deba@2440: /* -*- C++ -*-
deba@2440:  *
deba@2440:  * This file is a part of LEMON, a generic C++ optimization library
deba@2440:  *
alpar@2553:  * Copyright (C) 2003-2008
deba@2440:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@2440:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@2440:  *
deba@2440:  * Permission to use, modify and distribute this software is granted
deba@2440:  * provided that this copyright notice appears in all copies. For
deba@2440:  * precise terms see the accompanying LICENSE file.
deba@2440:  *
deba@2440:  * This software is provided "AS IS" with no warranty of any kind,
deba@2440:  * express or implied, and with no claim as to its suitability for any
deba@2440:  * purpose.
deba@2440:  *
deba@2440:  */
deba@2440: 
deba@2440: #ifndef LEMON_NETWORK_SIMPLEX_H
deba@2440: #define LEMON_NETWORK_SIMPLEX_H
deba@2440: 
deba@2440: /// \ingroup min_cost_flow
deba@2440: ///
deba@2440: /// \file
kpeter@2575: /// \brief Network simplex algorithm for finding a minimum cost flow.
deba@2440: 
kpeter@2575: #include <vector>
deba@2440: #include <limits>
kpeter@2630: #include <algorithm>
kpeter@2575: 
kpeter@2509: #include <lemon/graph_utils.h>
kpeter@2575: #include <lemon/math.h>
deba@2440: 
deba@2440: namespace lemon {
deba@2440: 
deba@2440:   /// \addtogroup min_cost_flow
deba@2440:   /// @{
deba@2440: 
kpeter@2619:   /// \brief Implementation of the primal network simplex algorithm
kpeter@2619:   /// for finding a minimum cost flow.
deba@2440:   ///
kpeter@2619:   /// \ref NetworkSimplex implements the primal network simplex algorithm
kpeter@2619:   /// for finding a minimum cost flow.
deba@2440:   ///
kpeter@2575:   /// \tparam Graph The directed graph type the algorithm runs on.
kpeter@2575:   /// \tparam LowerMap The type of the lower bound map.
kpeter@2575:   /// \tparam CapacityMap The type of the capacity (upper bound) map.
kpeter@2575:   /// \tparam CostMap The type of the cost (length) map.
kpeter@2575:   /// \tparam SupplyMap The type of the supply map.
deba@2440:   ///
deba@2440:   /// \warning
kpeter@2575:   /// - Edge capacities and costs should be \e non-negative \e integers.
kpeter@2575:   /// - Supply values should be \e signed \e integers.
kpeter@2581:   /// - The value types of the maps should be convertible to each other.
kpeter@2581:   /// - \c CostMap::Value must be signed type.
kpeter@2575:   ///
kpeter@2619:   /// \note \ref NetworkSimplex provides five different pivot rule
kpeter@2575:   /// implementations that significantly affect the efficiency of the
kpeter@2575:   /// algorithm.
kpeter@2619:   /// By default "Block Search" pivot rule is used, which proved to be
kpeter@2619:   /// by far the most efficient according to our benchmark tests.
kpeter@2619:   /// However another pivot rule can be selected using \ref run()
kpeter@2619:   /// function with the proper parameter.
deba@2440:   ///
deba@2440:   /// \author Peter Kovacs
kpeter@2533:   template < typename Graph,
kpeter@2533:              typename LowerMap = typename Graph::template EdgeMap<int>,
kpeter@2575:              typename CapacityMap = typename Graph::template EdgeMap<int>,
kpeter@2533:              typename CostMap = typename Graph::template EdgeMap<int>,
kpeter@2575:              typename SupplyMap = typename Graph::template NodeMap<int> >
deba@2440:   class NetworkSimplex
deba@2440:   {
kpeter@2634:     GRAPH_TYPEDEFS(typename Graph);
kpeter@2634: 
deba@2440:     typedef typename CapacityMap::Value Capacity;
deba@2440:     typedef typename CostMap::Value Cost;
deba@2440:     typedef typename SupplyMap::Value Supply;
deba@2440: 
kpeter@2634:     typedef std::vector<Edge> EdgeVector;
kpeter@2634:     typedef std::vector<Node> NodeVector;
kpeter@2634:     typedef std::vector<int> IntVector;
kpeter@2634:     typedef std::vector<bool> BoolVector;
kpeter@2634:     typedef std::vector<Capacity> CapacityVector;
kpeter@2634:     typedef std::vector<Cost> CostVector;
kpeter@2634:     typedef std::vector<Supply> SupplyVector;
deba@2440: 
kpeter@2634:     typedef typename Graph::template NodeMap<int> IntNodeMap;
kpeter@2619: 
deba@2440:   public:
deba@2440: 
kpeter@2556:     /// The type of the flow map.
deba@2440:     typedef typename Graph::template EdgeMap<Capacity> FlowMap;
kpeter@2556:     /// The type of the potential map.
deba@2440:     typedef typename Graph::template NodeMap<Cost> PotentialMap;
deba@2440: 
kpeter@2575:   public:
deba@2440: 
kpeter@2575:     /// Enum type to select the pivot rule used by \ref run().
kpeter@2575:     enum PivotRuleEnum {
kpeter@2575:       FIRST_ELIGIBLE_PIVOT,
kpeter@2575:       BEST_ELIGIBLE_PIVOT,
kpeter@2575:       BLOCK_SEARCH_PIVOT,
kpeter@2575:       CANDIDATE_LIST_PIVOT,
kpeter@2619:       ALTERING_LIST_PIVOT
kpeter@2575:     };
kpeter@2575: 
kpeter@2575:   private:
kpeter@2575: 
kpeter@2575:     /// \brief Implementation of the "First Eligible" pivot rule for the
kpeter@2575:     /// \ref NetworkSimplex "network simplex" algorithm.
kpeter@2575:     ///
kpeter@2575:     /// This class implements the "First Eligible" pivot rule
kpeter@2575:     /// for the \ref NetworkSimplex "network simplex" algorithm.
kpeter@2619:     ///
kpeter@2619:     /// For more information see \ref NetworkSimplex::run().
kpeter@2575:     class FirstEligiblePivotRule
kpeter@2575:     {
kpeter@2575:     private:
deba@2440: 
kpeter@2619:       // References to the NetworkSimplex class
kpeter@2634:       const EdgeVector &_edge;
kpeter@2634:       const IntVector  &_source;
kpeter@2634:       const IntVector  &_target;
kpeter@2634:       const CostVector &_cost;
kpeter@2634:       const IntVector  &_state;
kpeter@2634:       const CostVector &_pi;
kpeter@2634:       int &_in_edge;
kpeter@2634:       int _edge_num;
kpeter@2619: 
kpeter@2634:       // Pivot rule data
kpeter@2619:       int _next_edge;
deba@2440: 
kpeter@2575:     public:
deba@2440: 
kpeter@2619:       /// Constructor
kpeter@2634:       FirstEligiblePivotRule(NetworkSimplex &ns) :
kpeter@2634:         _edge(ns._edge), _source(ns._source), _target(ns._target),
kpeter@2634:         _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@2634:         _in_edge(ns._in_edge), _edge_num(ns._edge_num), _next_edge(0)
kpeter@2634:       {}
kpeter@2575: 
kpeter@2619:       /// Find next entering edge
kpeter@2630:       bool findEnteringEdge() {
kpeter@2634:         Cost c;
kpeter@2634:         for (int e = _next_edge; e < _edge_num; ++e) {
kpeter@2634:           c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@2634:           if (c < 0) {
kpeter@2634:             _in_edge = e;
kpeter@2634:             _next_edge = e + 1;
kpeter@2575:             return true;
kpeter@2575:           }
kpeter@2575:         }
kpeter@2634:         for (int e = 0; e < _next_edge; ++e) {
kpeter@2634:           c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@2634:           if (c < 0) {
kpeter@2634:             _in_edge = e;
kpeter@2634:             _next_edge = e + 1;
kpeter@2575:             return true;
kpeter@2575:           }
kpeter@2575:         }
kpeter@2575:         return false;
kpeter@2575:       }
kpeter@2634: 
kpeter@2575:     }; //class FirstEligiblePivotRule
kpeter@2575: 
kpeter@2634: 
kpeter@2575:     /// \brief Implementation of the "Best Eligible" pivot rule for the
kpeter@2575:     /// \ref NetworkSimplex "network simplex" algorithm.
