kpeter@593: /* -*- mode: C++; indent-tabs-mode: nil; -*-
kpeter@593:  *
kpeter@593:  * This file is a part of LEMON, a generic C++ optimization library.
kpeter@593:  *
kpeter@593:  * Copyright (C) 2003-2009
kpeter@593:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
kpeter@593:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
kpeter@593:  *
kpeter@593:  * Permission to use, modify and distribute this software is granted
kpeter@593:  * provided that this copyright notice appears in all copies. For
kpeter@593:  * precise terms see the accompanying LICENSE file.
kpeter@593:  *
kpeter@593:  * This software is provided "AS IS" with no warranty of any kind,
kpeter@593:  * express or implied, and with no claim as to its suitability for any
kpeter@593:  * purpose.
kpeter@593:  *
kpeter@593:  */
kpeter@593: 
kpeter@593: #ifndef LEMON_NETWORK_SIMPLEX_H
kpeter@593: #define LEMON_NETWORK_SIMPLEX_H
kpeter@593: 
kpeter@593: /// \ingroup min_cost_flow
kpeter@593: ///
kpeter@593: /// \file
kpeter@593: /// \brief Network simplex algorithm for finding a minimum cost flow.
kpeter@593: 
kpeter@593: #include <vector>
kpeter@593: #include <limits>
kpeter@593: #include <algorithm>
kpeter@593: 
kpeter@593: #include <lemon/math.h>
kpeter@593: 
kpeter@593: namespace lemon {
kpeter@593: 
kpeter@593:   /// \addtogroup min_cost_flow
kpeter@593:   /// @{
kpeter@593: 
kpeter@593:   /// \brief Implementation of the primal network simplex algorithm
kpeter@593:   /// for finding a \ref min_cost_flow "minimum cost flow".
kpeter@593:   ///
kpeter@593:   /// \ref NetworkSimplex implements the primal network simplex algorithm
kpeter@593:   /// for finding a \ref min_cost_flow "minimum cost flow".
kpeter@593:   ///
kpeter@593:   /// \tparam Digraph The digraph type the algorithm runs on.
kpeter@593:   /// \tparam LowerMap The type of the lower bound map.
kpeter@593:   /// \tparam CapacityMap The type of the capacity (upper bound) map.
kpeter@593:   /// \tparam CostMap The type of the cost (length) map.
kpeter@593:   /// \tparam SupplyMap The type of the supply map.
kpeter@593:   ///
kpeter@593:   /// \warning
kpeter@593:   /// - Arc capacities and costs should be \e non-negative \e integers.
kpeter@593:   /// - Supply values should be \e signed \e integers.
kpeter@593:   /// - The value types of the maps should be convertible to each other.
kpeter@593:   /// - \c CostMap::Value must be signed type.
kpeter@593:   ///
kpeter@593:   /// \note \ref NetworkSimplex provides five different pivot rule
kpeter@593:   /// implementations that significantly affect the efficiency of the
kpeter@593:   /// algorithm.
kpeter@593:   /// By default "Block Search" pivot rule is used, which proved to be
kpeter@593:   /// by far the most efficient according to our benchmark tests.
kpeter@593:   /// However another pivot rule can be selected using \ref run()
kpeter@593:   /// function with the proper parameter.
kpeter@593: #ifdef DOXYGEN
kpeter@593:   template < typename Digraph,
kpeter@593:              typename LowerMap,
kpeter@593:              typename CapacityMap,
kpeter@593:              typename CostMap,
kpeter@593:              typename SupplyMap >
kpeter@593: 
kpeter@593: #else
kpeter@593:   template < typename Digraph,
kpeter@593:              typename LowerMap = typename Digraph::template ArcMap<int>,
kpeter@593:              typename CapacityMap = typename Digraph::template ArcMap<int>,
kpeter@593:              typename CostMap = typename Digraph::template ArcMap<int>,
kpeter@593:              typename SupplyMap = typename Digraph::template NodeMap<int> >
kpeter@593: #endif
kpeter@593:   class NetworkSimplex
kpeter@593:   {
kpeter@593:     TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
kpeter@593: 
kpeter@593:     typedef typename CapacityMap::Value Capacity;
kpeter@593:     typedef typename CostMap::Value Cost;
kpeter@593:     typedef typename SupplyMap::Value Supply;
kpeter@593: 
kpeter@593:     typedef std::vector<Arc> ArcVector;
kpeter@593:     typedef std::vector<Node> NodeVector;
kpeter@593:     typedef std::vector<int> IntVector;
kpeter@593:     typedef std::vector<bool> BoolVector;
kpeter@593:     typedef std::vector<Capacity> CapacityVector;
kpeter@593:     typedef std::vector<Cost> CostVector;
kpeter@593:     typedef std::vector<Supply> SupplyVector;
kpeter@593: 
kpeter@593:   public:
kpeter@593: 
kpeter@593:     /// The type of the flow map
kpeter@593:     typedef typename Digraph::template ArcMap<Capacity> FlowMap;
kpeter@593:     /// The type of the potential map
kpeter@593:     typedef typename Digraph::template NodeMap<Cost> PotentialMap;
kpeter@593: 
kpeter@593:   public:
kpeter@593: 
kpeter@593:     /// Enum type for selecting the pivot rule used by \ref run()
kpeter@593:     enum PivotRuleEnum {
kpeter@593:       FIRST_ELIGIBLE_PIVOT,
kpeter@593:       BEST_ELIGIBLE_PIVOT,
kpeter@593:       BLOCK_SEARCH_PIVOT,
kpeter@593:       CANDIDATE_LIST_PIVOT,
kpeter@593:       ALTERING_LIST_PIVOT
kpeter@593:     };
kpeter@593: 
