteringListPivotRule kpeter@593: kpeter@593: public: kpeter@593: kpeter@597: /// \brief Constructor. kpeter@593: /// kpeter@601: /// The constructor of the class. kpeter@593: /// kpeter@595: /// \param graph The digraph the algorithm runs on. kpeter@597: NetworkSimplex(const GR& graph) : kpeter@638: _graph(graph), _node_id(graph), _arc_id(graph), kpeter@637: INF(std::numeric_limits::has_infinity ? kpeter@637: std::numeric_limits::infinity() : kpeter@637: std::numeric_limits::max()) kpeter@597: { kpeter@636: // Check the value types kpeter@637: LEMON_ASSERT(std::numeric_limits::is_signed, kpeter@636: "The flow type of NetworkSimplex must be signed"); kpeter@636: LEMON_ASSERT(std::numeric_limits::is_signed, kpeter@636: "The cost type of NetworkSimplex must be signed"); kpeter@638: kpeter@638: // Resize vectors kpeter@638: _node_num = countNodes(_graph); kpeter@638: _arc_num = countArcs(_graph); kpeter@638: int all_node_num = _node_num + 1; kpeter@661: int max_arc_num = _arc_num + 2 * _node_num; kpeter@593: kpeter@661: _source.resize(max_arc_num); kpeter@661: _target.resize(max_arc_num); kpeter@638: kpeter@661: _lower.resize(_arc_num); kpeter@661: _upper.resize(_arc_num); kpeter@661: _cap.resize(max_arc_num); kpeter@661: _cost.resize(max_arc_num); kpeter@638: _supply.resize(all_node_num); kpeter@661: _flow.resize(max_arc_num); kpeter@638: _pi.resize(all_node_num); kpeter@638: kpeter@638: _parent.resize(all_node_num); kpeter@638: _pred.resize(all_node_num); kpeter@638: _forward.resize(all_node_num); kpeter@638: _thread.resize(all_node_num); kpeter@638: _rev_thread.resize(all_node_num); kpeter@638: _succ_num.resize(all_node_num); kpeter@638: _last_succ.resize(all_node_num); kpeter@661: _state.resize(max_arc_num); kpeter@638: kpeter@638: // Copy the graph (store the arcs in a mixed order) kpeter@638: int i = 0; kpeter@638: for (NodeIt n(_graph); n != INVALID; ++n, ++i) { kpeter@638: _node_id[n] = i; kpeter@638: } kpeter@638: int k = std::max(int(std::sqrt(double(_arc_num))), 10); kpeter@638: i = 0; kpeter@638: for (ArcIt a(_graph); a != INVALID; ++a) { kpeter@638: _arc_id[a] = i; kpeter@638: _source[i] = _node_id[_graph.source(a)]; kpeter@638: _target[i] = _node_id[_graph.target(a)]; kpeter@638: if ((i += k) >= _arc_num) i = (i % k) + 1; kpeter@638: } kpeter@638: kpeter@638: // Initialize maps kpeter@638: for (int i = 0; i != _node_num; ++i) { kpeter@638: _supply[i] = 0; kpeter@638: } kpeter@638: for (int i = 0; i != _arc_num; ++i) { kpeter@638: _lower[i] = 0; kpeter@638: _upper[i] = INF; kpeter@638: _cost[i] = 1; kpeter@638: } kpeter@638: _have_lower = false; kpeter@638: _stype = GEQ; kpeter@593: } kpeter@593: kpeter@601: /// \name Parameters kpeter@601: /// The parameters of the algorithm can be specified using these kpeter@601: /// functions. kpeter@601: kpeter@601: /// @{ kpeter@601: kpeter@597: /// \brief Set the lower bounds on the arcs. kpeter@597: /// kpeter@597: /// This function sets the lower bounds on the arcs. kpeter@636: /// If it is not used before calling \ref run(), the lower bounds kpeter@636: /// will be set to zero on all arcs. kpeter@597: /// kpeter@597: /// \param map An arc map storing the lower bounds. kpeter@637: /// Its \c Value type must be convertible to the \c Value type kpeter@597: /// of the algorithm. kpeter@597: /// kpeter@597: /// \return (*this) kpeter@636: template kpeter@636: NetworkSimplex& lowerMap(const LowerMap& map) { kpeter@638: _have_lower = true; kpeter@597: for (ArcIt a(_graph); a != INVALID; ++a) { kpeter@638: _lower[_arc_id[a]] = map[a]; kpeter@597: } kpeter@597: return *this; kpeter@597: } kpeter@597: kpeter@597: /// \brief Set the upper bounds (capacities) on the arcs. kpeter@597: /// kpeter@597: /// This function sets the upper bounds (capacities) on the arcs. kpeter@636: /// If it is not used before calling \ref run(), the upper bounds kpeter@636: /// will be set to \ref INF on all arcs (i.e. the flow value will be kpeter@636: /// unbounded from above on each arc). kpeter@597: /// kpeter@597: /// \param map An arc map storing the upper bounds. kpeter@637: /// Its \c Value type must be convertible to the \c Value type kpeter@597: /// of the algorithm. kpeter@597: /// kpeter@597: /// \return (*this) kpeter@636: template kpeter@636: NetworkSimplex& upperMap(const UpperMap& map) { kpeter@597: for (ArcIt a(_graph); a != INVALID; ++a) { kpeter@638: _upper[_arc_id[a]] = map[a]; kpeter@597: } kpeter@597: return *this; kpeter@597: } kpeter@597: kpeter@597: /// \brief Set the costs of the arcs. kpeter@597: /// kpeter@597: /// This function sets the costs of the arcs. kpeter@597: /// If it is not used before calling \ref run(), the costs kpeter@597: /// will be set to \c 1 on all arcs. kpeter@597: /// kpeter@597: /// \param map An arc map storing the costs. kpeter@599: /// Its \c Value type must be convertible to the \c Cost type kpeter@597: /// of the algorithm. kpeter@597: /// kpeter@597: /// \return (*this) kpeter@636: template kpeter@636: NetworkSimplex& costMap(const CostMap& map) { kpeter@597: for (ArcIt a(_graph); a != INVALID; ++a) { kpeter@638: _cost[_arc_id[a]] = map[a]; kpeter@597: } kpeter@597: return *this; kpeter@597: } kpeter@597: kpeter@597: /// \brief Set the supply values of the nodes. kpeter@597: /// kpeter@597: /// This function sets the supply values of the nodes. kpeter@597: /// If neither this function nor \ref stSupply() is used before kpeter@597: /// calling \ref run(), the supply of each node will be set to zero. kpeter@597: /// (It makes sense only if non-zero lower bounds are given.) kpeter@597: /// kpeter@597: /// \param map A node map storing the supply values. kpeter@637: /// Its \c Value type must be convertible to the \c Value type kpeter@597: /// of the algorithm. kpeter@597: /// kpeter@597: /// \return (*this) kpeter@636: template kpeter@636: NetworkSimplex& supplyMap(const SupplyMap& map) { kpeter@597: for (NodeIt n(_graph); n != INVALID; ++n) { kpeter@638: _supply[_node_id[n]] = map[n]; kpeter@597: } kpeter@597: return *this; kpeter@597: } kpeter@597: kpeter@597: /// \brief Set single source and target nodes and a supply value. kpeter@597: /// kpeter@597: /// This function sets a single source node and a single target node kpeter@597: /// and the required flow value. kpeter@597: /// If neither this function nor \ref supplyMap() is used before kpeter@597: /// calling \ref run(), the supply of each node will be set to zero. kpeter@597: /// (It makes sense only if non-zero lower bounds are given.) kpeter@597: /// kpeter@636: /// Using this function has the same effect as using \ref supplyMap() kpeter@636: /// with such a map in which \c k is assigned to \c s, \c -k is kpeter@636: /// assigned to \c t and all other nodes have zero supply value. kpeter@636: /// kpeter@597: /// \param s The source node. kpeter@597: /// \param t The target node. kpeter@597: /// \param k The required amount of flow from node \c s to node \c t kpeter@597: /// (i.e. the supply of \c s and the demand of \c t). kpeter@597: /// kpeter@597: /// \return (*this) kpeter@637: NetworkSimplex& stSupply(const Node& s, const Node& t, Value k) { kpeter@638: for (int i = 0; i != _node_num; ++i) { kpeter@638: _supply[i] = 0; kpeter@638: } kpeter@638: _supply[_node_id[s]] = k; kpeter@638: _supply[_node_id[t]] = -k; kpeter@597: return *this; kpeter@597: } kpeter@601: kpeter@636: /// \brief Set the type of the supply constraints. kpeter@601: /// kpeter@636: /// This function sets the type of the supply/demand constraints. kpeter@636: /// If it is not used before calling \ref run(), the \ref GEQ supply kpeter@601: /// type will be used. kpeter@601: /// kpeter@636: /// For more information see \ref SupplyType. kpeter@601: /// kpeter@601: /// \return (*this) kpeter@636: NetworkSimplex& supplyType(SupplyType supply_type) { kpeter@636: _stype = supply_type; kpeter@601: return *this; kpeter@601: } kpeter@597: kpeter@601: /// @} kpeter@593: kpeter@597: /// \name Execution Control kpeter@597: /// The algorithm can be executed using \ref run(). kpeter@597: kpeter@593: /// @{ kpeter@593: kpeter@593: /// \brief Run the algorithm. kpeter@593: /// kpeter@593: /// This function runs the algorithm. kpeter@601: /// The paramters can be specified using functions \ref lowerMap(), kpeter@636: /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(), kpeter@638: /// \ref supplyType(). kpeter@601: /// For example, kpeter@597: /// \code kpeter@597: /// NetworkSimplex ns(graph); kpeter@636: /// ns.lowerMap(lower).upperMap(upper).costMap(cost) kpeter@597: /// .supplyMap(sup).run(); kpeter@597: /// \endcode kpeter@593: /// kpeter@598: /// This function can be called more than once. All the parameters kpeter@598: /// that have been given are kept for the next call, unless kpeter@598: /// \ref reset() is called, thus only the modified parameters kpeter@598: /// have to be set again. See \ref reset() for examples. kpeter@638: /// However the underlying digraph must not be modified after this kpeter@638: /// class have been constructed, since it copies and extends the graph. kpeter@598: /// kpeter@597: /// \param pivot_rule The pivot rule that will be used during the kpeter@597: /// algorithm. For more information see \ref PivotRule. kpeter@593: /// kpeter@636: /// \return \c INFEASIBLE if no feasible flow exists, kpeter@636: /// \n \c OPTIMAL if the problem has optimal solution kpeter@636: /// (i.e. it is feasible and bounded), and the algorithm has found kpeter@636: /// optimal flow and node potentials (primal and dual solutions), kpeter@636: /// \n \c UNBOUNDED if the objective function of the problem is kpeter@636: /// unbounded, i.e. there is a directed cycle having negative total kpeter@636: /// cost and infinite upper bound. kpeter@636: /// kpeter@636: /// \see ProblemType, PivotRule kpeter@636: ProblemType run(PivotRule pivot_rule = BLOCK_SEARCH) { kpeter@636: if (!init()) return INFEASIBLE; kpeter@636: return start(pivot_rule); kpeter@593: } kpeter@593: kpeter@598: /// \brief Reset all the parameters that have been given before. kpeter@598: /// kpeter@598: /// This function resets all the paramaters that have been given kpeter@601: /// before using functions \ref lowerMap(), \ref upperMap(), kpeter@638: /// \ref costMap(), \ref supplyMap(), \ref stSupply(), \ref supplyType(). kpeter@598: /// kpeter@598: /// It is useful for multiple run() calls. If this function is not kpeter@598: /// used, all the parameters given before are kept for the next kpeter@598: /// \ref run() call. kpeter@638: /// However the underlying digraph must not be modified after this kpeter@638: /// class have been constructed, since it copies and extends the graph. kpeter@598: /// kpeter@598: /// For example, kpeter@598: /// \code kpeter@598: /// NetworkSimplex ns(graph); kpeter@598: /// kpeter@598: /// // First run kpeter@636: /// ns.lowerMap(lower).upperMap(upper).costMap(cost) kpeter@598: /// .supplyMap(sup).run(); kpeter@598: /// kpeter@598: /// // Run again with modified cost map (reset() is not called, kpeter@598: /// // so only the cost map have to be set again) kpeter@598: /// cost[e] += 100; kpeter@598: /// ns.costMap(cost).run(); kpeter@598: /// kpeter@598: /// // Run again from scratch using reset() kpeter@598: /// // (the lower bounds will be set to zero on all arcs) kpeter@598: /// ns.reset(); kpeter@636: /// ns.upperMap(capacity).costMap(cost) kpeter@598: /// .supplyMap(sup).run(); kpeter@598: /// \endcode kpeter@598: /// kpeter@598: /// \return (*this) kpeter@598: NetworkSimplex& reset() { kpeter@638: for (int i = 0; i != _node_num; ++i) { kpeter@638: _supply[i] = 0; kpeter@638: } kpeter@638: for (int i = 0; i != _arc_num; ++i) { kpeter@638: _lower[i] = 0; kpeter@638: _upper[i] = INF; kpeter@638: _cost[i] = 1; kpeter@638: } kpeter@638: _have_lower = false; kpeter@636: _stype = GEQ; kpeter@598: return *this; kpeter@598: } kpeter@598: kpeter@593: /// @} kpeter@593: kpeter@593: /// \name Query Functions kpeter@593: /// The results of the algorithm can be obtained using these kpeter@593: /// functions.