kpeter@2575:     ///
kpeter@2575:     /// This class implements the "Best Eligible" pivot rule
kpeter@2575:     /// for the \ref NetworkSimplex "network simplex" algorithm.
kpeter@2619:     ///
kpeter@2619:     /// For more information see \ref NetworkSimplex::run().
kpeter@2575:     class BestEligiblePivotRule
kpeter@2575:     {
kpeter@2575:     private:
kpeter@2575: 
kpeter@2619:       // References to the NetworkSimplex class
kpeter@2634:       const EdgeVector &_edge;
kpeter@2634:       const IntVector  &_source;
kpeter@2634:       const IntVector  &_target;
kpeter@2634:       const CostVector &_cost;
kpeter@2634:       const IntVector  &_state;
kpeter@2634:       const CostVector &_pi;
kpeter@2634:       int &_in_edge;
kpeter@2634:       int _edge_num;
kpeter@2575: 
kpeter@2575:     public:
kpeter@2575: 
kpeter@2619:       /// Constructor
kpeter@2634:       BestEligiblePivotRule(NetworkSimplex &ns) :
kpeter@2634:         _edge(ns._edge), _source(ns._source), _target(ns._target),
kpeter@2634:         _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@2634:         _in_edge(ns._in_edge), _edge_num(ns._edge_num)
kpeter@2634:       {}
kpeter@2575: 
kpeter@2619:       /// Find next entering edge
kpeter@2630:       bool findEnteringEdge() {
kpeter@2634:         Cost c, min = 0;
kpeter@2634:         for (int e = 0; e < _edge_num; ++e) {
kpeter@2634:           c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@2634:           if (c < min) {
kpeter@2634:             min = c;
kpeter@2634:             _in_edge = e;
kpeter@2575:           }
kpeter@2575:         }
kpeter@2575:         return min < 0;
kpeter@2575:       }
kpeter@2634: 
kpeter@2575:     }; //class BestEligiblePivotRule
kpeter@2575: 
kpeter@2634: 
kpeter@2575:     /// \brief Implementation of the "Block Search" pivot rule for the
kpeter@2575:     /// \ref NetworkSimplex "network simplex" algorithm.
kpeter@2575:     ///
kpeter@2575:     /// This class implements the "Block Search" pivot rule
kpeter@2575:     /// for the \ref NetworkSimplex "network simplex" algorithm.
kpeter@2619:     ///
kpeter@2619:     /// For more information see \ref NetworkSimplex::run().
kpeter@2575:     class BlockSearchPivotRule
kpeter@2575:     {
kpeter@2575:     private:
kpeter@2575: 
kpeter@2619:       // References to the NetworkSimplex class
kpeter@2634:       const EdgeVector &_edge;
kpeter@2634:       const IntVector  &_source;
kpeter@2634:       const IntVector  &_target;
kpeter@2634:       const CostVector &_cost;
kpeter@2634:       const IntVector  &_state;
kpeter@2634:       const CostVector &_pi;
kpeter@2634:       int &_in_edge;
kpeter@2634:       int _edge_num;
kpeter@2619: 
kpeter@2634:       // Pivot rule data
kpeter@2575:       int _block_size;
kpeter@2634:       int _next_edge;
kpeter@2575: 
kpeter@2575:     public:
kpeter@2575: 
kpeter@2619:       /// Constructor
kpeter@2634:       BlockSearchPivotRule(NetworkSimplex &ns) :
kpeter@2634:         _edge(ns._edge), _source(ns._source), _target(ns._target),
kpeter@2634:         _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@2635:         _in_edge(ns._in_edge), _edge_num(ns._edge_num + ns._node_num), _next_edge(0)
kpeter@2575:       {
kpeter@2619:         // The main parameters of the pivot rule
kpeter@2619:         const double BLOCK_SIZE_FACTOR = 2.0;
kpeter@2619:         const int MIN_BLOCK_SIZE = 10;
kpeter@2619: 
kpeter@2634:         _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_edge_num)),
kpeter@2619:                                 MIN_BLOCK_SIZE );
kpeter@2575:       }
kpeter@2575: 
kpeter@2619:       /// Find next entering edge
kpeter@2630:       bool findEnteringEdge() {
kpeter@2634:         Cost c, min = 0;
kpeter@2619:         int cnt = _block_size;
kpeter@2634:         int e, min_edge = _next_edge;
kpeter@2634:         for (e = _next_edge; e < _edge_num; ++e) {
kpeter@2634:           c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@2634:           if (c < min) {
kpeter@2634:             min = c;
kpeter@2634:             min_edge = e;
kpeter@2575:           }
kpeter@2619:           if (--cnt == 0) {
kpeter@2575:             if (min < 0) break;
kpeter@2619:             cnt = _block_size;
kpeter@2575:           }
kpeter@2575:         }
kpeter@2619:         if (min == 0 || cnt > 0) {
kpeter@2634:           for (e = 0; e < _next_edge; ++e) {
kpeter@2634:             c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@2634:             if (c < min) {
kpeter@2634:               min = c;
kpeter@2634:               min_edge = e;
kpeter@2575:             }
kpeter@2619:             if (--cnt == 0) {
kpeter@2575:               if (min < 0) break;
kpeter@2619:               cnt = _block_size;
kpeter@2575:             }
kpeter@2575:           }
kpeter@2575:         }
kpeter@2619:         if (min >= 0) return false;
kpeter@2634:         _in_edge = min_edge;
kpeter@2634:         _next_edge = e;
kpeter@2619:         return true;
kpeter@2575:       }
kpeter@2634: 
kpeter@2575:     }; //class BlockSearchPivotRule
kpeter@2575: 
kpeter@2634: 
kpeter@2575:     /// \brief Implementation of the "Candidate List" pivot rule for the
kpeter@2575:     /// \ref NetworkSimplex "network simplex" algorithm.
kpeter@2575:     ///
kpeter@2575:     /// This class implements the "Candidate List" pivot rule
kpeter@2575:     /// for the \ref NetworkSimplex "network simplex" algorithm.
kpeter@2619:     ///
kpeter@2619:     /// For more information see \ref NetworkSimplex::run().