kpeter@593:   private:
kpeter@593: 
kpeter@593:     // State constants for arcs
kpeter@593:     enum ArcStateEnum {
kpeter@593:       STATE_UPPER = -1,
kpeter@593:       STATE_TREE  =  0,
kpeter@593:       STATE_LOWER =  1
kpeter@593:     };
kpeter@593: 
kpeter@593:   private:
kpeter@593: 
kpeter@593:     // References for the original data
kpeter@593:     const Digraph &_orig_graph;
kpeter@593:     const LowerMap *_orig_lower;
kpeter@593:     const CapacityMap &_orig_cap;
kpeter@593:     const CostMap &_orig_cost;
kpeter@593:     const SupplyMap *_orig_supply;
kpeter@593:     Node _orig_source;
kpeter@593:     Node _orig_target;
kpeter@593:     Capacity _orig_flow_value;
kpeter@593: 
kpeter@593:     // Result maps
kpeter@593:     FlowMap *_flow_result;
kpeter@593:     PotentialMap *_potential_result;
kpeter@593:     bool _local_flow;
kpeter@593:     bool _local_potential;
kpeter@593: 
kpeter@593:     // Data structures for storing the graph
kpeter@593:     ArcVector _arc;
kpeter@593:     NodeVector _node;
kpeter@593:     IntNodeMap _node_id;
kpeter@593:     IntVector _source;
kpeter@593:     IntVector _target;
kpeter@593: 
kpeter@593:     // The number of nodes and arcs in the original graph
kpeter@593:     int _node_num;
kpeter@593:     int _arc_num;
kpeter@593: 
kpeter@593:     // Node and arc maps
kpeter@593:     CapacityVector _cap;
kpeter@593:     CostVector _cost;
kpeter@593:     CostVector _supply;
kpeter@593:     CapacityVector _flow;
kpeter@593:     CostVector _pi;
kpeter@593: 
kpeter@593:     // Node and arc maps for the spanning tree structure
kpeter@593:     IntVector _depth;
kpeter@593:     IntVector _parent;
kpeter@593:     IntVector _pred;
kpeter@593:     IntVector _thread;
kpeter@593:     BoolVector _forward;
kpeter@593:     IntVector _state;
kpeter@593: 
kpeter@593:     // The root node
kpeter@593:     int _root;
kpeter@593: 
kpeter@593:     // The entering arc in the current pivot iteration
kpeter@593:     int _in_arc;
kpeter@593: 
kpeter@593:     // Temporary data used in the current pivot iteration
kpeter@593:     int join, u_in, v_in, u_out, v_out;
kpeter@593:     int right, first, second, last;
kpeter@593:     int stem, par_stem, new_stem;
kpeter@593:     Capacity delta;
kpeter@593: 
kpeter@593:   private:
kpeter@593: 
kpeter@593:     /// \brief Implementation of the "First Eligible" pivot rule for the
kpeter@593:     /// \ref NetworkSimplex "network simplex" algorithm.
kpeter@593:     ///
kpeter@593:     /// This class implements the "First Eligible" pivot rule
kpeter@593:     /// for the \ref NetworkSimplex "network simplex" algorithm.
kpeter@593:     ///
kpeter@593:     /// For more information see \ref NetworkSimplex::run().
kpeter@593:     class FirstEligiblePivotRule
kpeter@593:     {
kpeter@593:     private:
kpeter@593: 
kpeter@593:       // References to the NetworkSimplex class
kpeter@593:       const ArcVector &_arc;
kpeter@593:       const IntVector  &_source;
kpeter@593:       const IntVector  &_target;
kpeter@593:       const CostVector &_cost;
kpeter@593:       const IntVector  &_state;
kpeter@593:       const CostVector &_pi;
kpeter@593:       int &_in_arc;
kpeter@593:       int _arc_num;
kpeter@593: 
kpeter@593:       // Pivot rule data
kpeter@593:       int _next_arc;
kpeter@593: 
kpeter@593:     public:
kpeter@593: 
kpeter@593:       /// Constructor
kpeter@593:       FirstEligiblePivotRule(NetworkSimplex &ns) :
kpeter@593:         _arc(ns._arc), _source(ns._source), _target(ns._target),
kpeter@593:         _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@593:         _in_arc(ns._in_arc), _arc_num(ns._arc_num), _next_arc(0)
kpeter@593:       {}
kpeter@593: 
kpeter@593:       /// Find next entering arc
kpeter@593:       bool findEnteringArc() {
kpeter@593:         Cost c;
kpeter@593:         for (int e = _next_arc; e < _arc_num; ++e) {
kpeter@593:           c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@593:           if (c < 0) {
kpeter@593:             _in_arc = e;
kpeter@593:             _next_arc = e + 1;
kpeter@593:             return true;
kpeter@593:           }
kpeter@593:         }
kpeter@593:         for (int e = 0; e < _next_arc; ++e) {
kpeter@593:           c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@593:           if (c < 0) {
kpeter@593:             _in_arc = e;
kpeter@593:             _next_arc = e + 1;
kpeter@593:             return true;
kpeter@593:           }
kpeter@593:         }
kpeter@593:         return false;
kpeter@593:       }
kpeter@593: 
kpeter@593:     }; //class FirstEligiblePivotRule
kpeter@593: 
kpeter@593: 
kpeter@593:     /// \brief Implementation of the "Best Eligible" pivot rule for the
kpeter@593:     /// \ref NetworkSimplex "network simplex" algorithm.
kpeter@593:     ///
kpeter@593:     /// This class implements the "Best Eligible" pivot rule
kpeter@593:     /// for the \ref NetworkSimplex "network simplex" algorithm.
kpeter@593:     ///
kpeter@593:     /// For more information see \ref NetworkSimplex::run().
