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: * kpeter@601: * Copyright (C) 2003-2009 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@601: /// \ingroup min_cost_flow 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@609: #include kpeter@609: #include kpeter@609: #include kpeter@601: kpeter@601: namespace lemon { kpeter@601: kpeter@601: /// \addtogroup min_cost_flow 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@601: /// for finding a \ref min_cost_flow "minimum cost flow". kpeter@606: /// This algorithm is a specialized version of the linear programming kpeter@606: /// simplex method directly for the minimum cost flow problem. kpeter@606: /// It is one of the most efficient solution methods. kpeter@606: /// kpeter@606: /// In general this class is the fastest implementation available kpeter@606: /// in LEMON for the minimum cost flow problem. kpeter@609: /// Moreover it supports both direction of the supply/demand inequality kpeter@609: /// constraints. For more information see \ref ProblemType. kpeter@601: /// kpeter@605: /// \tparam GR The digraph type the algorithm runs on. kpeter@607: /// \tparam F The value type used for flow amounts, capacity bounds kpeter@607: /// and supply values in the algorithm. By default it is \c int. kpeter@607: /// \tparam C The value type used for costs and potentials in the kpeter@607: /// algorithm. By default it is the same as \c F. kpeter@601: /// kpeter@608: /// \warning Both value types must be signed and all input data 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@609: /// by default. For more information see \ref PivotRule. kpeter@607: template kpeter@601: class NetworkSimplex kpeter@601: { kpeter@605: public: kpeter@601: kpeter@607: /// The flow type of the algorithm kpeter@607: typedef F Flow; kpeter@607: /// The cost type of the algorithm kpeter@607: typedef C Cost; kpeter@609: #ifdef DOXYGEN kpeter@609: /// The type of the flow map kpeter@609: typedef GR::ArcMap FlowMap; kpeter@609: /// The type of the potential map kpeter@609: typedef GR::NodeMap PotentialMap; kpeter@609: #else kpeter@605: /// The type of the flow map kpeter@607: typedef typename GR::template ArcMap FlowMap; kpeter@605: /// The type of the potential map kpeter@607: typedef typename GR::template NodeMap PotentialMap; kpeter@609: #endif kpeter@605: kpeter@605: public: kpeter@605: kpeter@605: /// \brief Enum type for selecting the pivot rule. kpeter@605: /// kpeter@605: /// Enum type for selecting the pivot rule for the \ref run() kpeter@605: /// function. kpeter@605: /// kpeter@605: /// \ref NetworkSimplex provides five different pivot rule kpeter@605: /// implementations that significantly affect the running time kpeter@605: /// of the algorithm. kpeter@605: /// By default \ref BLOCK_SEARCH "Block Search" is used, which kpeter@605: /// proved to be the most efficient and the most robust on various kpeter@605: /// test inputs according to our benchmark tests. kpeter@605: /// However another pivot rule can be selected using the \ref run() kpeter@605: /// function with the proper parameter. kpeter@605: enum PivotRule { kpeter@605: kpeter@605: /// The First 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@605: /// The Best Eligible pivot rule. kpeter@605: /// The best eligible arc is selected in every iteration. kpeter@605: BEST_ELIGIBLE, kpeter@605: kpeter@605: /// The Block 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@605: /// The Candidate 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@605: /// The Altering Candidate List pivot rule. kpeter@605: /// It is a modified version of the Candidate List method. kpeter@605: /// It keeps only the several best eligible arcs from the former kpeter@605: /// candidate list and extends this list in every iteration. kpeter@605: ALTERING_LIST kpeter@605: }; kpeter@609: kpeter@609: /// \brief Enum type for selecting the problem type. kpeter@609: /// kpeter@609: /// Enum type for selecting the problem type, i.e. the direction of kpeter@609: /// the inequalities in the supply/demand constraints of the kpeter@609: /// \ref min_cost_flow "minimum cost flow problem". kpeter@609: /// kpeter@609: /// The default problem type is \c GEQ, since this form is supported kpeter@609: /// by other minimum cost flow algorithms and the \ref Circulation kpeter@609: /// algorithm as well. kpeter@609: /// The \c LEQ problem type can be selected using the \ref problemType() kpeter@609: /// function. kpeter@609: /// kpeter@609: /// Note that the equality form is a special case of both problem type. kpeter@609: enum ProblemType { kpeter@609: kpeter@609: /// This option means that there are "greater or equal" kpeter@609: /// constraints in the defintion, i.e. the exact formulation of the kpeter@609: /// problem is the following. kpeter@609: /** kpeter@609: \f[ \min\sum_{uv\in A} f(uv) \cdot cost(uv) \f] kpeter@609: \f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \geq kpeter@609: sup(u) \quad \forall u\in V \f] kpeter@609: \f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f] kpeter@609: */ kpeter@609: /// It means that the total demand must be greater or equal to the kpeter@609: /// total supply (i.e. \f$\sum_{u\in V} sup(u)\f$ must be zero or kpeter@609: /// negative) and all the supplies have to be carried out from kpeter@609: /// the supply nodes, but there could be demands that are not kpeter@609: /// satisfied. kpeter@609: GEQ, kpeter@609: /// It is just an alias for the \c GEQ option. kpeter@609: CARRY_SUPPLIES = GEQ, kpeter@609: kpeter@609: /// This option means that there are "less or equal" kpeter@609: /// constraints in the defintion, i.e. the exact formulation of the kpeter@609: /// problem is the following. kpeter@609: /** kpeter@609: \f[ \min\sum_{uv\in A} f(uv) \cdot cost(uv) \f] kpeter@609: \f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \leq kpeter@609: sup(u) \quad \forall u\in V \f] kpeter@609: \f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f] kpeter@609: */ kpeter@609: /// It means that the total demand must be less or equal to the kpeter@609: /// total supply (i.e. \f$\sum_{u\in V} sup(u)\f$ must be zero or kpeter@609: /// positive) and all the demands have to be satisfied, but there kpeter@609: /// could be supplies that are not carried out from the supply kpeter@609: /// nodes. kpeter@609: LEQ, kpeter@609: /// It is just an alias for the \c LEQ option. kpeter@609: SATISFY_DEMANDS = LEQ kpeter@609: }; kpeter@605: kpeter@605: private: kpeter@605: kpeter@605: TEMPLATE_DIGRAPH_TYPEDEFS(GR); kpeter@605: kpeter@607: typedef typename GR::template ArcMap FlowArcMap; kpeter@607: typedef typename GR::template ArcMap CostArcMap; kpeter@607: typedef typename GR::template NodeMap FlowNodeMap; kpeter@601: kpeter@601: typedef std::vector ArcVector; kpeter@601: typedef std::vector NodeVector; kpeter@601: typedef std::vector IntVector; kpeter@601: typedef std::vector BoolVector; kpeter@607: typedef std::vector FlowVector; kpeter@607: typedef std::vector CostVector; kpeter@601: kpeter@601: // State constants for arcs kpeter@601: enum ArcStateEnum { kpeter@601: STATE_UPPER = -1, kpeter@601: STATE_TREE = 0, kpeter@601: STATE_LOWER = 1 kpeter@601: }; kpeter@601: 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@605: kpeter@605: // Parameters of the problem kpeter@607: FlowArcMap *_plower; kpeter@607: FlowArcMap *_pupper; kpeter@607: CostArcMap *_pcost; kpeter@607: FlowNodeMap *_psupply; kpeter@605: bool _pstsup; kpeter@605: Node _psource, _ptarget; kpeter@607: Flow _pstflow; kpeter@609: ProblemType _ptype; kpeter@601: kpeter@601: // Result maps kpeter@603: FlowMap *_flow_map; kpeter@603: PotentialMap *_potential_map; kpeter@601: bool _local_flow; kpeter@601: bool _local_potential; kpeter@601: kpeter@605: // Data structures for storing the digraph kpeter@603: IntNodeMap _node_id; kpeter@603: ArcVector _arc_ref; kpeter@603: IntVector _source; kpeter@603: IntVector _target; kpeter@603: kpeter@605: // Node and arc data kpeter@607: FlowVector _cap; kpeter@607: CostVector _cost; kpeter@607: FlowVector _supply; kpeter@607: FlowVector _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@604: IntVector _dirty_revs; kpeter@601: BoolVector _forward; kpeter@601: IntVector _state; 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@603: int first, second, right, last; kpeter@601: int stem, par_stem, new_stem; kpeter@607: Flow delta; kpeter@601: 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@601: const IntVector &_state; kpeter@607: const CostVector &_pi; kpeter@601: int &_in_arc; kpeter@601: int _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@603: _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0) kpeter@601: {} kpeter@601: kpeter@605: // Find next entering arc kpeter@601: bool findEnteringArc() { kpeter@607: Cost c; kpeter@601: for (int e = _next_arc; e < _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@601: 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@601: const IntVector &_state; kpeter@607: const CostVector &_pi; kpeter@601: int &_in_arc; kpeter@601: int _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@603: _in_arc(ns.in_arc), _arc_num(ns._arc_num) kpeter@601: {} kpeter@601: kpeter@605: // Find next entering arc kpeter@601: bool findEnteringArc() { kpeter@607: Cost c, min = 0; kpeter@601: for (int e = 0; e < _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@601: const IntVector &_state; kpeter@607: const CostVector &_pi; kpeter@601: int &_in_arc; kpeter@601: int _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@603: _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0) kpeter@601: { kpeter@601: // The main parameters of the pivot rule kpeter@601: const double BLOCK_SIZE_FACTOR = 2.0; kpeter@601: const int MIN_BLOCK_SIZE = 10; kpeter@601: alpar@612: _block_size = std::max( int(BLOCK_SIZE_FACTOR * alpar@612: std::sqrt(double(_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@601: int e, min_arc = _next_arc; kpeter@601: for (e = _next_arc; e < _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: min_arc = e; kpeter@601: } kpeter@601: if (--cnt == 0) { kpeter@601: if (min < 0) break; kpeter@601: cnt = _block_size; kpeter@601: } kpeter@601: } kpeter@601: if (min == 0 || cnt > 0) { kpeter@601: for (e = 0; e < _next_arc; ++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: min_arc = e; kpeter@601: } kpeter@601: if (--cnt == 0) { kpeter@601: if (min < 