kpeter@2575:     class CandidateListPivotRule
kpeter@2575:     {
kpeter@2575:     private:
kpeter@2575: 
kpeter@2619:       // References to the NetworkSimplex class
kpeter@2634:       const EdgeVector &_edge;
kpeter@2634:       const IntVector  &_source;
kpeter@2634:       const IntVector  &_target;
kpeter@2634:       const CostVector &_cost;
kpeter@2634:       const IntVector  &_state;
kpeter@2634:       const CostVector &_pi;
kpeter@2634:       int &_in_edge;
kpeter@2634:       int _edge_num;
kpeter@2575: 
kpeter@2634:       // Pivot rule data
kpeter@2634:       IntVector _candidates;
kpeter@2619:       int _list_length, _minor_limit;
kpeter@2619:       int _curr_length, _minor_count;
kpeter@2634:       int _next_edge;
kpeter@2575: 
kpeter@2575:     public:
kpeter@2575: 
kpeter@2619:       /// Constructor
kpeter@2634:       CandidateListPivotRule(NetworkSimplex &ns) :
kpeter@2634:         _edge(ns._edge), _source(ns._source), _target(ns._target),
kpeter@2634:         _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@2634:         _in_edge(ns._in_edge), _edge_num(ns._edge_num), _next_edge(0)
kpeter@2575:       {
kpeter@2619:         // The main parameters of the pivot rule
kpeter@2619:         const double LIST_LENGTH_FACTOR = 1.0;
kpeter@2619:         const int MIN_LIST_LENGTH = 10;
kpeter@2619:         const double MINOR_LIMIT_FACTOR = 0.1;
kpeter@2619:         const int MIN_MINOR_LIMIT = 3;
kpeter@2619: 
kpeter@2634:         _list_length = std::max( int(LIST_LENGTH_FACTOR * sqrt(_edge_num)),
kpeter@2619:                                  MIN_LIST_LENGTH );
kpeter@2619:         _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length),
kpeter@2619:                                  MIN_MINOR_LIMIT );
kpeter@2619:         _curr_length = _minor_count = 0;
kpeter@2619:         _candidates.resize(_list_length);
kpeter@2575:       }
kpeter@2575: 
kpeter@2619:       /// Find next entering edge
kpeter@2630:       bool findEnteringEdge() {
kpeter@2634:         Cost min, c;
kpeter@2634:         int e, min_edge = _next_edge;
kpeter@2619:         if (_curr_length > 0 && _minor_count < _minor_limit) {
kpeter@2630:           // Minor iteration: select the best eligible edge from the
kpeter@2630:           // current candidate list
kpeter@2575:           ++_minor_count;
kpeter@2575:           min = 0;
kpeter@2619:           for (int i = 0; i < _curr_length; ++i) {
kpeter@2575:             e = _candidates[i];
kpeter@2634:             c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@2634:             if (c < min) {
kpeter@2634:               min = c;
kpeter@2634:               min_edge = e;
kpeter@2575:             }
kpeter@2634:             if (c >= 0) {
kpeter@2619:               _candidates[i--] = _candidates[--_curr_length];
kpeter@2619:             }
kpeter@2575:           }
kpeter@2634:           if (min < 0) {
kpeter@2634:             _in_edge = min_edge;
kpeter@2634:             return true;
kpeter@2634:           }
kpeter@2575:         }
kpeter@2575: 
kpeter@2630:         // Major iteration: build a new candidate list
kpeter@2575:         min = 0;
kpeter@2619:         _curr_length = 0;
kpeter@2634:         for (e = _next_edge; e < _edge_num; ++e) {
kpeter@2634:           c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@2634:           if (c < 0) {
kpeter@2619:             _candidates[_curr_length++] = e;
kpeter@2634:             if (c < min) {
kpeter@2634:               min = c;
kpeter@2634:               min_edge = e;
kpeter@2575:             }
kpeter@2619:             if (_curr_length == _list_length) break;
kpeter@2575:           }
kpeter@2575:         }
kpeter@2619:         if (_curr_length < _list_length) {
kpeter@2634:           for (e = 0; e < _next_edge; ++e) {
kpeter@2634:             c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@2634:             if (c < 0) {
kpeter@2619:               _candidates[_curr_length++] = e;
kpeter@2634:               if (c < min) {
kpeter@2634:                 min = c;
kpeter@2634:                 min_edge = e;
kpeter@2575:               }
kpeter@2619:               if (_curr_length == _list_length) break;
kpeter@2575:             }
kpeter@2575:           }
kpeter@2575:         }
kpeter@2619:         if (_curr_length == 0) return false;
kpeter@2575:         _minor_count = 1;
kpeter@2634:         _in_edge = min_edge;
kpeter@2634:         _next_edge = e;
kpeter@2575:         return true;
kpeter@2575:       }
kpeter@2634: 
kpeter@2575:     }; //class CandidateListPivotRule
kpeter@2575: 
kpeter@2634: 
kpeter@2619:     /// \brief Implementation of the "Altering Candidate List" pivot rule
kpeter@2619:     /// for the \ref NetworkSimplex "network simplex" algorithm.
kpeter@2619:     ///
kpeter@2619:     /// This class implements the "Altering Candidate List" pivot rule
kpeter@2619:     /// for the \ref NetworkSimplex "network simplex" algorithm.
kpeter@2619:     ///
kpeter@2619:     /// For more information see \ref NetworkSimplex::run().
kpeter@2619:     class AlteringListPivotRule
kpeter@2619:     {
kpeter@2619:     private:
kpeter@2619: 
kpeter@2619:       // References to the NetworkSimplex class
kpeter@2634:       const EdgeVector &_edge;
kpeter@2634:       const IntVector  &_source;
kpeter@2634:       const IntVector  &_target;
kpeter@2634:       const CostVector &_cost;
kpeter@2634:       const IntVector  &_state;
kpeter@2634:       const CostVector &_pi;
kpeter@2634:       int &_in_edge;
kpeter@2634:       int _edge_num;
kpeter@2619: 
kpeter@2619:       int _block_size, _head_length, _curr_length;
kpeter@2619:       int _next_edge;
kpeter@2634:       IntVector _candidates;
kpeter@2634:       CostVector _cand_cost;
kpeter@2619: 
kpeter@2619:       // Functor class to compare edges during sort of the candidate list
kpeter@2619:       class SortFunc
kpeter@2619:       {
kpeter@2619:       private:
kpeter@2634:         const CostVector &_map;
kpeter@2619:       public:
kpeter@2634:         SortFunc(const CostVector &map) : _map(map) {}
kpeter@2634:         bool operator()(int left, int right) {
kpeter@2634:           return _map[left] > _map[right];
kpeter@2619:         }
kpeter@2619:       };
kpeter@2619: 
kpeter@2619:       SortFunc _sort_func;
kpeter@2619: 
kpeter@2619:     public:
kpeter@2619: 
kpeter@2619:       /// Constructor
kpeter@2634:       AlteringListPivotRule(NetworkSimplex &ns) :
kpeter@2634:         _edge(ns._edge), _source(ns._source), _target(ns._target),
kpeter@2634:         _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@2634:         _in_edge(ns._in_edge), _edge_num(ns._edge_num),
kpeter@2634:          _next_edge(0), _cand_cost(ns._edge_num),_sort_func(_cand_cost)
kpeter@2619:       {
kpeter@2619:         // The main parameters of the pivot rule
kpeter@2630:         const double BLOCK_SIZE_FACTOR = 1.5;
kpeter@2619:         const int MIN_BLOCK_SIZE = 10;
kpeter@2619:         const double HEAD_LENGTH_FACTOR = 0.1;
kpeter@2630:         const int MIN_HEAD_LENGTH = 3;
kpeter@2619: 
kpeter@2634:         _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_edge_num)),
kpeter@2619:                                 MIN_BLOCK_SIZE );
kpeter@2619:         _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size),
kpeter@2619:                                  MIN_HEAD_LENGTH );
kpeter@2619:         _candidates.resize(_head_length + _block_size);
kpeter@2619:         _curr_length = 0;
kpeter@2619:       }
kpeter@2619: 
kpeter@2619:       /// Find next entering edge
kpeter@2630:       bool findEnteringEdge() {
kpeter@2630:         // Check the current candidate list
kpeter@2634:         int e;
kpeter@2634:         for (int i = 0; i < _curr_length; ++i) {
kpeter@2634:           e = _candidates[i];
kpeter@2634:           _cand_cost[e] = _state[e] * 
kpeter@2634:             (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@2634:           if (_cand_cost[e] >= 0) {