kpeter@593:     class BestEligiblePivotRule
kpeter@593:     {
kpeter@593:     private:
kpeter@593: 
kpeter@593:       // References to the NetworkSimplex class
kpeter@593:       const ArcVector &_arc;
kpeter@593:       const IntVector  &_source;
kpeter@593:       const IntVector  &_target;
kpeter@593:       const CostVector &_cost;
kpeter@593:       const IntVector  &_state;
kpeter@593:       const CostVector &_pi;
kpeter@593:       int &_in_arc;
kpeter@593:       int _arc_num;
kpeter@593: 
kpeter@593:     public:
kpeter@593: 
kpeter@593:       /// Constructor
kpeter@593:       BestEligiblePivotRule(NetworkSimplex &ns) :
kpeter@593:         _arc(ns._arc), _source(ns._source), _target(ns._target),
kpeter@593:         _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@593:         _in_arc(ns._in_arc), _arc_num(ns._arc_num)
kpeter@593:       {}
kpeter@593: 
kpeter@593:       /// Find next entering arc
kpeter@593:       bool findEnteringArc() {
kpeter@593:         Cost c, min = 0;
kpeter@593:         for (int e = 0; e < _arc_num; ++e) {
kpeter@593:           c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@593:           if (c < min) {
kpeter@593:             min = c;
kpeter@593:             _in_arc = e;
kpeter@593:           }
kpeter@593:         }
kpeter@593:         return min < 0;
kpeter@593:       }
kpeter@593: 
kpeter@593:     }; //class BestEligiblePivotRule
kpeter@593: 
kpeter@593: 
kpeter@593:     /// \brief Implementation of the "Block Search" pivot rule for the
kpeter@593:     /// \ref NetworkSimplex "network simplex" algorithm.
kpeter@593:     ///
kpeter@593:     /// This class implements the "Block Search" pivot rule
kpeter@593:     /// for the \ref NetworkSimplex "network simplex" algorithm.
kpeter@593:     ///
kpeter@593:     /// For more information see \ref NetworkSimplex::run().
kpeter@593:     class BlockSearchPivotRule
kpeter@593:     {
kpeter@593:     private:
kpeter@593: 
kpeter@593:       // References to the NetworkSimplex class
kpeter@593:       const ArcVector &_arc;
kpeter@593:       const IntVector  &_source;
kpeter@593:       const IntVector  &_target;
kpeter@593:       const CostVector &_cost;
kpeter@593:       const IntVector  &_state;
kpeter@593:       const CostVector &_pi;
kpeter@593:       int &_in_arc;
kpeter@593:       int _arc_num;
kpeter@593: 
kpeter@593:       // Pivot rule data
kpeter@593:       int _block_size;
kpeter@593:       int _next_arc;
kpeter@593: 
kpeter@593:     public:
kpeter@593: 
kpeter@593:       /// Constructor
kpeter@593:       BlockSearchPivotRule(NetworkSimplex &ns) :
kpeter@593:         _arc(ns._arc), _source(ns._source), _target(ns._target),
kpeter@593:         _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@593:         _in_arc(ns._in_arc), _arc_num(ns._arc_num), _next_arc(0)
kpeter@593:       {
kpeter@593:         // The main parameters of the pivot rule
kpeter@593:         const double BLOCK_SIZE_FACTOR = 2.0;
kpeter@593:         const int MIN_BLOCK_SIZE = 10;
kpeter@593: 
kpeter@593:         _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_arc_num)),
kpeter@593:                                 MIN_BLOCK_SIZE );
kpeter@593:       }
kpeter@593: 
kpeter@593:       /// Find next entering arc
kpeter@593:       bool findEnteringArc() {
kpeter@593:         Cost c, min = 0;
kpeter@593:         int cnt = _block_size;
kpeter@593:         int e, min_arc = _next_arc;
kpeter@593:         for (e = _next_arc; e < _arc_num; ++e) {
kpeter@593:           c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@593:           if (c < min) {
kpeter@593:             min = c;
kpeter@593:             min_arc = e;
kpeter@593:           }
kpeter@593:           if (--cnt == 0) {
kpeter@593:             if (min < 0) break;
kpeter@593:             cnt = _block_size;
kpeter@593:           }
kpeter@593:         }
kpeter@593:         if (min == 0 || cnt > 0) {
kpeter@593:           for (e = 0; e < _next_arc; ++e) {
kpeter@593:             c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@593:             if (c < min) {
kpeter@593:               min = c;
kpeter@593:               min_arc = e;
kpeter@593:             }
kpeter@593:             if (--cnt == 0) {
kpeter@593:               if (min < 0) break;
kpeter@593:               cnt = _block_size;
kpeter@593:             }
kpeter@593:           }
kpeter@593:         }
kpeter@593:         if (min >= 0) return false;
kpeter@593:         _in_arc = min_arc;
kpeter@593:         _next_arc = e;
kpeter@593:         return true;
kpeter@593:       }
kpeter@593: 
kpeter@593:     }; //class BlockSearchPivotRule
kpeter@593: 
kpeter@593: 
kpeter@593:     /// \brief Implementation of the "Candidate List" pivot rule for the
kpeter@593:     /// \ref NetworkSimplex "network simplex" algorithm.
kpeter@593:     ///
kpeter@593:     /// This class implements the "Candidate List" pivot rule
kpeter@593:     /// for the \ref NetworkSimplex "network simplex" algorithm.
kpeter@593:     ///
kpeter@593:     /// For more information see \ref NetworkSimplex::run().