\n kpeter@597: /// The \ref run() function must be called before using them. kpeter@597: kpeter@593: /// @{ kpeter@593: kpeter@597: /// \brief Return the total cost of the found flow. kpeter@597: /// kpeter@597: /// This function returns the total cost of the found flow. kpeter@636: /// Its complexity is O(e). kpeter@597: /// kpeter@597: /// \note The return type of the function can be specified as a kpeter@597: /// template parameter. For example, kpeter@597: /// \code kpeter@597: /// ns.totalCost(); kpeter@597: /// \endcode kpeter@599: /// It is useful if the total cost cannot be stored in the \c Cost kpeter@597: /// type of the algorithm, which is the default return type of the kpeter@597: /// function. kpeter@597: /// kpeter@597: /// \pre \ref run() must be called before using this function. kpeter@638: template kpeter@638: Number totalCost() const { kpeter@638: Number c = 0; kpeter@638: for (ArcIt a(_graph); a != INVALID; ++a) { kpeter@638: int i = _arc_id[a]; kpeter@638: c += Number(_flow[i]) * Number(_cost[i]); kpeter@597: } kpeter@597: return c; kpeter@597: } kpeter@597: kpeter@597: #ifndef DOXYGEN kpeter@599: Cost totalCost() const { kpeter@599: return totalCost(); kpeter@597: } kpeter@597: #endif kpeter@597: kpeter@597: /// \brief Return the flow on the given arc. kpeter@597: /// kpeter@597: /// This function returns the flow on the given arc. kpeter@597: /// kpeter@597: /// \pre \ref run() must be called before using this function. kpeter@637: Value flow(const Arc& a) const { kpeter@638: return _flow[_arc_id[a]]; kpeter@597: } kpeter@597: kpeter@638: /// \brief Return the flow map (the primal solution). kpeter@593: /// kpeter@638: /// This function copies the flow value on each arc into the given kpeter@638: /// map. The \c Value type of the algorithm must be convertible to kpeter@638: /// the \c Value type of the map. kpeter@593: /// kpeter@593: /// \pre \ref run() must be called before using this function. kpeter@638: template kpeter@638: void flowMap(FlowMap &map) const { kpeter@638: for (ArcIt a(_graph); a != INVALID; ++a) { kpeter@638: map.set(a, _flow[_arc_id[a]]); kpeter@638: } kpeter@593: } kpeter@593: kpeter@597: /// \brief Return the potential (dual value) of the given node. kpeter@597: /// kpeter@597: /// This function returns the potential (dual value) of the kpeter@597: /// given node. kpeter@597: /// kpeter@597: /// \pre \ref run() must be called before using this function. kpeter@599: Cost potential(const Node& n) const { kpeter@638: return _pi[_node_id[n]]; kpeter@597: } kpeter@597: kpeter@638: /// \brief Return the potential map (the dual solution). kpeter@593: /// kpeter@638: /// This function copies the potential (dual value) of each node kpeter@638: /// into the given map. kpeter@638: /// The \c Cost type of the algorithm must be convertible to the kpeter@638: /// \c Value type of the map. kpeter@593: /// kpeter@593: /// \pre \ref run() must be called before using this function. kpeter@638: template kpeter@638: void potentialMap(PotentialMap &map) const { kpeter@638: for (NodeIt n(_graph); n != INVALID; ++n) { kpeter@638: map.set(n, _pi[_node_id[n]]); kpeter@638: } kpeter@593: } kpeter@593: kpeter@593: /// @} kpeter@593: kpeter@593: private: kpeter@593: kpeter@593: // Initialize internal data structures kpeter@593: bool init() { kpeter@597: if (_node_num == 0) return false; kpeter@593: kpeter@638: // Check the sum of supply values kpeter@638: _sum_supply = 0; kpeter@638: for (int i = 0; i != _node_num; ++i) { kpeter@638: _sum_supply += _supply[i]; kpeter@638: } alpar@639: if ( !