kpeter@2634:             _candidates[i--] = _candidates[--_curr_length];
kpeter@2619:           }
kpeter@2619:         }
kpeter@2619: 
kpeter@2630:         // Extend the list
kpeter@2619:         int cnt = _block_size;
kpeter@2619:         int last_edge = 0;
kpeter@2619:         int limit = _head_length;
kpeter@2634:         
kpeter@2634:         for (int e = _next_edge; e < _edge_num; ++e) {
kpeter@2634:           _cand_cost[e] = _state[e] *
kpeter@2634:             (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@2634:           if (_cand_cost[e] < 0) {
kpeter@2619:             _candidates[_curr_length++] = e;
kpeter@2634:             last_edge = e;
kpeter@2619:           }
kpeter@2619:           if (--cnt == 0) {
kpeter@2619:             if (_curr_length > limit) break;
kpeter@2619:             limit = 0;
kpeter@2619:             cnt = _block_size;
kpeter@2619:           }
kpeter@2619:         }
kpeter@2619:         if (_curr_length <= limit) {
kpeter@2634:           for (int e = 0; e < _next_edge; ++e) {
kpeter@2634:             _cand_cost[e] = _state[e] *
kpeter@2634:               (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@2634:             if (_cand_cost[e] < 0) {
kpeter@2619:               _candidates[_curr_length++] = e;
kpeter@2634:               last_edge = e;
kpeter@2619:             }
kpeter@2619:             if (--cnt == 0) {
kpeter@2619:               if (_curr_length > limit) break;
kpeter@2619:               limit = 0;
kpeter@2619:               cnt = _block_size;
kpeter@2619:             }
kpeter@2619:           }
kpeter@2619:         }
kpeter@2619:         if (_curr_length == 0) return false;
kpeter@2619:         _next_edge = last_edge + 1;
kpeter@2619: 
kpeter@2630:         // Make heap of the candidate list (approximating a partial sort)
kpeter@2630:         make_heap( _candidates.begin(), _candidates.begin() + _curr_length,
kpeter@2630:                    _sort_func );
kpeter@2619: 
kpeter@2630:         // Pop the first element of the heap
kpeter@2634:         _in_edge = _candidates[0];
kpeter@2630:         pop_heap( _candidates.begin(), _candidates.begin() + _curr_length,
kpeter@2630:                   _sort_func );
kpeter@2630:         _curr_length = std::min(_head_length, _curr_length - 1);
kpeter@2619:         return true;
kpeter@2619:       }
kpeter@2634: 
kpeter@2619:     }; //class AlteringListPivotRule
kpeter@2619: 
kpeter@2575:   private:
kpeter@2575: 
kpeter@2579:     // State constants for edges
kpeter@2579:     enum EdgeStateEnum {
kpeter@2579:       STATE_UPPER = -1,
kpeter@2579:       STATE_TREE  =  0,
kpeter@2579:       STATE_LOWER =  1
kpeter@2579:     };
kpeter@2575: 
kpeter@2575:   private:
kpeter@2575: 
kpeter@2575:     // The original graph
kpeter@2634:     const Graph &_orig_graph;
kpeter@2575:     // The original lower bound map
kpeter@2634:     const LowerMap *_orig_lower;
kpeter@2634:     // The original capacity map
kpeter@2634:     const CapacityMap &_orig_cap;
kpeter@2634:     // The original cost map
kpeter@2634:     const CostMap &_orig_cost;
kpeter@2634:     // The original supply map
kpeter@2634:     const SupplyMap *_orig_supply;
kpeter@2634:     // The source node (if no supply map was given)
kpeter@2634:     Node _orig_source;
kpeter@2634:     // The target node (if no supply map was given)
kpeter@2634:     Node _orig_target;
kpeter@2634:     // The flow value (if no supply map was given)
kpeter@2634:     Capacity _orig_flow_value;
kpeter@2575: 
kpeter@2634:     // The flow result map
kpeter@2634:     FlowMap *_flow_result;
kpeter@2634:     // The potential result map
kpeter@2634:     PotentialMap *_potential_result;
kpeter@2634:     // Indicate if the flow result map is local
kpeter@2634:     bool _local_flow;
kpeter@2634:     // Indicate if the potential result map is local
kpeter@2634:     bool _local_potential;
kpeter@2575: 
kpeter@2634:     // The edge references
kpeter@2634:     EdgeVector _edge;
kpeter@2634:     // The node references
kpeter@2634:     NodeVector _node;
kpeter@2634:     // The node ids
kpeter@2634:     IntNodeMap _node_id;
kpeter@2634:     // The source nodes of the edges
kpeter@2634:     IntVector _source;
kpeter@2634:     // The target nodess of the edges
kpeter@2634:     IntVector _target;
kpeter@2575: 
kpeter@2634:     // The (modified) capacity vector
kpeter@2634:     CapacityVector _cap;
kpeter@2634:     // The cost vector
kpeter@2634:     CostVector _cost;
kpeter@2634:     // The (modified) supply vector
kpeter@2634:     CostVector _supply;
kpeter@2634:     // The current flow vector
kpeter@2634:     CapacityVector _flow;
kpeter@2634:     // The current potential vector
kpeter@2634:     CostVector _pi;
kpeter@2575: 
kpeter@2634:     // The number of nodes in the original graph
kpeter@2634:     int _node_num;
kpeter@2634:     // The number of edges in the original graph
kpeter@2634:     int _edge_num;
kpeter@2619: 
kpeter@2634:     // The parent vector of the spanning tree structure
kpeter@2634:     IntVector _parent;
kpeter@2634:     // The pred_edge vector of the spanning tree structure
kpeter@2634:     IntVector _pred;
kpeter@2634:     // The thread vector of the spanning tree structure
kpeter@2634:     IntVector _thread;
kpeter@2635: 
kpeter@2635:     IntVector _rev_thread;
kpeter@2635:     IntVector _succ_num;
kpeter@2635:     IntVector _last_succ;
kpeter@2635: 
kpeter@2635:     IntVector _dirty_revs;
kpeter@2635:     
kpeter@2634:     // The forward vector of the spanning tree structure
kpeter@2634:     BoolVector _forward;
kpeter@2634:     // The state vector
kpeter@2634:     IntVector _state;
kpeter@2634:     // The root node
kpeter@2634:     int _root;
deba@2440: 
kpeter@2630:     // The entering edge of the current pivot iteration
kpeter@2634:     int _in_edge;
kpeter@2575: 
kpeter@2630:     // Temporary nodes used in the current pivot iteration
kpeter@2634:     int join, u_in, v_in, u_out, v_out;
kpeter@2634:     int right, first, second, last;
kpeter@2634:     int stem, par_stem, new_stem;
kpeter@2634: 
kpeter@2556:     // The maximum augment amount along the found cycle in the current
kpeter@2630:     // pivot iteration
kpeter@2556:     Capacity delta;
deba@2440: 
kpeter@2634:   public:
deba@2440: 
kpeter@2581:     /// \brief General constructor (with lower bounds).
deba@2440:     ///
kpeter@2581:     /// General constructor (with lower bounds).
deba@2440:     ///
kpeter@2575:     /// \param graph The directed graph the algorithm runs on.
kpeter@2575:     /// \param lower The lower bounds of the edges.
kpeter@2575:     /// \param capacity The capacities (upper bounds) of the edges.
kpeter@2575:     /// \param cost The cost (length) values of the edges.
kpeter@2575:     /// \param supply The supply values of the nodes (signed).
kpeter@2575:     NetworkSimplex( const Graph &graph,
kpeter@2575:                     const LowerMap &lower,
kpeter@2575:                     const CapacityMap &capacity,
kpeter@2575:                     const CostMap &cost,
kpeter@2575:                     const SupplyMap &supply ) :
kpeter@2634:       _orig_graph(graph), _orig_lower(&lower), _orig_cap(capacity),
kpeter@2634:       _orig_cost(cost), _orig_supply(&supply),
kpeter@2623:       _flow_result(NULL), _potential_result(NULL),
kpeter@2581:       _local_flow(false), _local_potential(false),
kpeter@2634:       _node_id(graph)
kpeter@2634:     {}
deba@2440: 
kpeter@2581:     /// \brief General constructor (without lower bounds).
deba@2440:     ///
kpeter@2581:     /// General constructor (without lower bounds).
deba@2440:     ///
kpeter@2575:     /// \param graph The directed graph the algorithm runs on.
kpeter@2575:     /// \param capacity The capacities (upper bounds) of the edges.
kpeter@2575:     /// \param cost The cost (length) values of the edges.
kpeter@2575:     /// \param supply The supply values of the nodes (signed).