kpeter@593:     class CandidateListPivotRule
kpeter@593:     {
kpeter@593:     private:
kpeter@593: 
kpeter@593:       // References to the NetworkSimplex class
kpeter@593:       const ArcVector &_arc;
kpeter@593:       const IntVector  &_source;
kpeter@593:       const IntVector  &_target;
kpeter@593:       const CostVector &_cost;
kpeter@593:       const IntVector  &_state;
kpeter@593:       const CostVector &_pi;
kpeter@593:       int &_in_arc;
kpeter@593:       int _arc_num;
kpeter@593: 
kpeter@593:       // Pivot rule data
kpeter@593:       IntVector _candidates;
kpeter@593:       int _list_length, _minor_limit;
kpeter@593:       int _curr_length, _minor_count;
kpeter@593:       int _next_arc;
kpeter@593: 
kpeter@593:     public:
kpeter@593: 
kpeter@593:       /// Constructor
kpeter@593:       CandidateListPivotRule(NetworkSimplex &ns) :
kpeter@593:         _arc(ns._arc), _source(ns._source), _target(ns._target),
kpeter@593:         _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@593:         _in_arc(ns._in_arc), _arc_num(ns._arc_num), _next_arc(0)
kpeter@593:       {
kpeter@593:         // The main parameters of the pivot rule
kpeter@593:         const double LIST_LENGTH_FACTOR = 1.0;
kpeter@593:         const int MIN_LIST_LENGTH = 10;
kpeter@593:         const double MINOR_LIMIT_FACTOR = 0.1;
kpeter@593:         const int MIN_MINOR_LIMIT = 3;
kpeter@593: 
kpeter@593:         _list_length = std::max( int(LIST_LENGTH_FACTOR * sqrt(_arc_num)),
kpeter@593:                                  MIN_LIST_LENGTH );
kpeter@593:         _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length),
kpeter@593:                                  MIN_MINOR_LIMIT );
kpeter@593:         _curr_length = _minor_count = 0;
kpeter@593:         _candidates.resize(_list_length);
kpeter@593:       }
kpeter@593: 
kpeter@593:       /// Find next entering arc
kpeter@593:       bool findEnteringArc() {
kpeter@593:         Cost min, c;
kpeter@593:         int e, min_arc = _next_arc;
kpeter@593:         if (_curr_length > 0 && _minor_count < _minor_limit) {
kpeter@593:           // Minor iteration: select the best eligible arc from the
kpeter@593:           // current candidate list
kpeter@593:           ++_minor_count;
kpeter@593:           min = 0;
kpeter@593:           for (int i = 0; i < _curr_length; ++i) {
kpeter@593:             e = _candidates[i];
kpeter@593:             c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@593:             if (c < min) {
kpeter@593:               min = c;
kpeter@593:               min_arc = e;
kpeter@593:             }
kpeter@593:             if (c >= 0) {
kpeter@593:               _candidates[i--] = _candidates[--_curr_length];
kpeter@593:             }
kpeter@593:           }
kpeter@593:           if (min < 0) {
kpeter@593:             _in_arc = min_arc;
kpeter@593:             return true;
kpeter@593:           }
kpeter@593:         }
kpeter@593: 
kpeter@593:         // Major iteration: build a new candidate list
kpeter@593:         min = 0;
kpeter@593:         _curr_length = 0;
kpeter@593:         for (e = _next_arc; e < _arc_num; ++e) {
kpeter@593:           c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@593:           if (c < 0) {
kpeter@593:             _candidates[_curr_length++] = e;
kpeter@593:             if (c < min) {
kpeter@593:               min = c;
kpeter@593:               min_arc = e;
kpeter@593:             }
kpeter@593:             if (_curr_length == _list_length) break;
kpeter@593:           }
kpeter@593:         }
kpeter@593:         if (_curr_length < _list_length) {
kpeter@593:           for (e = 0; e < _next_arc; ++e) {
kpeter@593:             c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@593:             if (c < 0) {
kpeter@593:               _candidates[_curr_length++] = e;
kpeter@593:               if (c < min) {
kpeter@593:                 min = c;
kpeter@593:                 min_arc = e;
kpeter@593:               }
kpeter@593:               if (_curr_length == _list_length) break;
kpeter@593:             }
kpeter@593:           }
kpeter@593:         }
kpeter@593:         if (_curr_length == 0) return false;
kpeter@593:         _minor_count = 1;
kpeter@593:         _in_arc = min_arc;
kpeter@593:         _next_arc = e;
kpeter@593:         return true;
kpeter@593:       }
kpeter@593: 
kpeter@593:     }; //class CandidateListPivotRule
kpeter@593: 
kpeter@593: 
kpeter@593:     /// \brief Implementation of the "Altering Candidate List" pivot rule
kpeter@593:     /// for the \ref NetworkSimplex "network simplex" algorithm.
kpeter@593:     ///
kpeter@593:     /// This class implements the "Altering Candidate List" pivot rule
kpeter@593:     /// for the \ref NetworkSimplex "network simplex" algorithm.
kpeter@593:     ///
kpeter@593:     /// For more information see \ref NetworkSimplex::run().