0) break; kpeter@601: cnt = _block_size; kpeter@601: } kpeter@601: } kpeter@601: } kpeter@601: if (min >= 0) return false; kpeter@601: _in_arc = min_arc; 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@601: const IntVector &_state; kpeter@607: const CostVector &_pi; kpeter@601: int &_in_arc; kpeter@601: int _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@603: _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0) kpeter@601: { kpeter@601: // The main parameters of the pivot rule kpeter@601: const double LIST_LENGTH_FACTOR = 1.0; 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 * alpar@612: std::sqrt(double(_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@601: int e, min_arc = _next_arc; 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@601: min_arc = e; kpeter@601: } kpeter@601: if (c >= 0) { kpeter@601: _candidates[i--] = _candidates[--_curr_length]; kpeter@601: } kpeter@601: } kpeter@601: if (min < 0) { kpeter@601: _in_arc = min_arc; kpeter@601: return true; kpeter@601: } kpeter@601: } kpeter@601: kpeter@601: // Major iteration: build a new candidate list kpeter@601: min = 0; kpeter@601: _curr_length = 0; kpeter@601: for (e = _next_arc; e < _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@601: min_arc = e; kpeter@601: } kpeter@601: if (_curr_length == _list_length) break; kpeter@601: } kpeter@601: } kpeter@601: if (_curr_length < _list_length) { kpeter@601: for (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: _candidates[_curr_length++] = e; kpeter@601: if (c < min) { kpeter@601: min = c; kpeter@601: min_arc = e; kpeter@601: } kpeter@601: if (_curr_length == _list_length) break; kpeter@601: } kpeter@601: } kpeter@601: } kpeter@601: if (_curr_length == 0) return false; kpeter@601: _minor_count = 1; kpeter@601: _in_arc = min_arc; 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@601: const IntVector &_state; kpeter@607: const CostVector &_pi; kpeter@601: int &_in_arc; kpeter@601: int _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@601: 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@603: _in_arc(ns.in_arc), _arc_num(ns._arc_num), kpeter@601: _next_arc(0), _cand_cost(ns._arc_num), _sort_func(_cand_cost) kpeter@601: { kpeter@601: // The main parameters of the pivot rule kpeter@601: const double BLOCK_SIZE_FACTOR = 1.5; kpeter@601: const int MIN_BLOCK_SIZE = 10; kpeter@601: const double HEAD_LENGTH_FACTOR = 0.1; kpeter@601: const int MIN_HEAD_LENGTH = 3; kpeter@601: alpar@612: _block_size = std::max( int(BLOCK_SIZE_FACTOR * alpar@612: std::sqrt(double(_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@601: for (int i = 0; i < _curr_length; ++i) { kpeter@601: e = _candidates[i]; kpeter@601: _cand_cost[e] = _state[e] * kpeter@601: (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@601: if (_cand_cost[e] >= 0) { 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@603: int last_arc = 0; kpeter@601: int limit = _head_length; kpeter@601: kpeter@601: for (int e = _next_arc; e < _arc_num; ++e) { kpeter@601: _cand_cost[e] = _state[e] * kpeter@601: (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@601: if (_cand_cost[e] < 0) { kpeter@601: _candidates[_curr_length++] = e; kpeter@603: last_arc = e; kpeter@601: } kpeter@601: if (--cnt == 0) { kpeter@601: if (_curr_length > limit) break; kpeter@601: limit = 0; kpeter@601: cnt = _block_size; kpeter@601: } kpeter@601: } kpeter@601: if (_curr_length <= limit) { kpeter@601: for (int e = 0; e < _next_arc; ++e) { kpeter@601: _cand_cost[e] = _state[e] * kpeter@601: (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); kpeter@601: if (_cand_cost[e] < 0) { kpeter@601: _candidates[_curr_length++] = e; kpeter@603: last_arc = e; kpeter@601: } kpeter@601: if (--cnt == 0) { kpeter@601: if (_curr_length > limit) break; kpeter@601: limit = 0; kpeter@601: cnt = _block_size; kpeter@601: } kpeter@601: } kpeter@601: } kpeter@601: if (_curr_length == 0) return false; kpeter@603: _next_arc = last_arc + 1; kpeter@601: kpeter@601: // Make heap of the candidate list (approximating a partial sort) kpeter@601: make_heap( _candidates.begin(), _candidates.begin() + _curr_length, kpeter@601: _sort_func ); kpeter@601: kpeter@601: // Pop the first element of the heap kpeter@601: _in_arc = _candidates[0]; kpeter@601: pop_heap( _candidates.begin(), _candidates.begin() + _curr_length, kpeter@601: _sort_func ); kpeter@601: _curr_length = std::min(_head_length, _curr_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@605: NetworkSimplex(const GR& graph) : kpeter@605: _graph(graph), kpeter@605: _plower(NULL), _pupper(NULL), _pcost(NULL), kpeter@609: _psupply(NULL), _pstsup(false), _ptype(GEQ), kpeter@603: _flow_map(NULL), _potential_map(NULL), kpeter@601: _local_flow(false), _local_potential(false), kpeter@603: _node_id(graph) kpeter@605: { kpeter@607: LEMON_ASSERT(std::numeric_limits::is_integer && kpeter@607: std::numeric_limits::is_signed, kpeter@607: "The flow type of NetworkSimplex must be signed integer"); kpeter@607: LEMON_ASSERT(std::numeric_limits::is_integer && kpeter@607: std::numeric_limits::is_signed, kpeter@607: "The cost type of NetworkSimplex must be signed integer"); kpeter@605: } kpeter@601: kpeter@601: /// Destructor. kpeter@601: ~NetworkSimplex() { kpeter@603: if (_local_flow) delete _flow_map; kpeter@603: if (_local_potential) delete _potential_map; 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@605: /// If neither this function nor \ref boundMaps() is used before kpeter@605: /// calling \ref run(), the lower bounds will be set to zero kpeter@605: /// on all arcs. kpeter@605: /// kpeter@605: /// \param map An arc map storing the lower bounds. kpeter@607: /// Its \c Value type must be convertible to the \c Flow type kpeter@605: /// of the algorithm. kpeter@605: /// kpeter@605: /// \return (*this) kpeter@605: template kpeter@605: NetworkSimplex& lowerMap(const LOWER& map) { kpeter@605: delete _plower; kpeter@607: _plower = new FlowArcMap(_graph); kpeter@605: for (ArcIt a(_graph); a != INVALID; ++a) { kpeter@605: (*_plower)[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@605: /// If none of the functions \ref upperMap(), \ref capacityMap() kpeter@605: /// and \ref boundMaps() is used before calling \ref run(), kpeter@605: /// the upper bounds (capacities) will be set to kpeter@607: /// \c std::numeric_limits::max() on all arcs. kpeter@605: /// kpeter@605: /// \param map An arc map storing the upper bounds. kpeter@607: /// Its \c Value type must be convertible to the \c Flow type kpeter@605: /// of the algorithm. kpeter@605: /// kpeter@605: /// \return (*this) kpeter@605: template kpeter@605: NetworkSimplex& upperMap(const UPPER& map) { kpeter@605: delete _pupper; kpeter@607: _pupper = new FlowArcMap(_graph); kpeter@605: for (ArcIt a(_graph); a != INVALID; ++a) { kpeter@605: (*_pupper)[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@605: /// It is just an alias for \ref upperMap(). kpeter@605: /// kpeter@605: /// \return (*this) kpeter@605: template kpeter@605: NetworkSimplex& capacityMap(const CAP& map) { kpeter@605: return upperMap(map); kpeter@605: } kpeter@605: kpeter@605: /// \brief Set the lower and upper bounds on the arcs. kpeter@605: /// kpeter@605: /// This function sets the lower and upper bounds on the arcs. kpeter@605: /// If neither this function nor \ref lowerMap() is used before kpeter@605: /// calling \ref run(), the lower bounds will be set to zero kpeter@605: /// on all arcs. kpeter@605: /// If none of the functions \ref upperMap(), \ref capacityMap() kpeter@605: /// and \ref boundMaps() is used before calling \ref run(), kpeter@605: /// the upper bounds (capacities) will be set to kpeter@607: /// \c std::numeric_limits::max() on all arcs. kpeter@605: /// kpeter@605: /// \param lower An arc map storing the lower bounds. kpeter@605: /// \param upper An arc map storing the upper bounds. kpeter@605: /// kpeter@605: /// The \c Value type of the maps must be convertible to the kpeter@607: /// \c Flow type of the algorithm. kpeter@605: /// kpeter@605: /// \note This function is just a shortcut of calling \ref lowerMap() kpeter@605: /// and \ref upperMap() separately. kpeter@605: /// kpeter@605: /// \return (*this) kpeter@605: template kpeter@605: NetworkSimplex& boundMaps(const LOWER& lower, const UPPER& upper) { kpeter@605: return lowerMap(lower).upperMap(upper); 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@605: template kpeter@605: NetworkSimplex& costMap(const COST& map) { kpeter@605: delete _pcost; kpeter@607: _pcost = new CostArcMap(_graph); kpeter@605: for (ArcIt a(_graph); a != INVALID; ++a) { kpeter@605: (*_pcost)[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: /// (It makes sense only if non-zero lower bounds are given.) kpeter@605: /// kpeter@605: /// \param map A node map storing the supply values. kpeter@607: /// Its \c Value type must be convertible to the \c Flow type kpeter@605: /// of the algorithm. kpeter@605: /// kpeter@605: /// \return (*this) kpeter@605: template kpeter@605: NetworkSimplex& supplyMap(const SUP& map) { kpeter@605: delete _psupply; kpeter@605: _pstsup = false; kpeter@607: _psupply = new FlowNodeMap(_graph); kpeter@605: for (NodeIt n(_graph); n != INVALID; ++n) { kpeter@605: (*_psupply)[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: /// (It makes sense only if non-zero lower bounds are given.) kpeter@605: /// 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@607: NetworkSimplex& stSupply(const Node& s, const Node& t, Flow k) { kpeter@605: delete _psupply; kpeter@605: _psupply = NULL; kpeter@605: _pstsup = true; kpeter@605: _psource = s; kpeter@605: _ptarget = t; kpeter@605: _pstflow = k; kpeter@605: return *this; kpeter@605: } kpeter@609: kpeter@609: /// \brief Set the problem type. kpeter@609: /// kpeter@609: /// This function sets the problem type for the algorithm. kpeter@609: /// If it is not used before calling \ref run(), the \ref GEQ problem kpeter@609: /// type will be used. kpeter@609: /// kpeter@609: /// For more information see \ref ProblemType. kpeter@609: /// kpeter@609: /// \return (*this) kpeter@609: NetworkSimplex& problemType(ProblemType problem_type) { kpeter@609: _ptype = problem_type; kpeter@609: return *this; kpeter@609: } kpeter@605: kpeter@601: /// \brief Set the flow map. kpeter@601: /// kpeter@601: /// This function sets the flow map. kpeter@605: /// If it is not used before calling \ref run(), an instance