kpeter@2575:     NetworkSimplex( const Graph &graph,
kpeter@2575:                     const CapacityMap &capacity,
kpeter@2575:                     const CostMap &cost,
kpeter@2575:                     const SupplyMap &supply ) :
kpeter@2634:       _orig_graph(graph), _orig_lower(NULL), _orig_cap(capacity),
kpeter@2634:       _orig_cost(cost), _orig_supply(&supply),
kpeter@2623:       _flow_result(NULL), _potential_result(NULL),
kpeter@2581:       _local_flow(false), _local_potential(false),
kpeter@2634:       _node_id(graph)
kpeter@2634:     {}
deba@2440: 
kpeter@2581:     /// \brief Simple constructor (with lower bounds).
deba@2440:     ///
kpeter@2581:     /// Simple constructor (with lower bounds).
deba@2440:     ///
kpeter@2575:     /// \param graph The directed graph the algorithm runs on.
kpeter@2575:     /// \param lower The lower bounds of the edges.
kpeter@2575:     /// \param capacity The capacities (upper bounds) of the edges.
kpeter@2575:     /// \param cost The cost (length) values of the edges.
kpeter@2575:     /// \param s The source node.
kpeter@2575:     /// \param t The target node.
kpeter@2575:     /// \param flow_value The required amount of flow from node \c s
kpeter@2575:     /// to node \c t (i.e. the supply of \c s and the demand of \c t).
kpeter@2575:     NetworkSimplex( const Graph &graph,
kpeter@2575:                     const LowerMap &lower,
kpeter@2575:                     const CapacityMap &capacity,
kpeter@2575:                     const CostMap &cost,
kpeter@2634:                     Node s, Node t,
kpeter@2634:                     Capacity flow_value ) :
kpeter@2634:       _orig_graph(graph), _orig_lower(&lower), _orig_cap(capacity),
kpeter@2634:       _orig_cost(cost), _orig_supply(NULL),
kpeter@2634:       _orig_source(s), _orig_target(t), _orig_flow_value(flow_value),
kpeter@2623:       _flow_result(NULL), _potential_result(NULL),
kpeter@2581:       _local_flow(false), _local_potential(false),
kpeter@2634:       _node_id(graph)
kpeter@2634:     {}
deba@2440: 
kpeter@2581:     /// \brief Simple constructor (without lower bounds).
deba@2440:     ///
kpeter@2581:     /// Simple constructor (without lower bounds).
deba@2440:     ///
kpeter@2575:     /// \param graph The directed graph the algorithm runs on.
kpeter@2575:     /// \param capacity The capacities (upper bounds) of the edges.
kpeter@2575:     /// \param cost The cost (length) values of the edges.
kpeter@2575:     /// \param s The source node.
kpeter@2575:     /// \param t The target node.
kpeter@2575:     /// \param flow_value The required amount of flow from node \c s
kpeter@2575:     /// to node \c t (i.e. the supply of \c s and the demand of \c t).
kpeter@2575:     NetworkSimplex( const Graph &graph,
kpeter@2575:                     const CapacityMap &capacity,
kpeter@2575:                     const CostMap &cost,
kpeter@2634:                     Node s, Node t,
kpeter@2634:                     Capacity flow_value ) :
kpeter@2634:       _orig_graph(graph), _orig_lower(NULL), _orig_cap(capacity),
kpeter@2634:       _orig_cost(cost), _orig_supply(NULL),
kpeter@2634:       _orig_source(s), _orig_target(t), _orig_flow_value(flow_value),
kpeter@2623:       _flow_result(NULL), _potential_result(NULL),
kpeter@2581:       _local_flow(false), _local_potential(false),
kpeter@2634:       _node_id(graph)
kpeter@2634:     {}
deba@2440: 
kpeter@2581:     /// Destructor.
kpeter@2581:     ~NetworkSimplex() {
kpeter@2581:       if (_local_flow) delete _flow_result;
kpeter@2581:       if (_local_potential) delete _potential_result;
kpeter@2581:     }
kpeter@2581: 
kpeter@2619:     /// \brief Set the flow map.
kpeter@2581:     ///
kpeter@2619:     /// Set the flow map.
kpeter@2581:     ///
kpeter@2581:     /// \return \c (*this)
kpeter@2581:     NetworkSimplex& flowMap(FlowMap &map) {
kpeter@2581:       if (_local_flow) {
kpeter@2581:         delete _flow_result;
kpeter@2581:         _local_flow = false;
kpeter@2581:       }
kpeter@2581:       _flow_result = &map;
kpeter@2581:       return *this;
kpeter@2581:     }
kpeter@2581: 
kpeter@2619:     /// \brief Set the potential map.
kpeter@2581:     ///
kpeter@2619:     /// Set the potential map.
kpeter@2581:     ///
kpeter@2581:     /// \return \c (*this)
kpeter@2581:     NetworkSimplex& potentialMap(PotentialMap &map) {
kpeter@2581:       if (_local_potential) {
kpeter@2581:         delete _potential_result;
kpeter@2581:         _local_potential = false;
kpeter@2581:       }
kpeter@2581:       _potential_result = &map;
kpeter@2581:       return *this;
kpeter@2581:     }
kpeter@2581: 
kpeter@2581:     /// \name Execution control
kpeter@2581: 
kpeter@2581:     /// @{
kpeter@2581: 
kpeter@2556:     /// \brief Runs the algorithm.
kpeter@2556:     ///
kpeter@2556:     /// Runs the algorithm.
kpeter@2556:     ///
kpeter@2575:     /// \param pivot_rule The pivot rule that is used during the
kpeter@2575:     /// algorithm.
kpeter@2575:     ///
kpeter@2575:     /// The available pivot rules:
kpeter@2575:     ///
kpeter@2575:     /// - FIRST_ELIGIBLE_PIVOT The next eligible edge is selected in
kpeter@2575:     /// a wraparound fashion in every iteration
kpeter@2575:     /// (\ref FirstEligiblePivotRule).
kpeter@2575:     ///
kpeter@2575:     /// - BEST_ELIGIBLE_PIVOT The best eligible edge is selected in
kpeter@2575:     /// every iteration (\ref BestEligiblePivotRule).
kpeter@2575:     ///
kpeter@2575:     /// - BLOCK_SEARCH_PIVOT A specified number of edges are examined in
kpeter@2575:     /// every iteration in a wraparound fashion and the best eligible
kpeter@2575:     /// edge is selected from this block (\ref BlockSearchPivotRule).
kpeter@2575:     ///
kpeter@2619:     /// - CANDIDATE_LIST_PIVOT In a major iteration a candidate list is
kpeter@2619:     /// built from eligible edges in a wraparound fashion and in the
kpeter@2619:     /// following minor iterations the best eligible edge is selected
kpeter@2619:     /// from this list (\ref CandidateListPivotRule).
kpeter@2575:     ///
kpeter@2619:     /// - ALTERING_LIST_PIVOT It is a modified version of the
kpeter@2619:     /// "Candidate List" pivot rule. It keeps only the several best
kpeter@2619:     /// eligible edges from the former candidate list and extends this
kpeter@2619:     /// list in every iteration (\ref AlteringListPivotRule).
kpeter@2575:     ///
kpeter@2619:     /// According to our comprehensive benchmark tests the "Block Search"
kpeter@2630:     /// pivot rule proved to be the fastest and the most robust on
kpeter@2630:     /// various test inputs. Thus it is the default option.
kpeter@2575:     ///
kpeter@2556:     /// \return \c true if a feasible flow can be found.
kpeter@2619:     bool run(PivotRuleEnum pivot_rule = BLOCK_SEARCH_PIVOT) {
kpeter@2575:       return init() && start(pivot_rule);
kpeter@2556:     }
kpeter@2556: 
kpeter@2581:     /// @}
kpeter@2581: 
kpeter@2581:     /// \name Query Functions
kpeter@2619:     /// The results of the algorithm can be obtained using these
kpeter@2619:     /// functions.\n
kpeter@2619:     /// \ref lemon::NetworkSimplex::run() "run()" must be called before
kpeter@2619:     /// using them.
kpeter@2581: 
kpeter@2581:     /// @{
kpeter@2581: 
kpeter@2619:     /// \brief Return a const reference to the edge map storing the
kpeter@2575:     /// found flow.