kpeter@593:     class AlteringListPivotRule
kpeter@593:     {
kpeter@593:     private:
kpeter@593: 
kpeter@593:       // References to the NetworkSimplex class
kpeter@593:       const ArcVector &_arc;
kpeter@593:       const IntVector  &_source;
kpeter@593:       const IntVector  &_target;
kpeter@593:       const CostVector &_cost;
kpeter@593:       const IntVector  &_state;
kpeter@593:       const CostVector &_pi;
kpeter@593:       int &_in_arc;
kpeter@593:       int _arc_num;
kpeter@593: 
kpeter@593:       // Pivot rule data
kpeter@593:       int _block_size, _head_length, _curr_length;
kpeter@593:       int _next_arc;
kpeter@593:       IntVector _candidates;
kpeter@593:       CostVector _cand_cost;
kpeter@593: 
kpeter@593:       // Functor class to compare arcs during sort of the candidate list
kpeter@593:       class SortFunc
kpeter@593:       {
kpeter@593:       private:
kpeter@593:         const CostVector &_map;
kpeter@593:       public:
kpeter@593:         SortFunc(const CostVector &map) : _map(map) {}
kpeter@593:         bool operator()(int left, int right) {
kpeter@593:           return _map[left] > _map[right];
kpeter@593:         }
kpeter@593:       };
kpeter@593: 
kpeter@593:       SortFunc _sort_func;
kpeter@593: 
kpeter@593:     public:
kpeter@593: 
kpeter@593:       /// Constructor
kpeter@593:       AlteringListPivotRule(NetworkSimplex &ns) :
kpeter@593:         _arc(ns._arc), _source(ns._source), _target(ns._target),
kpeter@593:         _cost(ns._cost), _state(ns._state), _pi(ns._pi),
kpeter@593:         _in_arc(ns._in_arc), _arc_num(ns._arc_num),
kpeter@593:         _next_arc(0), _cand_cost(ns._arc_num), _sort_func(_cand_cost)
kpeter@593:       {
kpeter@593:         // The main parameters of the pivot rule
kpeter@593:         const double BLOCK_SIZE_FACTOR = 1.5;
kpeter@593:         const int MIN_BLOCK_SIZE = 10;
kpeter@593:         const double HEAD_LENGTH_FACTOR = 0.1;
kpeter@593:         const int MIN_HEAD_LENGTH = 3;
kpeter@593: 
kpeter@593:         _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_arc_num)),
kpeter@593:                                 MIN_BLOCK_SIZE );
kpeter@593:         _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size),
kpeter@593:                                  MIN_HEAD_LENGTH );
kpeter@593:         _candidates.resize(_head_length + _block_size);
kpeter@593:         _curr_length = 0;
kpeter@593:       }
kpeter@593: 
kpeter@593:       /// Find next entering arc
kpeter@593:       bool findEnteringArc() {
kpeter@593:         // Check the current candidate list
kpeter@593:         int e;
kpeter@593:         for (int i = 0; i < _curr_length; ++i) {
kpeter@593:           e = _candidates[i];
kpeter@593:           _cand_cost[e] = _state[e] *
kpeter@593:             (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@593:           if (_cand_cost[e] >= 0) {
kpeter@593:             _candidates[i--] = _candidates[--_curr_length];
kpeter@593:           }
kpeter@593:         }
kpeter@593: 
kpeter@593:         // Extend the list
kpeter@593:         int cnt = _block_size;
kpeter@593:         int last_edge = 0;
kpeter@593:         int limit = _head_length;
kpeter@593: 
kpeter@593:         for (int e = _next_arc; e < _arc_num; ++e) {
kpeter@593:           _cand_cost[e] = _state[e] *
kpeter@593:             (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@593:           if (_cand_cost[e] < 0) {
kpeter@593:             _candidates[_curr_length++] = e;
kpeter@593:             last_edge = e;
kpeter@593:           }
kpeter@593:           if (--cnt == 0) {
kpeter@593:             if (_curr_length > limit) break;
kpeter@593:             limit = 0;
kpeter@593:             cnt = _block_size;
kpeter@593:           }
kpeter@593:         }
kpeter@593:         if (_curr_length <= limit) {
kpeter@593:           for (int e = 0; e < _next_arc; ++e) {
kpeter@593:             _cand_cost[e] = _state[e] *
kpeter@593:               (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
kpeter@593:             if (_cand_cost[e] < 0) {
kpeter@593:               _candidates[_curr_length++] = e;
kpeter@593:               last_edge = e;
kpeter@593:             }
kpeter@593:             if (--cnt == 0) {
kpeter@593:               if (_curr_length > limit) break;
kpeter@593:               limit = 0;
kpeter@593:               cnt = _block_size;
kpeter@593:             }
kpeter@593:           }
kpeter@593:         }
kpeter@593:         if (_curr_length == 0) return false;
kpeter@593:         _next_arc = last_edge + 1;
kpeter@593: 
kpeter@593:         // Make heap of the candidate list (approximating a partial sort)
kpeter@593:         make_heap( _candidates.begin(), _candidates.begin() + _curr_length,
kpeter@593:                    _sort_func );
kpeter@593: 
kpeter@593:         // Pop the first element of the heap
kpeter@593:         _in_arc = _candidates[0];
kpeter@593:         pop_heap( _candidates.begin(), _candidates.begin() + _curr_length,
kpeter@593:                   _sort_func );
kpeter@593:         _curr_length = std::min(_head_length, _curr_length - 1);
kpeter@593:         return true;
kpeter@593:       }
kpeter@593: 
kpeter@593:     }; //class AlteringListPivotRule
kpeter@593: 
kpeter@593:   public:
kpeter@593: 
kpeter@593:     /// \brief General constructor (with lower bounds).
kpeter@593:     ///
kpeter@593:     /// General constructor (with lower bounds).
kpeter@593:     ///
kpeter@593:     /// \param digraph The digraph the algorithm runs on.
kpeter@593:     /// \param lower The lower bounds of the arcs.
kpeter@593:     /// \param capacity The capacities (upper bounds) of the arcs.
kpeter@593:     /// \param cost The cost (length) values of the arcs.
kpeter@593:     /// \param supply The supply values of the nodes (signed).
kpeter@593:     NetworkSimplex( const Digraph &digraph,
kpeter@593:                     const LowerMap &lower,
kpeter@593:                     const CapacityMap &capacity,
kpeter@593:                     const CostMap &cost,
kpeter@593:                     const SupplyMap &supply ) :
kpeter@593:       _orig_graph(digraph), _orig_lower(&lower), _orig_cap(capacity),
kpeter@593:       _orig_cost(cost), _orig_supply(&supply),
kpeter@593:       _flow_result(NULL), _potential_result(NULL),
kpeter@593:       _local_flow(false), _local_potential(false),
kpeter@593:       _node_id(digraph)
kpeter@593:     {}
kpeter@593: 
kpeter@593:     /// \brief General constructor (without lower bounds).
kpeter@593:     ///
kpeter@593:     /// General constructor (without lower bounds).
kpeter@593:     ///
kpeter@593:     /// \param digraph The digraph the algorithm runs on.
kpeter@593:     /// \param capacity The capacities (upper bounds) of the arcs.
kpeter@593:     /// \param cost The cost (length) values of the arcs.
kpeter@593:     /// \param supply The supply values of the nodes (signed).