will kpeter@605: /// be allocated automatically. The destructor deallocates this kpeter@605: /// automatically allocated map, of course. kpeter@601: /// kpeter@601: /// \return (*this) kpeter@605: NetworkSimplex& flowMap(FlowMap& map) { kpeter@601: if (_local_flow) { kpeter@603: delete _flow_map; kpeter@601: _local_flow = false; kpeter@601: } kpeter@603: _flow_map = ↦ kpeter@601: return *this; kpeter@601: } kpeter@601: kpeter@601: /// \brief Set the potential map. kpeter@601: /// kpeter@605: /// This function sets the potential map, which is used for storing kpeter@605: /// the dual solution. kpeter@605: /// If it is not used before calling \ref run(), an instance will kpeter@605: /// be allocated automatically. The destructor deallocates this kpeter@605: /// automatically allocated map, of course. kpeter@601: /// kpeter@601: /// \return (*this) kpeter@605: NetworkSimplex& potentialMap(PotentialMap& map) { kpeter@601: if (_local_potential) { kpeter@603: delete _potential_map; kpeter@601: _local_potential = false; kpeter@601: } kpeter@603: _potential_map = ↦ kpeter@601: return *this; kpeter@601: } kpeter@609: 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(), kpeter@606: /// \ref upperMap(), \ref capacityMap(), \ref boundMaps(), kpeter@609: /// \ref costMap(), \ref supplyMap(), \ref stSupply(), kpeter@609: /// \ref problemType(), \ref flowMap() and \ref potentialMap(). kpeter@609: /// For example, kpeter@605: /// \code kpeter@605: /// NetworkSimplex ns(graph); kpeter@605: /// ns.boundMaps(lower, upper).costMap(cost) kpeter@605: /// .supplyMap(sup).run(); kpeter@605: /// \endcode kpeter@601: /// kpeter@606: /// This function can be called more than once. All the parameters kpeter@606: /// that have been given are kept for the next call, unless kpeter@606: /// \ref reset() is called, thus only the modified parameters kpeter@606: /// have to be set again. See \ref reset() for examples. kpeter@606: /// kpeter@605: /// \param pivot_rule The pivot rule that will be used during the kpeter@605: /// algorithm. For more information see \ref PivotRule. kpeter@601: /// kpeter@601: /// \return \c true if a feasible flow can be found. kpeter@605: bool run(PivotRule pivot_rule = BLOCK_SEARCH) { kpeter@601: return init() && 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@609: /// \ref capacityMap(), \ref boundMaps(), \ref costMap(), kpeter@609: /// \ref supplyMap(), \ref stSupply(), \ref problemType(), kpeter@609: /// \ref flowMap() and \ref potentialMap(). kpeter@606: /// kpeter@606: /// It is useful for multiple run() calls. If this function is not kpeter@606: /// used, all the parameters given before are kept for the next kpeter@606: /// \ref run() call. kpeter@606: /// kpeter@606: /// For example, kpeter@606: /// \code kpeter@606: /// NetworkSimplex ns(graph); kpeter@606: /// kpeter@606: /// // First run kpeter@606: /// ns.lowerMap(lower).capacityMap(cap).costMap(cost) kpeter@606: /// .supplyMap(sup).run(); kpeter@606: /// kpeter@606: /// // Run again with modified cost map (reset() 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@606: /// // Run again from scratch using reset() kpeter@606: /// // (the lower bounds will be set to zero on all arcs) kpeter@606: /// ns.reset(); kpeter@606: /// ns.capacityMap(cap).costMap(cost) kpeter@606: /// .supplyMap(sup).run(); kpeter@606: /// \endcode kpeter@606: /// kpeter@606: /// \return (*this) kpeter@606: NetworkSimplex& reset() { kpeter@606: delete _plower; kpeter@606: delete _pupper; kpeter@606: delete _pcost; kpeter@606: delete _psupply; kpeter@606: _plower = NULL; kpeter@606: _pupper = NULL; kpeter@606: _pcost = NULL; kpeter@606: _psupply = NULL; kpeter@606: _pstsup = false; kpeter@609: _ptype = GEQ; kpeter@609: if (_local_flow) delete _flow_map; kpeter@609: if (_local_potential) delete _potential_map; kpeter@609: _flow_map = NULL; kpeter@609: _potential_map = NULL; kpeter@609: _local_flow = false; kpeter@609: _local_potential = false; kpeter@609: kpeter@606: return *this; kpeter@606: } kpeter@606: 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@607: /// The complexity of the function is O(e). 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@605: template kpeter@605: Num totalCost() const { kpeter@605: Num c = 0; kpeter@605: if (_pcost) { kpeter@605: for (ArcIt e(_graph); e != INVALID; ++e) kpeter@605: c += (*_flow_map)[e] * (*_pcost)[e]; kpeter@605: } else { kpeter@605: for (ArcIt e(_graph); e != INVALID; ++e) kpeter@605: c += (*_flow_map)[e]; 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@607: Flow flow(const Arc& a) const { kpeter@605: return (*_flow_map)[a]; kpeter@605: } kpeter@605: kpeter@601: /// \brief Return a const reference to the flow map. kpeter@601: /// kpeter@601: /// This function returns a const reference to an arc map storing kpeter@601: /// the found flow. kpeter@601: /// kpeter@601: /// \pre \ref run() must be called before using this function. kpeter@601: const FlowMap& flowMap() const { kpeter@603: return *_flow_map; 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@605: return (*_potential_map)[n]; kpeter@605: } kpeter@605: kpeter@601: /// \brief Return a const reference to the potential map kpeter@601: /// (the dual solution). kpeter@601: /// kpeter@601: /// This function returns a const reference to a node map storing kpeter@605: /// the found potentials, which form the dual solution of the kpeter@605: /// \ref min_cost_flow "minimum cost flow" problem. kpeter@601: /// kpeter@601: /// \pre \ref run() must be called before using this function. kpeter@601: const PotentialMap& potentialMap() const { kpeter@603: return *_potential_map; kpeter@601: } kpeter@601: kpeter@601: /// @} kpeter@601: kpeter@601: private: kpeter@601: kpeter@601: // Initialize internal data structures kpeter@601: bool init() { kpeter@601: // Initialize result maps kpeter@603: if (!