deba@2440:     ///
kpeter@2619:     /// Return a const reference to the edge map storing the found flow.
deba@2440:     ///
deba@2440:     /// \pre \ref run() must be called before using this function.
deba@2440:     const FlowMap& flowMap() const {
kpeter@2581:       return *_flow_result;
deba@2440:     }
deba@2440: 
kpeter@2619:     /// \brief Return a const reference to the node map storing the
kpeter@2575:     /// found potentials (the dual solution).
deba@2440:     ///
kpeter@2619:     /// Return a const reference to the node map storing the found
kpeter@2575:     /// potentials (the dual solution).
deba@2440:     ///
deba@2440:     /// \pre \ref run() must be called before using this function.
deba@2440:     const PotentialMap& potentialMap() const {
kpeter@2581:       return *_potential_result;
kpeter@2581:     }
kpeter@2581: 
kpeter@2619:     /// \brief Return the flow on the given edge.
kpeter@2581:     ///
kpeter@2619:     /// Return the flow on the given edge.
kpeter@2581:     ///
kpeter@2581:     /// \pre \ref run() must be called before using this function.
kpeter@2581:     Capacity flow(const typename Graph::Edge& edge) const {
kpeter@2581:       return (*_flow_result)[edge];
kpeter@2581:     }
kpeter@2581: 
kpeter@2619:     /// \brief Return the potential of the given node.
kpeter@2581:     ///
kpeter@2619:     /// Return the potential of the given node.
kpeter@2581:     ///
kpeter@2581:     /// \pre \ref run() must be called before using this function.
kpeter@2581:     Cost potential(const typename Graph::Node& node) const {
kpeter@2581:       return (*_potential_result)[node];
deba@2440:     }
deba@2440: 
kpeter@2619:     /// \brief Return the total cost of the found flow.
deba@2440:     ///
kpeter@2619:     /// Return the total cost of the found flow. The complexity of the
deba@2440:     /// function is \f$ O(e) \f$.
deba@2440:     ///
deba@2440:     /// \pre \ref run() must be called before using this function.
deba@2440:     Cost totalCost() const {
deba@2440:       Cost c = 0;
kpeter@2634:       for (EdgeIt e(_orig_graph); e != INVALID; ++e)
kpeter@2634:         c += (*_flow_result)[e] * _orig_cost[e];
deba@2440:       return c;
deba@2440:     }
deba@2440: 
kpeter@2581:     /// @}
kpeter@2581: 
kpeter@2575:   private:
deba@2440: 
kpeter@2634:     // Initialize internal data structures
deba@2440:     bool init() {
kpeter@2630:       // Initialize result maps
kpeter@2581:       if (!_flow_result) {
kpeter@2634:         _flow_result = new FlowMap(_orig_graph);
kpeter@2581:         _local_flow = true;
kpeter@2581:       }
kpeter@2581:       if (!_potential_result) {
kpeter@2634:         _potential_result = new PotentialMap(_orig_graph);
kpeter@2581:         _local_potential = true;
kpeter@2581:       }
kpeter@2634:       
kpeter@2634:       // Initialize vectors
kpeter@2634:       _node_num = countNodes(_orig_graph);
kpeter@2634:       _edge_num = countEdges(_orig_graph);
kpeter@2634:       int all_node_num = _node_num + 1;
kpeter@2634:       int all_edge_num = _edge_num + _node_num;
kpeter@2634:       
kpeter@2634:       _edge.resize(_edge_num);
kpeter@2634:       _node.reserve(_node_num);
kpeter@2634:       _source.resize(all_edge_num);
kpeter@2634:       _target.resize(all_edge_num);
kpeter@2634:       
kpeter@2634:       _cap.resize(all_edge_num);
kpeter@2634:       _cost.resize(all_edge_num);
kpeter@2634:       _supply.resize(all_node_num);
kpeter@2634:       _flow.resize(all_edge_num, 0);
kpeter@2634:       _pi.resize(all_node_num, 0);
kpeter@2634:       
kpeter@2634:       _parent.resize(all_node_num);
kpeter@2634:       _pred.resize(all_node_num);
kpeter@2635:       _forward.resize(all_node_num);
kpeter@2634:       _thread.resize(all_node_num);
kpeter@2635:       _rev_thread.resize(all_node_num);
kpeter@2635:       _succ_num.resize(all_node_num);
kpeter@2635:       _last_succ.resize(all_node_num);
kpeter@2634:       _state.resize(all_edge_num, STATE_LOWER);
kpeter@2634:       
kpeter@2634:       // Initialize node related data
kpeter@2634:       bool valid_supply = true;
kpeter@2634:       if (_orig_supply) {
kpeter@2634:         Supply sum = 0;
kpeter@2634:         int i = 0;
kpeter@2634:         for (NodeIt n(_orig_graph); n != INVALID; ++n, ++i) {
kpeter@2634:           _node.push_back(n);
kpeter@2634:           _node_id[n] = i;
kpeter@2634:           _supply[i] = (*_orig_supply)[n];
kpeter@2634:           sum += _supply[i];
kpeter@2634:         }
kpeter@2634:         valid_supply = (sum == 0);
kpeter@2634:       } else {
kpeter@2634:         int i = 0;
kpeter@2634:         for (NodeIt n(_orig_graph); n != INVALID; ++n, ++i) {
kpeter@2634:           _node.push_back(n);
kpeter@2634:           _node_id[n] = i;
kpeter@2634:           _supply[i] = 0;
kpeter@2634:         }
kpeter@2634:         _supply[_node_id[_orig_source]] =  _orig_flow_value;
kpeter@2634:         _supply[_node_id[_orig_target]] = -_orig_flow_value;
kpeter@2634:       }
kpeter@2634:       if (!valid_supply) return false;
kpeter@2634:       
kpeter@2634:       // Set data for the artificial root node
kpeter@2634:       _root = _node_num;
kpeter@2634:       _parent[_root] = -1;
kpeter@2634:       _pred[_root] = -1;
kpeter@2634:       _thread[_root] = 0;
kpeter@2635:       _rev_thread[0] = _root;
kpeter@2635:       _succ_num[_root] = all_node_num;
kpeter@2635:       _last_succ[_root] = _root - 1;
kpeter@2634:       _supply[_root] = 0;
kpeter@2634:       _pi[_root] = 0;
kpeter@2634:       
kpeter@2634:       // Store the edges in a mixed order
kpeter@2634:       int k = std::max(int(sqrt(_edge_num)), 10);
kpeter@2634:       int i = 0;
kpeter@2634:       for (EdgeIt e(_orig_graph); e != INVALID; ++e) {
kpeter@2634:         _edge[i] = e;
kpeter@2634:         if ((i += k) >= _edge_num) i = (i % k) + 1;
deba@2440:       }
deba@2440: 
kpeter@2634:       // Initialize edge maps
kpeter@2634:       for (int i = 0; i != _edge_num; ++i) {
kpeter@2634:         Edge e = _edge[i];
kpeter@2634:         _source[i] = _node_id[_orig_graph.source(e)];
kpeter@2634:         _target[i] = _node_id[_orig_graph.target(e)];
kpeter@2634:         _cost[i] = _orig_cost[e];
kpeter@2634:         _cap[i] = _orig_cap[e];
kpeter@2634:       }
deba@2440: 
kpeter@2634:       // Remove non-zero lower bounds
kpeter@2634:       if (_orig_lower) {
kpeter@2634:         for (int i = 0; i != _edge_num; ++i) {
kpeter@2634:           Capacity c = (*_orig_lower)[_edge[i]];
kpeter@2634:           if (c != 0) {
kpeter@2634:             _cap[i] -= c;
kpeter@2634:             _supply[_source[i]] -= c;
kpeter@2634:             _supply[_target[i]] += c;
kpeter@2634:           }
kpeter@2634:         }
kpeter@2634:       }
kpeter@2634: 
kpeter@2634:       // Add artificial edges and initialize the spanning tree data structure