kpeter@593:     NetworkSimplex( const Digraph &digraph,
kpeter@593:                     const CapacityMap &capacity,
kpeter@593:                     const CostMap &cost,
kpeter@593:                     const SupplyMap &supply ) :
kpeter@593:       _orig_graph(digraph), _orig_lower(NULL), _orig_cap(capacity),
kpeter@593:       _orig_cost(cost), _orig_supply(&supply),
kpeter@593:       _flow_result(NULL), _potential_result(NULL),
kpeter@593:       _local_flow(false), _local_potential(false),
kpeter@593:       _node_id(digraph)
kpeter@593:     {}
kpeter@593: 
kpeter@593:     /// \brief Simple constructor (with lower bounds).
kpeter@593:     ///
kpeter@593:     /// Simple constructor (with lower bounds).
kpeter@593:     ///
kpeter@593:     /// \param digraph The digraph the algorithm runs on.
kpeter@593:     /// \param lower The lower bounds of the arcs.
kpeter@593:     /// \param capacity The capacities (upper bounds) of the arcs.
kpeter@593:     /// \param cost The cost (length) values of the arcs.
kpeter@593:     /// \param s The source node.
kpeter@593:     /// \param t The target node.
kpeter@593:     /// \param flow_value The required amount of flow from node \c s
kpeter@593:     /// to node \c t (i.e. the supply of \c s and the demand of \c t).
kpeter@593:     NetworkSimplex( const Digraph &digraph,
kpeter@593:                     const LowerMap &lower,
kpeter@593:                     const CapacityMap &capacity,
kpeter@593:                     const CostMap &cost,
kpeter@593:                     Node s, Node t,
kpeter@593:                     Capacity flow_value ) :
kpeter@593:       _orig_graph(digraph), _orig_lower(&lower), _orig_cap(capacity),
kpeter@593:       _orig_cost(cost), _orig_supply(NULL),
kpeter@593:       _orig_source(s), _orig_target(t), _orig_flow_value(flow_value),
kpeter@593:       _flow_result(NULL), _potential_result(NULL),
kpeter@593:       _local_flow(false), _local_potential(false),
kpeter@593:       _node_id(digraph)
kpeter@593:     {}
kpeter@593: 
kpeter@593:     /// \brief Simple constructor (without lower bounds).
kpeter@593:     ///
kpeter@593:     /// Simple constructor (without lower bounds).
kpeter@593:     ///
kpeter@593:     /// \param digraph The digraph the algorithm runs on.
kpeter@593:     /// \param capacity The capacities (upper bounds) of the arcs.
kpeter@593:     /// \param cost The cost (length) values of the arcs.
kpeter@593:     /// \param s The source node.
kpeter@593:     /// \param t The target node.
kpeter@593:     /// \param flow_value The required amount of flow from node \c s
kpeter@593:     /// to node \c t (i.e. the supply of \c s and the demand of \c t).
kpeter@593:     NetworkSimplex( const Digraph &digraph,
kpeter@593:                     const CapacityMap &capacity,
kpeter@593:                     const CostMap &cost,
kpeter@593:                     Node s, Node t,
kpeter@593:                     Capacity flow_value ) :
kpeter@593:       _orig_graph(digraph), _orig_lower(NULL), _orig_cap(capacity),
kpeter@593:       _orig_cost(cost), _orig_supply(NULL),
kpeter@593:       _orig_source(s), _orig_target(t), _orig_flow_value(flow_value),
kpeter@593:       _flow_result(NULL), _potential_result(NULL),
kpeter@593:       _local_flow(false), _local_potential(false),
kpeter@593:       _node_id(digraph)
kpeter@593:     {}
kpeter@593: 
kpeter@593:     /// Destructor.
kpeter@593:     ~NetworkSimplex() {
kpeter@593:       if (_local_flow) delete _flow_result;
kpeter@593:       if (_local_potential) delete _potential_result;
kpeter@593:     }
kpeter@593: 
kpeter@593:     /// \brief Set the flow map.
kpeter@593:     ///
kpeter@593:     /// This function sets the flow map.
kpeter@593:     ///
kpeter@593:     /// \return <tt>(*this)</tt>
kpeter@593:     NetworkSimplex& flowMap(FlowMap &map) {
kpeter@593:       if (_local_flow) {
kpeter@593:         delete _flow_result;
kpeter@593:         _local_flow = false;
kpeter@593:       }
kpeter@593:       _flow_result = &map;
kpeter@593:       return *this;
kpeter@593:     }
kpeter@593: 
kpeter@593:     /// \brief Set the potential map.
kpeter@593:     ///
kpeter@593:     /// This function sets the potential map.
kpeter@593:     ///
kpeter@593:     /// \return <tt>(*this)</tt>
kpeter@593:     NetworkSimplex& potentialMap(PotentialMap &map) {
kpeter@593:       if (_local_potential) {
kpeter@593:         delete _potential_result;
kpeter@593:         _local_potential = false;
kpeter@593:       }
kpeter@593:       _potential_result = &map;
kpeter@593:       return *this;
kpeter@593:     }
kpeter@593: 
kpeter@593:     /// \name Execution control
kpeter@593:     /// The algorithm can be executed using the
kpeter@593:     /// \ref lemon::NetworkSimplex::run() "run()" function.
kpeter@593:     /// @{
kpeter@593: 
kpeter@593:     /// \brief Run the algorithm.
kpeter@593:     ///
kpeter@593:     /// This function runs the algorithm.
kpeter@593:     ///
kpeter@593:     /// \param pivot_rule The pivot rule that is used during the
kpeter@593:     /// algorithm.
kpeter@593:     ///
kpeter@593:     /// The available pivot rules:
kpeter@593:     ///
kpeter@593:     /// - FIRST_ELIGIBLE_PIVOT The next eligible arc is selected in
kpeter@593:     /// a wraparound fashion in every iteration
kpeter@593:     /// (\ref FirstEligiblePivotRule).
kpeter@593:     ///
kpeter@593:     /// - BEST_ELIGIBLE_PIVOT The best eligible arc is selected in
kpeter@593:     /// every iteration (\ref BestEligiblePivotRule).