_flow_map) { kpeter@603: _flow_map = new FlowMap(_graph); kpeter@601: _local_flow = true; kpeter@601: } kpeter@603: if (!_potential_map) { kpeter@603: _potential_map = new PotentialMap(_graph); kpeter@601: _local_potential = true; kpeter@601: } kpeter@601: kpeter@601: // Initialize vectors kpeter@603: _node_num = countNodes(_graph); kpeter@603: _arc_num = countArcs(_graph); kpeter@601: int all_node_num = _node_num + 1; kpeter@603: int all_arc_num = _arc_num + _node_num; kpeter@605: if (_node_num == 0) return false; kpeter@601: kpeter@603: _arc_ref.resize(_arc_num); kpeter@603: _source.resize(all_arc_num); kpeter@603: _target.resize(all_arc_num); kpeter@601: kpeter@603: _cap.resize(all_arc_num); kpeter@603: _cost.resize(all_arc_num); kpeter@601: _supply.resize(all_node_num); kpeter@606: _flow.resize(all_arc_num); kpeter@606: _pi.resize(all_node_num); kpeter@601: kpeter@601: _parent.resize(all_node_num); kpeter@601: _pred.resize(all_node_num); kpeter@603: _forward.resize(all_node_num); kpeter@601: _thread.resize(all_node_num); kpeter@604: _rev_thread.resize(all_node_num); kpeter@604: _succ_num.resize(all_node_num); kpeter@604: _last_succ.resize(all_node_num); kpeter@606: _state.resize(all_arc_num); kpeter@601: kpeter@601: // Initialize node related data kpeter@601: bool valid_supply = true; kpeter@609: Flow sum_supply = 0; kpeter@605: if (!_pstsup && !_psupply) { kpeter@605: _pstsup = true; kpeter@605: _psource = _ptarget = NodeIt(_graph); kpeter@605: _pstflow = 0; kpeter@605: } kpeter@605: if (_psupply) { kpeter@601: int i = 0; kpeter@603: for (NodeIt n(_graph); n != INVALID; ++n, ++i) { kpeter@601: _node_id[n] = i; kpeter@605: _supply[i] = (*_psupply)[n]; kpeter@609: sum_supply += _supply[i]; kpeter@601: } kpeter@609: valid_supply = (_ptype == GEQ && sum_supply <= 0) || kpeter@609: (_ptype == LEQ && sum_supply >= 0); kpeter@601: } else { kpeter@601: int i = 0; kpeter@603: for (NodeIt n(_graph); n != INVALID; ++n, ++i) { kpeter@601: _node_id[n] = i; kpeter@601: _supply[i] = 0; kpeter@601: } kpeter@605: _supply[_node_id[_psource]] = _pstflow; kpeter@609: _supply[_node_id[_ptarget]] = -_pstflow; kpeter@601: } kpeter@601: if (!valid_supply) return false; kpeter@601: kpeter@609: // Infinite capacity value kpeter@609: Flow inf_cap = kpeter@609: std::numeric_limits::has_infinity ? kpeter@609: std::numeric_limits::infinity() : kpeter@609: std::numeric_limits::max(); kpeter@609: kpeter@609: // Initialize artifical cost kpeter@609: Cost art_cost; kpeter@609: if (std::numeric_limits::is_exact) { kpeter@609: art_cost = std::numeric_limits::max() / 4 + 1; kpeter@609: } else { kpeter@609: art_cost = std::numeric_limits::min(); kpeter@609: for (int i = 0; i != _arc_num; ++i) { kpeter@609: if (_cost[i] > art_cost) art_cost = _cost[i]; kpeter@609: } kpeter@609: art_cost = (art_cost + 1) * _node_num; kpeter@609: } kpeter@609: kpeter@609: // Run Circulation to check if a feasible solution exists kpeter@609: typedef ConstMap ConstArcMap; kpeter@613: ConstArcMap zero_arc_map(0), inf_arc_map(inf_cap); kpeter@609: FlowNodeMap *csup = NULL; kpeter@609: bool local_csup = false; kpeter@609: if (_psupply) { kpeter@609: csup = _psupply; kpeter@609: } else { kpeter@609: csup = new FlowNodeMap(_graph, 0); kpeter@609: (*csup)[_psource] = _pstflow; kpeter@609: (*csup)[_ptarget] = -_pstflow; kpeter@609: local_csup = true; kpeter@609: } kpeter@609: bool circ_result = false; kpeter@609: if (_ptype == GEQ || (_ptype == LEQ && sum_supply == 0)) { kpeter@609: // GEQ problem type kpeter@609: if (_plower) { kpeter@609: if (_pupper) { kpeter@609: Circulation kpeter@609: circ(_graph, *_plower, *_pupper, *csup); kpeter@609: circ_result = circ.run(); kpeter@609: } else { kpeter@609: Circulation kpeter@613: circ(_graph, *_plower, inf_arc_map, *csup); kpeter@609: circ_result = circ.run(); kpeter@609: } kpeter@609: } else { kpeter@609: if (_pupper) { kpeter@609: Circulation kpeter@613: circ(_graph, zero_arc_map, *_pupper, *csup); kpeter@609: circ_result = circ.run(); kpeter@609: } else { kpeter@609: Circulation kpeter@613: circ(_graph, zero_arc_map, inf_arc_map, *csup); kpeter@609: circ_result = circ.run(); kpeter@609: } kpeter@609: } kpeter@609: } else { kpeter@609: // LEQ problem type kpeter@609: typedef ReverseDigraph RevGraph; kpeter@609: typedef NegMap NegNodeMap; kpeter@609: RevGraph rgraph(_graph); kpeter@609: NegNodeMap neg_csup(*csup); kpeter@609: if (_plower) { kpeter@609: if (_pupper) { kpeter@609: Circulation kpeter@609: circ(rgraph, *_plower, *_pupper, neg_csup); kpeter@609: circ_result = circ.run(); kpeter@609: } else { kpeter@609: Circulation kpeter@613: circ(rgraph, *_plower, inf_arc_map, neg_csup); kpeter@609: circ_result = circ.run(); kpeter@609: } kpeter@609: } else { kpeter@609: if (_pupper) { kpeter@609: Circulation kpeter@613: circ(rgraph, zero_arc_map, *_pupper, neg_csup); kpeter@609: circ_result = circ.run(); kpeter@609: } else { kpeter@609: Circulation kpeter@613: circ(rgraph, zero_arc_map, inf_arc_map, neg_csup); kpeter@609: circ_result = circ.run(); kpeter@609: } kpeter@609: } kpeter@609: } kpeter@609: if (local_csup) delete csup; kpeter@609: if (!circ_result) return false; kpeter@609: 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@604: _succ_num[_root] = all_node_num; kpeter@604: _last_succ[_root] = _root - 1; kpeter@609: _supply[_root] = -sum_supply; kpeter@609: if (sum_supply < 0) { kpeter@609: _pi[_root] = -art_cost; kpeter@609: } else { kpeter@609: _pi[_root] = art_cost; kpeter@609: } kpeter@601: kpeter@601: // Store the arcs in a mixed order alpar@612: int k = std::max(int(std::sqrt(double(_arc_num))), 10); kpeter@601: int i = 0; kpeter@603: for (ArcIt e(_graph); e != INVALID; ++e) { kpeter@603: _arc_ref[i] = e; kpeter@601: if ((i += k) >= _arc_num) i = (i % k) + 1; kpeter@601: } kpeter@601: kpeter@601: // Initialize arc maps kpeter@605: if (_pupper && _pcost) { kpeter@605: for (int i = 0; i != _arc_num; ++i) { kpeter@605: Arc e = _arc_ref[i]; kpeter@605: _source[i] = _node_id[_graph.source(e)]; kpeter@605: _target[i] = _node_id[_graph.target(e)]; kpeter@605: _cap[i] = (*_pupper)[e]; kpeter@605: _cost[i] = (*_pcost)[e]; kpeter@606: _flow[i] = 0; kpeter@606: _state[i] = STATE_LOWER; kpeter@605: } kpeter@605: } else { kpeter@605: for (int i = 0; i != _arc_num; ++i) { kpeter@605: Arc e = _arc_ref[i]; kpeter@605: _source[i] = _node_id[_graph.source(e)]; kpeter@605: _target[i] = _node_id[_graph.target(e)]; kpeter@606: _flow[i] = 0; kpeter@606: _state[i] = STATE_LOWER; kpeter@605: } kpeter@605: if (_pupper) { kpeter@605: for (int i = 0; i != _arc_num; ++i) kpeter@605: _cap[i] = (*_pupper)[_arc_ref[i]]; kpeter@605: } else { kpeter@605: for (int i = 0; i != _arc_num; ++i) kpeter@608: _cap[i] = inf_cap; kpeter@605: } kpeter@605: if (_pcost) { kpeter@605: for (int i = 0; i != _arc_num; ++i) kpeter@605: _cost[i] = (*_pcost)[_arc_ref[i]]; kpeter@605: } else { kpeter@605: for (int i = 0; i != _arc_num; ++i) kpeter@605: _cost[i] = 1; kpeter@605: } kpeter@601: } kpeter@608: kpeter@601: // Remove non-zero lower bounds kpeter@605: if (_plower) { kpeter@601: for (int i = 0; i != _arc_num; ++i) { kpeter@607: Flow c = (*_plower)[_arc_ref[i]]; kpeter@601: if (c != 0) { kpeter@601: _cap[i] -= c; kpeter@601: _supply[_source[i]] -= c; kpeter@601: _supply[_target[i]] += c; kpeter@601: } kpeter@601: } kpeter@601: } kpeter@601: kpeter@601: // Add artificial arcs and initialize the spanning tree data structure kpeter@601: for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { kpeter@601: _thread[u] = u + 1; kpeter@604: _rev_thread[u + 1] = u; kpeter@604: _succ_num[u] = 1; kpeter@604: _last_succ[u] = u; kpeter@601: _parent[u] = _root; kpeter@601: _pred[u] = e; kpeter@608: _cost[e] = art_cost; kpeter@608: _cap[e] = inf_cap; kpeter@606: _state[e] = STATE_TREE; kpeter@609: if (_supply[u] > 0 || (_supply[u] == 0 && sum_supply <= 0)) { kpeter@601: _flow[e] = _supply[u]; kpeter@601: _forward[u] = true; kpeter@609: _pi[u] = -art_cost + _pi[_root]; kpeter@601: } else { kpeter@601: _flow[e] = -_supply[u]; kpeter@601: _forward[u] = false; kpeter@609: _pi[u] = art_cost + _pi[_root]; kpeter@601: } kpeter@601: } kpeter@601: kpeter@601: return true; kpeter@601: } 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@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@607: Flow d; kpeter@601: int e; kpeter@601: kpeter@601: // Search the cycle along the path form the first node to the root kpeter@601: for (int u = first; u != join; u = _parent[u]) { kpeter@601: e = _pred[u]; kpeter@601: d = _forward[u] ? _flow[e] : _cap[e] - _flow[e]; kpeter@601: if (d < delta) { kpeter@601: delta = d; kpeter@601: u_out = u; kpeter@601: result = 1; kpeter@601: } kpeter@601: } kpeter@601: // Search the cycle along the path form the second node to the root kpeter@601: for (int u = second; u != join; u = _parent[u]) { kpeter@601: e = _pred[u]; kpeter@601: d = _forward[u] ? _cap[e] - _flow[e] : _flow[e]; 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@607: Flow 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@601: _flow[_pred[u]] += _forward[u] ? -val : val; kpeter@601: } kpeter@603: for (int u = _target[in_arc]; u != join; u = _parent[u]) { kpeter@601: _flow[_pred[u]] += _forward[u] ? val : -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 u, w; 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@604: u = _last_succ[u_in]; // the last successor of u_in kpeter@604: right = _thread[u]; // the node after it kpeter@604: kpeter@604: // Handle the case when old_rev_thread equals to v_in kpeter@604: // (it also means that join and v_out coincide) kpeter@604: if (old_rev_thread == v_in) { kpeter@604: last = _thread[_last_succ[u_out]]; kpeter@604: } else { kpeter@604: last = _thread[v_in]; kpeter@601: } kpeter@601: kpeter@604: // Update _thread and _parent along the stem nodes (i.e. the nodes kpeter@604: // between u_in and u_out, whose parent have to be changed) kpeter@601: _thread[v_in] = stem = u_in; kpeter@604: _dirty_revs.clear(); kpeter@604: _dirty_revs.push_back(v_in); kpeter@601: par_stem = v_in; kpeter@601: while (stem != u_out) { kpeter@604: // Insert the next stem node into the thread list kpeter@604: new_stem = _parent[stem]; kpeter@604: _thread[u] = new_stem; kpeter@604: _dirty_revs.push_back(u); kpeter@601: kpeter@604: // Remove the subtree of stem from the thread list kpeter@604: w = _rev_thread[stem]; kpeter@604: _thread[w] = right; kpeter@604: _rev_thread[right] = w; kpeter@601: kpeter@604: // Change the parent node and shift stem nodes kpeter@601: _parent[stem] = par_stem; kpeter@601: par_stem = stem; kpeter@601: stem = new_stem; kpeter@601: kpeter@604: // Update u and right kpeter@604: u = _last_succ[stem] == _last_succ[par_stem] ? kpeter@604: _rev_thread[par_stem] : _last_succ[stem]; kpeter@601: right = _thread[u]; kpeter@601: } kpeter@601: _parent[u_out] = par_stem; kpeter@601: _thread[u] = last; kpeter@604: _rev_thread[last] = u; kpeter@604: _last_succ[u_out] = u; kpeter@601: kpeter@604: // Remove the subtree of u_out from the thread list except for kpeter@604: // the case when old_rev_thread equals to v_in kpeter@604: // (it also means that join and v_out coincide) kpeter@604: if (old_rev_thread != v_in) { kpeter@604: _thread[old_rev_thread] = right; kpeter@604: _rev_thread[right] = old_rev_thread; kpeter@604: } kpeter@604: kpeter@604: // Update _rev_thread using the new _thread values kpeter@604: for (int i = 0; i < int(_dirty_revs.size()); ++i) { kpeter@604: u = _dirty_revs[i]; kpeter@604: _rev_thread[_thread[u]] = u; kpeter@604: } kpeter@604: kpeter@604: // Update _pred, _forward, _last_succ and _succ_num for the kpeter@604: // stem nodes from u_out to u_in kpeter@604: int tmp_sc = 0, tmp_ls = _last_succ[u_out]; kpeter@604: u = u_out; kpeter@604: while (u != u_in) { kpeter@604: w = _parent[u]; kpeter@604: _pred[u] = _pred[w]; kpeter@604: _forward[u] = !_forward[w]; kpeter@604: tmp_sc += _succ_num[u] - _succ_num[w]; kpeter@604: _succ_num[u] = tmp_sc; kpeter@604: _last_succ[w] = tmp_ls; kpeter@604: u = w; kpeter@604: } kpeter@604: _pred[u_in] = in_arc; kpeter@604: _forward[u_in] = (u_in == _source[in_arc]); kpeter@604: _succ_num[u_in] = old_succ_num; kpeter@604: kpeter@604: // Set limits for updating _last_succ form v_in and v_out kpeter@604: // towards the root kpeter@604: int up_limit_in = -1; kpeter@604: int up_limit_out = -1; kpeter@604: if (_last_succ[join] == v_in) { kpeter@604: up_limit_out = join; kpeter@601: } else { kpeter@604: up_limit_in = join; kpeter@604: } kpeter@604: kpeter@604: // Update _last_succ from v_in towards the root kpeter@604: for (u = v_in; u != up_limit_in && _last_succ[u] == v_in; kpeter@604: u = _parent[u]) { kpeter@604: _last_succ[u] = _last_succ[u_out]; kpeter@604: } kpeter@604: // Update _last_succ from v_out towards the root kpeter@604: if (join != old_rev_thread && v_in != old_rev_thread) { kpeter@604: for (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@604: } else { kpeter@604: for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; kpeter@604: u = _parent[u]) { kpeter@604: _last_succ[u] = _last_succ[u_out]; kpeter@604: } kpeter@604: } kpeter@604: kpeter@604: // Update _succ_num from v_in to join kpeter@604: for (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@604: for (u = v_out; u != join; u = _parent[u]) { kpeter@604: _succ_num[u] -= old_succ_num; kpeter@601: } kpeter@601: } kpeter@601: kpeter@604: // Update potentials kpeter@604: void updatePotential() { kpeter@607: Cost sigma = _forward[u_in] ? kpeter@601: _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] : kpeter@601: _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]]; kpeter@608: // Update potentials in the subtree, which has been moved 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@601: // Execute the algorithm kpeter@605: bool 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@601: return false; kpeter@601: } kpeter@601: kpeter@605: template kpeter@601: bool start() { kpeter@605: PivotRuleImpl pivot(*this); kpeter@601: kpeter@605: // Execute the Network Simplex algorithm kpeter@601: while (pivot.findEnteringArc()) { kpeter@601: findJoinNode(); kpeter@601: bool change = findLeavingArc(); kpeter@601: changeFlow(change); kpeter@601: if (change) { kpeter@604: updateTreeStructure(); kpeter@604: updatePotential(); kpeter@601: } kpeter@601: } kpeter@601: kpeter@603: // Copy flow values to _flow_map kpeter@605: if (_plower) { kpeter@601: for (int i = 0; i != _arc_num; ++i) { kpeter@603: Arc e = _arc_ref[i]; kpeter@605: _flow_map->set(e, (*_plower)[e] + _flow[i]); kpeter@601: } kpeter@601: } else { kpeter@601: for (int i = 0; i != _arc_num; ++i) { kpeter@603: _flow_map->set(_arc_ref[i], _flow[i]); kpeter@601: } kpeter@601: } kpeter@603: // Copy potential values to _potential_map kpeter@603: for (NodeIt n(_graph); n != INVALID; ++n) { kpeter@603: _potential_map->set(n, _pi[_node_id[n]]); kpeter@601: } kpeter@601: kpeter@601: return true; 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