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