kpeter@593:     ///
kpeter@593:     /// - BLOCK_SEARCH_PIVOT A specified number of arcs are examined in
kpeter@593:     /// every iteration in a wraparound fashion and the best eligible
kpeter@593:     /// arc is selected from this block (\ref BlockSearchPivotRule).
kpeter@593:     ///
kpeter@593:     /// - CANDIDATE_LIST_PIVOT In a major iteration a candidate list is
kpeter@593:     /// built from eligible arcs in a wraparound fashion and in the
kpeter@593:     /// following minor iterations the best eligible arc is selected
kpeter@593:     /// from this list (\ref CandidateListPivotRule).
kpeter@593:     ///
kpeter@593:     /// - ALTERING_LIST_PIVOT It is a modified version of the
kpeter@593:     /// "Candidate List" pivot rule. It keeps only the several best
kpeter@593:     /// eligible arcs from the former candidate list and extends this
kpeter@593:     /// list in every iteration (\ref AlteringListPivotRule).
kpeter@593:     ///
kpeter@593:     /// According to our comprehensive benchmark tests the "Block Search"
kpeter@593:     /// pivot rule proved to be the fastest and the most robust on
kpeter@593:     /// various test inputs. Thus it is the default option.
kpeter@593:     ///
kpeter@593:     /// \return \c true if a feasible flow can be found.
kpeter@593:     bool run(PivotRuleEnum pivot_rule = BLOCK_SEARCH_PIVOT) {
kpeter@593:       return init() && start(pivot_rule);
kpeter@593:     }
kpeter@593: 
kpeter@593:     /// @}
kpeter@593: 
kpeter@593:     /// \name Query Functions
kpeter@593:     /// The results of the algorithm can be obtained using these
kpeter@593:     /// functions.\n
kpeter@593:     /// \ref lemon::NetworkSimplex::run() "run()" must be called before
kpeter@593:     /// using them.
kpeter@593:     /// @{
kpeter@593: 
kpeter@593:     /// \brief Return a const reference to the flow map.
kpeter@593:     ///
kpeter@593:     /// This function returns a const reference to an arc map storing
kpeter@593:     /// the found flow.
kpeter@593:     ///
kpeter@593:     /// \pre \ref run() must be called before using this function.
kpeter@593:     const FlowMap& flowMap() const {
kpeter@593:       return *_flow_result;
kpeter@593:     }
kpeter@593: 
kpeter@593:     /// \brief Return a const reference to the potential map
kpeter@593:     /// (the dual solution).
kpeter@593:     ///
kpeter@593:     /// This function returns a const reference to a node map storing
kpeter@593:     /// the found potentials (the dual solution).
kpeter@593:     ///
kpeter@593:     /// \pre \ref run() must be called before using this function.
kpeter@593:     const PotentialMap& potentialMap() const {
kpeter@593:       return *_potential_result;
kpeter@593:     }
kpeter@593: 
kpeter@593:     /// \brief Return the flow on the given arc.
kpeter@593:     ///
kpeter@593:     /// This function returns the flow on the given arc.
kpeter@593:     ///
kpeter@593:     /// \pre \ref run() must be called before using this function.
kpeter@593:     Capacity flow(const Arc& arc) const {
kpeter@593:       return (*_flow_result)[arc];
kpeter@593:     }
kpeter@593: 
kpeter@593:     /// \brief Return the potential of the given node.
kpeter@593:     ///
kpeter@593:     /// This function returns the potential of the given node.
kpeter@593:     ///
kpeter@593:     /// \pre \ref run() must be called before using this function.
kpeter@593:     Cost potential(const Node& node) const {
kpeter@593:       return (*_potential_result)[node];
kpeter@593:     }
kpeter@593: 
kpeter@593:     /// \brief Return the total cost of the found flow.
kpeter@593:     ///
kpeter@593:     /// This function returns the total cost of the found flow.
kpeter@593:     /// The complexity of the function is \f$ O(e) \f$.
kpeter@593:     ///
kpeter@593:     /// \pre \ref run() must be called before using this function.
kpeter@593:     Cost totalCost() const {
kpeter@593:       Cost c = 0;
kpeter@593:       for (ArcIt e(_orig_graph); e != INVALID; ++e)
kpeter@593:         c += (*_flow_result)[e] * _orig_cost[e];
kpeter@593:       return c;
kpeter@593:     }
kpeter@593: 
kpeter@593:     /// @}
kpeter@593: 
kpeter@593:   private:
kpeter@593: 
kpeter@593:     // Initialize internal data structures
kpeter@593:     bool init() {
kpeter@593:       // Initialize result maps
kpeter@593:       if (!_flow_result) {
kpeter@593:         _flow_result = new FlowMap(_orig_graph);
kpeter@593:         _local_flow = true;
kpeter@593:       }
kpeter@593:       if (!_potential_result) {
kpeter@593:         _potential_result = new PotentialMap(_orig_graph);
kpeter@593:         _local_potential = true;
kpeter@593:       }
kpeter@593: 
kpeter@593:       // Initialize vectors
kpeter@593:       _node_num = countNodes(_orig_graph);
kpeter@593:       _arc_num = countArcs(_orig_graph);
kpeter@593:       int all_node_num = _node_num + 1;
kpeter@593:       int all_edge_num = _arc_num + _node_num;
kpeter@593: 
kpeter@593:       _arc.resize(_arc_num);
kpeter@593:       _node.reserve(_node_num);
kpeter@593:       _source.resize(all_edge_num);
kpeter@593:       _target.resize(all_edge_num);
kpeter@593: 
kpeter@593:       _cap.resize(all_edge_num);