deba@2440:       Cost max_cost = std::numeric_limits<Cost>::max() / 4;
kpeter@2634:       Capacity max_cap = std::numeric_limits<Capacity>::max();
kpeter@2634:       for (int u = 0, e = _edge_num; u != _node_num; ++u, ++e) {
kpeter@2575:         _parent[u] = _root;
kpeter@2634:         _pred[u] = e;
kpeter@2635:         _thread[u] = u + 1;
kpeter@2635:         _rev_thread[u + 1] = u;
kpeter@2635:         _succ_num[u] = 1;
kpeter@2635:         _last_succ[u] = u;
kpeter@2635:         _cap[e] = max_cap;
kpeter@2635:         _state[e] = STATE_TREE;
kpeter@2575:         if (_supply[u] >= 0) {
kpeter@2635:           _forward[u] = true;
kpeter@2635:           _pi[u] = 0;
kpeter@2635:           _source[e] = u;
kpeter@2635:           _target[e] = _root;
kpeter@2575:           _flow[e] = _supply[u];
kpeter@2635:           _cost[e] = 0;
kpeter@2635:         }
kpeter@2635:         else {
kpeter@2575:           _forward[u] = false;
kpeter@2634:           _pi[u] = max_cost;
kpeter@2635:           _source[e] = _root;
kpeter@2635:           _target[e] = u;
kpeter@2635:           _flow[e] = -_supply[u];
kpeter@2635:           _cost[e] = max_cost;
kpeter@2556:         }
deba@2440:       }
deba@2440: 
kpeter@2575:       return true;
deba@2440:     }
deba@2440: 
kpeter@2630:     // Find the join node
kpeter@2630:     void findJoinNode() {
kpeter@2634:       int u = _source[_in_edge];
kpeter@2634:       int v = _target[_in_edge];
kpeter@2575:       while (u != v) {
kpeter@2635:         if (_succ_num[u] < _succ_num[v]) {
kpeter@2635:           u = _parent[u];
kpeter@2635:         } else {
kpeter@2635:           v = _parent[v];
kpeter@2635:         }
deba@2440:       }
kpeter@2630:       join = u;
deba@2440:     }
deba@2440: 
kpeter@2634:     // Find the leaving edge of the cycle and returns true if the
kpeter@2630:     // leaving edge is not the same as the entering edge
kpeter@2630:     bool findLeavingEdge() {
kpeter@2630:       // Initialize first and second nodes according to the direction
deba@2440:       // of the cycle
kpeter@2575:       if (_state[_in_edge] == STATE_LOWER) {
kpeter@2634:         first  = _source[_in_edge];
kpeter@2634:         second = _target[_in_edge];
deba@2440:       } else {
kpeter@2634:         first  = _target[_in_edge];
kpeter@2634:         second = _source[_in_edge];
deba@2440:       }
kpeter@2634:       delta = _cap[_in_edge];
kpeter@2634:       int result = 0;
deba@2440:       Capacity d;
kpeter@2634:       int e;
deba@2440: 
kpeter@2630:       // Search the cycle along the path form the first node to the root
kpeter@2634:       for (int u = first; u != join; u = _parent[u]) {
kpeter@2634:         e = _pred[u];
kpeter@2634:         d = _forward[u] ? _flow[e] : _cap[e] - _flow[e];
kpeter@2556:         if (d < delta) {
kpeter@2556:           delta = d;
kpeter@2556:           u_out = u;
kpeter@2634:           result = 1;
kpeter@2556:         }
deba@2440:       }
kpeter@2630:       // Search the cycle along the path form the second node to the root
kpeter@2634:       for (int u = second; u != join; u = _parent[u]) {
kpeter@2634:         e = _pred[u];
kpeter@2634:         d = _forward[u] ? _cap[e] - _flow[e] : _flow[e];
kpeter@2556:         if (d <= delta) {
kpeter@2556:           delta = d;
kpeter@2556:           u_out = u;
kpeter@2634:           result = 2;
kpeter@2556:         }
deba@2440:       }
kpeter@2634: 
kpeter@2634:       if (result == 1) {
kpeter@2634:         u_in = first;
kpeter@2634:         v_in = second;
kpeter@2634:       } else {
kpeter@2634:         u_in = second;
kpeter@2634:         v_in = first;
kpeter@2634:       }
kpeter@2634:       return result != 0;
deba@2440:     }
deba@2440: 
kpeter@2634:     // Change _flow and _state vectors
kpeter@2634:     void changeFlow(bool change) {
kpeter@2630:       // Augment along the cycle
deba@2440:       if (delta > 0) {
kpeter@2575:         Capacity val = _state[_in_edge] * delta;
kpeter@2575:         _flow[_in_edge] += val;
kpeter@2634:         for (int u = _source[_in_edge]; u != join; u = _parent[u]) {
kpeter@2634:           _flow[_pred[u]] += _forward[u] ? -val : val;
kpeter@2556:         }
kpeter@2634:         for (int u = _target[_in_edge]; u != join; u = _parent[u]) {
kpeter@2634:           _flow[_pred[u]] += _forward[u] ? val : -val;
kpeter@2556:         }
deba@2440:       }
kpeter@2630:       // Update the state of the entering and leaving edges
deba@2440:       if (change) {
kpeter@2575:         _state[_in_edge] = STATE_TREE;
kpeter@2634:         _state[_pred[u_out]] =
kpeter@2634:           (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER;
deba@2440:       } else {
kpeter@2575:         _state[_in_edge] = -_state[_in_edge];
deba@2440:       }
deba@2440:     }
kpeter@2635:     
kpeter@2635:     // Update the tree structure
kpeter@2635:     void updateTreeStructure() {
kpeter@2635:       int u, w;
kpeter@2635:       int old_rev_thread = _rev_thread[u_out];
kpeter@2635:       int old_succ_num = _succ_num[u_out];
kpeter@2635:       int old_last_succ = _last_succ[u_out];
kpeter@2575:       v_out = _parent[u_out];
deba@2440: 
kpeter@2635:       u = _last_succ[u_in];  // the last successor of u_in
kpeter@2635:       right = _thread[u];    // the node after it
kpeter@2635:       
kpeter@2635:       // Handle the case when old_rev_thread equals to v_in 
kpeter@2635:       // (it also means that join and v_out coincide)
kpeter@2635:       if (old_rev_thread == v_in) {
kpeter@2635:         last = _thread[_last_succ[u_out]];
kpeter@2635:       } else {
kpeter@2635:         last = _thread[v_in];
kpeter@2635:       }
kpeter@2635: 
kpeter@2635:       // Update _thread and _parent along the stem nodes (i.e. the nodes 
kpeter@2635:       // between u_in and u_out, whose parent have to be changed)
kpeter@2635:       _thread[v_in] = stem = u_in;
kpeter@2635:       _dirty_revs.clear();
kpeter@2635:       _dirty_revs.push_back(v_in);
kpeter@2635:       par_stem = v_in;
kpeter@2635:       while (stem != u_out) {
kpeter@2635:         // Insert the next stem node into the thread list
kpeter@2635:         new_stem = _parent[stem];
kpeter@2635:         _thread[u] = new_stem;
kpeter@2635:         _dirty_revs.push_back(u);
kpeter@2635:         
kpeter@2635:         // Remove the subtree of stem from the thread list
kpeter@2635:         w = _rev_thread[stem];
kpeter@2635:         _thread[w] = right;
kpeter@2635:         _rev_thread[right] = w;
kpeter@2635: 
kpeter@2635:         // Change the parent node and shift stem nodes
kpeter@2635:         _parent[stem] = par_stem;        
kpeter@2635:         par_stem = stem;
kpeter@2635:         stem = new_stem;
kpeter@2635: 
kpeter@2635:         // Update u and right nodes
kpeter@2635:         u = _last_succ[stem] == _last_succ[par_stem] ?