((_stype == GEQ && _sum_supply <= 0) || alpar@639: (_stype == LEQ && _sum_supply >= 0)) ) return false; kpeter@593: kpeter@638: // Remove non-zero lower bounds kpeter@638: if (_have_lower) { kpeter@638: for (int i = 0; i != _arc_num; ++i) { kpeter@638: Value c = _lower[i]; kpeter@638: if (c >= 0) { kpeter@638: _cap[i] = _upper[i] < INF ? _upper[i] - c : INF; kpeter@638: } else { kpeter@638: _cap[i] = _upper[i] < INF + c ? _upper[i] - c : INF; kpeter@638: } kpeter@638: _supply[_source[i]] -= c; kpeter@638: _supply[_target[i]] += c; kpeter@638: } kpeter@638: } else { kpeter@638: for (int i = 0; i != _arc_num; ++i) { kpeter@638: _cap[i] = _upper[i]; kpeter@638: } kpeter@597: } kpeter@593: kpeter@601: // Initialize artifical cost kpeter@636: Cost ART_COST; kpeter@601: if (std::numeric_limits::is_exact) { kpeter@661: ART_COST = std::numeric_limits::max() / 2 + 1; kpeter@601: } else { kpeter@729: ART_COST = 0; kpeter@601: for (int i = 0; i != _arc_num; ++i) { kpeter@636: if (_cost[i] > ART_COST) ART_COST = _cost[i]; kpeter@601: } kpeter@636: ART_COST = (ART_COST + 1) * _node_num; kpeter@601: } kpeter@601: kpeter@638: // Initialize arc maps kpeter@638: for (int i = 0; i != _arc_num; ++i) { kpeter@638: _flow[i] = 0; kpeter@638: _state[i] = STATE_LOWER; kpeter@638: } kpeter@638: kpeter@593: // Set data for the artificial root node kpeter@593: _root = _node_num; kpeter@593: _parent[_root] = -1; kpeter@593: _pred[_root] = -1; kpeter@593: _thread[_root] = 0; kpeter@596: _rev_thread[0] = _root; kpeter@638: _succ_num[_root] = _node_num + 1; kpeter@596: _last_succ[_root] = _root - 1; kpeter@636: _supply[_root] = -_sum_supply; kpeter@661: _pi[_root] = 0; kpeter@593: kpeter@593: // Add artificial arcs and initialize the spanning tree data structure kpeter@661: if (_sum_supply == 0) { kpeter@661: // EQ supply constraints kpeter@661: _search_arc_num = _arc_num; kpeter@661: _all_arc_num = _arc_num + _node_num; kpeter@661: for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { kpeter@661: _parent[u] = _root; kpeter@661: _pred[u] = e; kpeter@661: _thread[u] = u + 1; kpeter@661: _rev_thread[u + 1] = u; kpeter@661: _succ_num[u] = 1; kpeter@661: _last_succ[u] = u; kpeter@661: _cap[e] = INF; kpeter@661: _state[e] = STATE_TREE; kpeter@661: if (_supply[u] >= 0) { kpeter@661: _forward[u] = true; kpeter@661: _pi[u] = 0; kpeter@661: _source[e] = u; kpeter@661: _target[e] = _root; kpeter@661: _flow[e] = _supply[u]; kpeter@661: _cost[e] = 0; kpeter@661: } else { kpeter@661: _forward[u] = false; kpeter@661: _pi[u] = ART_COST; kpeter@661: _source[e] = _root; kpeter@661: _target[e] = u; kpeter@661: _flow[e] = -_supply[u]; kpeter@661: _cost[e] = ART_COST; kpeter@661: } kpeter@593: } kpeter@593: } kpeter@661: else if (_sum_supply > 0) { kpeter@661: // LEQ supply constraints kpeter@661: _search_arc_num = _arc_num + _node_num; kpeter@661: int f = _arc_num + _node_num; kpeter@661: for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { kpeter@661: _parent[u] = _root; kpeter@661: _thread[u] = u + 1; kpeter@661: _rev_thread[u + 1] = u; kpeter@661: _succ_num[u] = 1; kpeter@661: _last_succ[u] = u; kpeter@661: if (_supply[u] >= 0) { kpeter@661: _forward[u] = true; kpeter@661: _pi[u] = 0; kpeter@661: _pred[u] = e; kpeter@661: _source[e] = u; kpeter@661: _target[e] = _root; kpeter@661: _cap[e] = INF; kpeter@661: _flow[e] = _supply[u]; kpeter@661: _cost[e] = 0; kpeter@661: _state[e] = STATE_TREE; kpeter@661: } else { kpeter@661: _forward[u] = false; kpeter@661: _pi[u] = ART_COST; kpeter@661: _pred[u] = f; kpeter@661: _source[f] = _root; kpeter@661: _target[f] = u; kpeter@661: _cap[f] = INF; kpeter@661: _flow[f] = -_supply[u]; kpeter@661: _cost[f] = ART_COST; kpeter@661: _state[f] = STATE_TREE; kpeter@661: _source[e] = u; kpeter@661: _target[e] = _root; kpeter@661: _cap[e] = INF; kpeter@661: _flow[e] = 0; kpeter@661: _cost[e] = 0; kpeter@661: _state[e] = STATE_LOWER; kpeter@661: ++f; kpeter@661: } kpeter@661: } kpeter@661: _all_arc_num = f; kpeter@661: } kpeter@661: else { kpeter@661: // GEQ supply constraints kpeter@661: _search_arc_num = _arc_num + _node_num; kpeter@661: int f = _arc_num + _node_num; kpeter@661: for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { kpeter@661: _parent[u] = _root; kpeter@661: _thread[u] = u + 1; kpeter@661: _rev_thread[u + 1] = u; kpeter@661: _succ_num[u] = 1; kpeter@661: _last_succ[u] = u; kpeter@661: if (_supply[u] <= 0) { kpeter@661: _forward[u] = false; kpeter@661: _pi[u] = 0; kpeter@661: _pred[u] = e; kpeter@661: _source[e] = _root; kpeter@661: _target[e] = u; kpeter@661: _cap[e] = INF; kpeter@661: _flow[e] = -_supply[u]; kpeter@661: _cost[e] = 0; kpeter@661: _state[e] = STATE_TREE; kpeter@661: } else { kpeter@661: _forward[u] = true; kpeter@661: _pi[u] = -ART_COST; kpeter@661: _pred[u] = f; kpeter@661: _source[f] = u; kpeter@661: _target[f] = _root; kpeter@661: _cap[f] = INF; kpeter@661: _flow[f] = _supply[u]; kpeter@661: _state[f] = STATE_TREE; kpeter@661: _cost[f] = ART_COST; kpeter@661: _source[e] = _root; kpeter@661: _target[e] = u; kpeter@661: _cap[e] = INF; kpeter@661: _flow[e] = 0; kpeter@661: _cost[e] = 0; kpeter@661: _state[e] = STATE_LOWER; kpeter@661: ++f; kpeter@661: } kpeter@661: } kpeter@661: _all_arc_num = f; kpeter@661: } kpeter@593: kpeter@593: return true; kpeter@593: } kpeter@593: kpeter@593: // Find the join node kpeter@593: void findJoinNode() { kpeter@595: int u = _source[in_arc]; kpeter@595: int v = _target[in_arc]; kpeter@593: while (u != v) { kpeter@596: if (_succ_num[u] < _succ_num[v]) { kpeter@596: u = _parent[u]; kpeter@596: } else { kpeter@596: v = _parent[v]; kpeter@596: } kpeter@593: } kpeter@593: join = u; kpeter@593: } kpeter@593: kpeter@593: // Find the leaving arc of the cycle and returns true if the kpeter@593: // leaving arc is not the same as the entering arc kpeter@593: bool findLeavingArc() { kpeter@593: // Initialize first and second nodes according to the direction kpeter@593: // of the cycle kpeter@595: if (_state[in_arc] == STATE_LOWER) { kpeter@595: first = _source[in_arc]; kpeter@595: second = _target[in_arc]; kpeter@593: } else { kpeter@595: first = _target[in_arc]; kpeter@595: second = _source[in_arc]; kpeter@593: } kpeter@595: delta = _cap[in_arc]; kpeter@593: int result = 0; kpeter@637: Value d; kpeter@593: int e; kpeter@593: kpeter@593: // Search the cycle along the path form the first node to the root kpeter@593: for (int u = first; u != join; u = _parent[u]) { kpeter@593: e = _pred[u]; kpeter@636: d = _forward[u] ? kpeter@636: _flow[e] : (_cap[e] == INF ? INF : _cap[e] - _flow[e]); kpeter@593: if (d < delta) { kpeter@593: delta = d; kpeter@593: u_out = u; kpeter@593: result = 1; kpeter@593: } kpeter@593: } kpeter@593: // Search the cycle along the path form the second node to the root kpeter@593: for (int u = second; u != join; u = _parent[u]) { kpeter@593: e = _pred[u]; kpeter@636: d = _forward[u] ? kpeter@636: (_cap[e] == INF ? INF : _cap[e] - _flow[e]) : _flow[e]; kpeter@593: if (d <= delta) { kpeter@593: delta = d; kpeter@593: u_out = u; kpeter@593: result = 2; kpeter@593: } kpeter@593: } kpeter@593: kpeter@593: if (result == 1) { kpeter@593: u_in = first; kpeter@593: v_in = second; kpeter@593: } else { kpeter@593: u_in = second; kpeter@593: v_in = first; kpeter@593: } kpeter@593: return result != 0; kpeter@593: } kpeter@593: kpeter@593: // Change _flow and _state vectors kpeter@593: void changeFlow(bool change) { kpeter@593: // Augment along the cycle kpeter@593: if (delta > 0) { kpeter@637: Value val = _state[in_arc] * delta; kpeter@595: _flow[in_arc] += val; kpeter@595: for (int u = _source[in_arc]; u != join; u = _parent[u]) { kpeter@593: _flow[_pred[u]] += _forward[u] ? -val : val; kpeter@593: } kpeter@595: for (int u = _target[in_arc]; u != join; u = _parent[u]) { kpeter@593: _flow[_pred[u]] += _forward[u] ? val : -val; kpeter@593: } kpeter@593: } kpeter@593: // Update the state of the entering and leaving arcs kpeter@593: if (change) { kpeter@595: _state[in_arc] = STATE_TREE; kpeter@593: _state[_pred[u_out]] = kpeter@593: (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER; kpeter@593: } else { kpeter@595: _state[in_arc] = -_state[in_arc]; kpeter@593: } kpeter@593: } kpeter@593: kpeter@596: // Update the tree structure kpeter@596: void updateTreeStructure() { kpeter@596: int u, w; kpeter@596: int old_rev_thread = _rev_thread[u_out]; kpeter@596: int old_succ_num = _succ_num[u_out]; kpeter@596: int old_last_succ = _last_succ[u_out]; kpeter@593: v_out = _parent[u_out]; kpeter@593: kpeter@596: u = _last_succ[u_in]; // the last successor of u_in kpeter@596: right = _thread[u]; // the node after it kpeter@596: kpeter@596: // Handle the case when old_rev_thread equals to v_in kpeter@596: // (it also means that join and v_out coincide) kpeter@596: if (old_rev_thread == v_in) { kpeter@596: last = _thread[_last_succ[u_out]]; kpeter@596: } else { kpeter@596: last = _thread[v_in]; kpeter@593: } kpeter@593: kpeter@596: // Update _thread and _parent along the stem nodes (i.e. the nodes kpeter@596: // between u_in and u_out, whose parent have to be changed) kpeter@593: _thread[v_in] = stem = u_in; kpeter@596: _dirty_revs.clear(); kpeter@596: _dirty_revs.push_back(v_in); kpeter@593: par_stem = v_in; kpeter@593: while (stem != u_out) { kpeter@596: // Insert the next stem node into the thread list kpeter@596: new_stem = _parent[stem]; kpeter@596: _thread[u] = new_stem; kpeter@596: _dirty_revs.push_back(u); kpeter@593: kpeter@596: // Remove the subtree of stem from the thread list kpeter@596: w = _rev_thread[stem]; kpeter@596: _thread[w] = right; kpeter@596: _rev_thread[right] = w; kpeter@593: kpeter@596: // Change the parent node and shift stem nodes kpeter@593: _parent[stem] = par_stem; kpeter@593: par_stem = stem; kpeter@593: stem = new_stem; kpeter@593: kpeter@596: // Update u and right kpeter@596: u = _last_succ[stem] == _last_succ[par_stem] ? kpeter@596: _rev_thread[par_stem] : _last_succ[stem]; kpeter@593: right = _thread[u]; kpeter@593: } kpeter@593: _parent[u_out] = par_stem; kpeter@593: _thread[u] = last; kpeter@596: _rev_thread[last] = u; kpeter@596: _last_succ[u_out] = u; kpeter@593: kpeter@596: // Remove the subtree of u_out from the thread list except for kpeter@596: // the case when old_rev_thread equals to v_in kpeter@596: // (it also means that join and v_out coincide) kpeter@596: if (old_rev_thread != v_in) { kpeter@596: _thread[old_rev_thread] = right; kpeter@596: _rev_thread[right] = old_rev_thread; kpeter@596: } kpeter@596: kpeter@596: // Update _rev_thread using the new _thread values kpeter@596: for (int i = 0; i < int(_dirty_revs.size()); ++i) { kpeter@596: u = _dirty_revs[i]; kpeter@596: _rev_thread[_thread[u]] = u; kpeter@596: } kpeter@596: kpeter@596: // Update _pred, _forward, _last_succ and _succ_num for the kpeter@596: // stem nodes from u_out to u_in kpeter@596: int tmp_sc = 0, tmp_ls = _last_succ[u_out]; kpeter@596: u = u_out; kpeter@596: while (u != u_in) { kpeter@596: w = _parent[u]; kpeter@596: _pred[u] = _pred[w]; kpeter@596: _forward[u] = !_forward[w]; kpeter@596: tmp_sc += _succ_num[u] - _succ_num[w]; kpeter@596: _succ_num[u] = tmp_sc; kpeter@596: _last_succ[w] = tmp_ls; kpeter@596: u = w; kpeter@596: } kpeter@596: _pred[u_in] = in_arc; kpeter@596: _forward[u_in] = (u_in == _source[in_arc]); kpeter@596: _succ_num[u_in] = old_succ_num; kpeter@596: kpeter@596: // Set limits for updating _last_succ form v_in and v_out kpeter@596: // towards the root kpeter@596: int up_limit_in = -1; kpeter@596: int up_limit_out = -1; kpeter@596: if (_last_succ[join] == v_in) { kpeter@596: up_limit_out = join; kpeter@593: } else { kpeter@596: up_limit_in = join; kpeter@596: } kpeter@596: kpeter@596: // Update _last_succ from v_in towards the root kpeter@596: for (u = v_in; u != up_limit_in && _last_succ[u] == v_in; kpeter@596: u = _parent[u]) { kpeter@596: _last_succ[u] = _last_succ[u_out]; kpeter@596: } kpeter@596: // Update _last_succ from v_out towards the root kpeter@596: if (join != old_rev_thread && v_in != old_rev_thread) { kpeter@596: for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; kpeter@596: u = _parent[u]) { kpeter@596: _last_succ[u] = old_rev_thread; kpeter@596: } kpeter@596: } else { kpeter@596: for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; kpeter@596: u = _parent[u]) { kpeter@596: _last_succ[u] = _last_succ[u_out]; kpeter@596: } kpeter@596: } kpeter@596: kpeter@596: // Update _succ_num from v_in to join kpeter@596: for (u = v_in; u != join; u = _parent[u]) { kpeter@596: _succ_num[u] += old_succ_num; kpeter@596: } kpeter@596: // Update _succ_num from v_out to join kpeter@596: for (u = v_out; u != join; u = _parent[u]) { kpeter@596: _succ_num[u] -= old_succ_num; kpeter@593: } kpeter@593: } kpeter@593: kpeter@596: // Update potentials kpeter@596: void updatePotential() { kpeter@599: Cost sigma = _forward[u_in] ? kpeter@593: _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] : kpeter@593: _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]]; kpeter@600: // Update potentials in the subtree, which has been moved kpeter@600: int end = _thread[_last_succ[u_in]]; kpeter@600: for (int u = u_in; u != end; u = _thread[u]) { kpeter@600: _pi[u] += sigma; kpeter@593: } kpeter@593: } kpeter@593: kpeter@593: // Execute the algorithm kpeter@636: ProblemType start(PivotRule pivot_rule) { kpeter@593: // Select the pivot rule implementation kpeter@593: switch (pivot_rule) { kpeter@597: case FIRST_ELIGIBLE: kpeter@593: return start(); kpeter@597: case BEST_ELIGIBLE: kpeter@593: return start(); kpeter@597: case BLOCK_SEARCH: kpeter@593: return start(); kpeter@597: case CANDIDATE_LIST: kpeter@593: return start(); kpeter@597: case ALTERING_LIST: kpeter@593: return start(); kpeter@593: } kpeter@636: return INFEASIBLE; // avoid warning kpeter@593: } kpeter@593: kpeter@597: template kpeter@636: ProblemType start() { kpeter@597: PivotRuleImpl pivot(*this); kpeter@593: kpeter@597: // Execute the Network Simplex algorithm kpeter@593: while (pivot.findEnteringArc()) { kpeter@593: findJoinNode(); kpeter@593: bool change = findLeavingArc(); kpeter@636: if (delta >= INF) return UNBOUNDED; kpeter@593: changeFlow(change); kpeter@593: if (change) { kpeter@596: updateTreeStructure(); kpeter@596: updatePotential(); kpeter@593: } kpeter@593: } kpeter@636: kpeter@636: // Check feasibility kpeter@661: for (int e = _search_arc_num; e != _all_arc_num; ++e) { kpeter@661: if (_flow[e] != 0) return INFEASIBLE; kpeter@636: } kpeter@593: kpeter@638: // Transform the solution and the supply map to the original form kpeter@638: if (_have_lower) { kpeter@593: for (int i = 0; i != _arc_num; ++i) { kpeter@638: Value c = _lower[i]; kpeter@638: if (c != 0) { kpeter@638: _flow[i] += c; kpeter@638: _supply[_source[i]] += c; kpeter@638: _supply[_target[i]] -= c; kpeter@638: } kpeter@593: } kpeter@593: } kpeter@661: kpeter@661: // Shift potentials to meet the requirements of the GEQ/LEQ type kpeter@661: // optimality conditions kpeter@661: if (_sum_supply == 0) { kpeter@661: if (_stype == GEQ) { kpeter@729: Cost max_pot = -std::numeric_limits::max(); kpeter@661: for (int i = 0; i != _node_num; ++i) { kpeter@661: if (_pi[i] > max_pot) max_pot = _pi[i]; kpeter@661: } kpeter@661: if (max_pot > 0) { kpeter@661: for (int i = 0; i != _node_num; ++i) kpeter@661: _pi[i] -= max_pot; kpeter@661: } kpeter@661: } else { kpeter@661: Cost min_pot = std::numeric_limits::max(); kpeter@661: for (int i = 0; i != _node_num; ++i) { kpeter@661: if (_pi[i] < min_pot) min_pot = _pi[i]; kpeter@661: } kpeter@661: if (min_pot < 0) { kpeter@661: for (int i = 0; i != _node_num; ++i) kpeter@661: _pi[i] -= min_pot; kpeter@661: } kpeter@661: } kpeter@661: } kpeter@593: kpeter@636: return OPTIMAL; kpeter@593: } kpeter@593: kpeter@593: }; //class NetworkSimplex kpeter@593: kpeter@593: ///@} kpeter@593: kpeter@593: } //namespace lemon kpeter@593: kpeter@593: #endif //LEMON_NETWORK_SIMPLEX_H