kpeter@2635:           _rev_thread[par_stem] : _last_succ[stem];
kpeter@2635:         right = _thread[u];
kpeter@2635:       }
kpeter@2635:       _parent[u_out] = par_stem;
kpeter@2635:       _last_succ[u_out] = u;
kpeter@2635:       _thread[u] = last;
kpeter@2635:       _rev_thread[last] = u;
kpeter@2635: 
kpeter@2635:       // Remove the subtree of u_out from the thread list except for 
kpeter@2635:       // the case when old_rev_thread equals to v_in 
kpeter@2635:       // (it also means that join and v_out coincide)
kpeter@2635:       if (old_rev_thread != v_in) {
kpeter@2635:         _thread[old_rev_thread] = right;
kpeter@2635:         _rev_thread[right] = old_rev_thread;
kpeter@2635:       }
kpeter@2635:       
kpeter@2635:       // Update _rev_thread using the new _thread values
kpeter@2635:       for (int i = 0; i < int(_dirty_revs.size()); ++i) {
kpeter@2635:         u = _dirty_revs[i];
kpeter@2635:         _rev_thread[_thread[u]] = u;
kpeter@2635:       }
kpeter@2635:       
kpeter@2635:       // Update _last_succ for the stem nodes from u_out to u_in
kpeter@2635:       for (u = u_out; u != u_in; u = _parent[u]) {
kpeter@2635:         _last_succ[_parent[u]] = _last_succ[u];      
kpeter@2635:       }
kpeter@2635: 
kpeter@2635:       // Set limits for updating _last_succ form v_in and v_out
kpeter@2635:       // towards the root
kpeter@2635:       int up_limit_in = -1;
kpeter@2635:       int up_limit_out = -1;
kpeter@2635:       if (_last_succ[join] == v_in) {
kpeter@2635:         up_limit_out = join;
kpeter@2635:       } else {
kpeter@2635:         up_limit_in = join;
kpeter@2635:       }
kpeter@2635: 
kpeter@2635:       // Update _last_succ from v_in towards the root
kpeter@2635:       for (u = v_in; u != up_limit_in && _last_succ[u] == v_in; 
kpeter@2635:            u = _parent[u]) {
kpeter@2635:         _last_succ[u] = _last_succ[u_out];
kpeter@2635:       }
kpeter@2635:       // Update _last_succ from v_out towards the root
kpeter@2635:       if (join != old_rev_thread && v_in != old_rev_thread) {
kpeter@2635:         for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; 
kpeter@2635:              u = _parent[u]) {
kpeter@2635:           _last_succ[u] = old_rev_thread;
kpeter@2635:         }
kpeter@2635:       } else {
kpeter@2635:         for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
kpeter@2635:              u = _parent[u]) {
kpeter@2635:           _last_succ[u] = _last_succ[u_out];
kpeter@2556:         }
deba@2440:       }
deba@2440: 
kpeter@2635:       // Update _pred and _forward for the stem nodes from u_out to u_in
kpeter@2635:       u = u_out;
deba@2440:       while (u != u_in) {
kpeter@2635:         w = _parent[u];
kpeter@2635:         _pred[u] = _pred[w];
kpeter@2635:         _forward[u] = !_forward[w];
kpeter@2635:         u = w;
deba@2440:       }
kpeter@2634:       _pred[u_in] = _in_edge;
kpeter@2634:       _forward[u_in] = (u_in == _source[_in_edge]);
kpeter@2635:       
kpeter@2635:       // Update _succ_num from v_in to join
kpeter@2635:       for (u = v_in; u != join; u = _parent[u]) {
kpeter@2635:         _succ_num[u] += old_succ_num;
kpeter@2635:       }
kpeter@2635:       // Update _succ_num from v_out to join
kpeter@2635:       for (u = v_out; u != join; u = _parent[u]) {
kpeter@2635:         _succ_num[u] -= old_succ_num;
kpeter@2635:       }
kpeter@2635:       // Update _succ_num for the stem nodes from u_out to u_in
kpeter@2635:       int tmp = 0;
kpeter@2635:       u = u_out;
kpeter@2635:       while (u != u_in) {
kpeter@2635:         w = _parent[u];
kpeter@2635:         tmp = _succ_num[u] - _succ_num[w] + tmp;
kpeter@2635:         _succ_num[u] = tmp;
kpeter@2635:         u = w;
kpeter@2635:       }
kpeter@2635:       _succ_num[u_in] = old_succ_num;
deba@2440:     }
deba@2440: 
kpeter@2635:     // Update potentials
kpeter@2635:     void updatePotential() {
kpeter@2628:       Cost sigma = _forward[u_in] ?
kpeter@2634:         _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] :
kpeter@2634:         _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]];
kpeter@2635:       // Update in the lower subtree (which has been moved)
kpeter@2635:       int end = _thread[_last_succ[u_in]];
kpeter@2635:       for (int u = u_in; u != end; u = _thread[u]) {
kpeter@2634:         _pi[u] += sigma;
deba@2440:       }
deba@2440:     }
deba@2440: 
kpeter@2630:     // Execute the algorithm
kpeter@2575:     bool start(PivotRuleEnum pivot_rule) {
kpeter@2630:       // Select the pivot rule implementation
kpeter@2575:       switch (pivot_rule) {
kpeter@2575:         case FIRST_ELIGIBLE_PIVOT:
kpeter@2575:           return start<FirstEligiblePivotRule>();
kpeter@2575:         case BEST_ELIGIBLE_PIVOT:
kpeter@2575:           return start<BestEligiblePivotRule>();
kpeter@2575:         case BLOCK_SEARCH_PIVOT:
kpeter@2575:           return start<BlockSearchPivotRule>();
kpeter@2575:         case CANDIDATE_LIST_PIVOT:
kpeter@2575:           return start<CandidateListPivotRule>();
kpeter@2619:         case ALTERING_LIST_PIVOT:
kpeter@2619:           return start<AlteringListPivotRule>();
kpeter@2575:       }
kpeter@2575:       return false;
kpeter@2575:     }
kpeter@2575: 
kpeter@2575:     template<class PivotRuleImplementation>
deba@2440:     bool start() {
kpeter@2634:       PivotRuleImplementation pivot(*this);
kpeter@2635:       
kpeter@2630:       // Execute the network simplex algorithm
kpeter@2575:       while (pivot.findEnteringEdge()) {
kpeter@2630:         findJoinNode();
kpeter@2556:         bool change = findLeavingEdge();
kpeter@2634:         changeFlow(change);
kpeter@2556:         if (change) {
kpeter@2635:           updateTreeStructure();
kpeter@2635:           updatePotential();
kpeter@2556:         }
deba@2440:       }
kpeter@2635:       
kpeter@2630:       // Check if the flow amount equals zero on all the artificial edges
kpeter@2634:       for (int e = _edge_num; e != _edge_num + _node_num; ++e) {
kpeter@2575:         if (_flow[e] > 0) return false;
kpeter@2634:       }
deba@2440: 
kpeter@2630:       // Copy flow values to _flow_result
kpeter@2634:       if (_orig_lower) {
kpeter@2634:         for (int i = 0; i != _edge_num; ++i) {
kpeter@2634:           Edge e = _edge[i];
kpeter@2634:           (*_flow_result)[e] = (*_orig_lower)[e] + _flow[i];
kpeter@2634:         }
deba@2440:       } else {
kpeter@2634:         for (int i = 0; i != _edge_num; ++i) {
kpeter@2634:           (*_flow_result)[_edge[i]] = _flow[i];
kpeter@2634:         }
deba@2440:       }
kpeter@2630:       // Copy potential values to _potential_result
kpeter@2634:       for (int i = 0; i != _node_num; ++i) {
kpeter@2634:         (*_potential_result)[_node[i]] = _pi[i];
kpeter@2634:       }
kpeter@2635:       
deba@2440:       return true;
deba@2440:     }
deba@2440: 
deba@2440:   }; //class NetworkSimplex
deba@2440: 
deba@2440:   ///@}
deba@2440: 
deba@2440: } //namespace lemon
deba@2440: 
deba@2440: #endif //LEMON_NETWORK_SIMPLEX_H