kpeter@593:       _cost.resize(all_edge_num);
kpeter@593:       _supply.resize(all_node_num);
kpeter@593:       _flow.resize(all_edge_num, 0);
kpeter@593:       _pi.resize(all_node_num, 0);
kpeter@593: 
kpeter@593:       _depth.resize(all_node_num);
kpeter@593:       _parent.resize(all_node_num);
kpeter@593:       _pred.resize(all_node_num);
kpeter@593:       _thread.resize(all_node_num);
kpeter@593:       _forward.resize(all_node_num);
kpeter@593:       _state.resize(all_edge_num, STATE_LOWER);
kpeter@593: 
kpeter@593:       // Initialize node related data
kpeter@593:       bool valid_supply = true;
kpeter@593:       if (_orig_supply) {
kpeter@593:         Supply sum = 0;
kpeter@593:         int i = 0;
kpeter@593:         for (NodeIt n(_orig_graph); n != INVALID; ++n, ++i) {
kpeter@593:           _node.push_back(n);
kpeter@593:           _node_id[n] = i;
kpeter@593:           _supply[i] = (*_orig_supply)[n];
kpeter@593:           sum += _supply[i];
kpeter@593:         }
kpeter@593:         valid_supply = (sum == 0);
kpeter@593:       } else {
kpeter@593:         int i = 0;
kpeter@593:         for (NodeIt n(_orig_graph); n != INVALID; ++n, ++i) {
kpeter@593:           _node.push_back(n);
kpeter@593:           _node_id[n] = i;
kpeter@593:           _supply[i] = 0;
kpeter@593:         }
kpeter@593:         _supply[_node_id[_orig_source]] =  _orig_flow_value;
kpeter@593:         _supply[_node_id[_orig_target]] = -_orig_flow_value;
kpeter@593:       }
kpeter@593:       if (!valid_supply) return false;
kpeter@593: 
kpeter@593:       // Set data for the artificial root node
kpeter@593:       _root = _node_num;
kpeter@593:       _depth[_root] = 0;
kpeter@593:       _parent[_root] = -1;
kpeter@593:       _pred[_root] = -1;
kpeter@593:       _thread[_root] = 0;
kpeter@593:       _supply[_root] = 0;
kpeter@593:       _pi[_root] = 0;
kpeter@593: 
kpeter@593:       // Store the arcs in a mixed order
kpeter@593:       int k = std::max(int(sqrt(_arc_num)), 10);
kpeter@593:       int i = 0;
kpeter@593:       for (ArcIt e(_orig_graph); e != INVALID; ++e) {
kpeter@593:         _arc[i] = e;
kpeter@593:         if ((i += k) >= _arc_num) i = (i % k) + 1;
kpeter@593:       }
kpeter@593: 
kpeter@593:       // Initialize arc maps
kpeter@593:       for (int i = 0; i != _arc_num; ++i) {
kpeter@593:         Arc e = _arc[i];
kpeter@593:         _source[i] = _node_id[_orig_graph.source(e)];
kpeter@593:         _target[i] = _node_id[_orig_graph.target(e)];
kpeter@593:         _cost[i] = _orig_cost[e];
kpeter@593:         _cap[i] = _orig_cap[e];
kpeter@593:       }
kpeter@593: 
kpeter@593:       // Remove non-zero lower bounds
kpeter@593:       if (_orig_lower) {
kpeter@593:         for (int i = 0; i != _arc_num; ++i) {
kpeter@593:           Capacity c = (*_orig_lower)[_arc[i]];
kpeter@593:           if (c != 0) {
kpeter@593:             _cap[i] -= c;
kpeter@593:             _supply[_source[i]] -= c;
kpeter@593:             _supply[_target[i]] += c;
kpeter@593:           }
kpeter@593:         }
kpeter@593:       }
kpeter@593: 
kpeter@593:       // Add artificial arcs and initialize the spanning tree data structure
kpeter@593:       Cost max_cost = std::numeric_limits<Cost>::max() / 4;
kpeter@593:       Capacity max_cap = std::numeric_limits<Capacity>::max();
kpeter@593:       for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
kpeter@593:         _thread[u] = u + 1;
kpeter@593:         _depth[u] = 1;
kpeter@593:         _parent[u] = _root;
kpeter@593:         _pred[u] = e;
kpeter@593:         if (_supply[u] >= 0) {
kpeter@593:           _flow[e] = _supply[u];
kpeter@593:           _forward[u] = true;
kpeter@593:           _pi[u] = -max_cost;
kpeter@593:         } else {
kpeter@593:           _flow[e] = -_supply[u];
kpeter@593:           _forward[u] = false;
kpeter@593:           _pi[u] = max_cost;
kpeter@593:         }
kpeter@593:         _cost[e] = max_cost;
kpeter@593:         _cap[e] = max_cap;
kpeter@593:         _state[e] = STATE_TREE;
kpeter@593:       }
kpeter@593: 
kpeter@593:       return true;
kpeter@593:     }
kpeter@593: 
kpeter@593:     // Find the join node
kpeter@593:     void findJoinNode() {
kpeter@593:       int u = _source[_in_arc];
kpeter@593:       int v = _target[_in_arc];
kpeter@593:       while (_depth[u] > _depth[v]) u = _parent[u];
kpeter@593:       while (_depth[v] > _depth[u]) v = _parent[v];
kpeter@593:       while (u != v) {
kpeter@593:         u = _parent[u];
kpeter@593:         v = _parent[v];
kpeter@593:       }
kpeter@593:       join = u;
kpeter@593:     }
kpeter@593: 
kpeter@593:     // Find the leaving arc of the cycle and returns true if the
kpeter@593:     // leaving arc is not the same as the entering arc
kpeter@593:     bool findLeavingArc() {
kpeter@593:       // Initialize first and second nodes according to the direction
kpeter@593:       // of the cycle
kpeter@593:       if (_state[_in_arc] == STATE_LOWER) {
kpeter@593:         first  = _source[_in_arc];
kpeter@593:         second = _target[_in_arc];
kpeter@593:       } else {
kpeter@593:         first  = _target[_in_arc];
kpeter@593:         second = _source[_in_arc];
kpeter@593:       }
kpeter@593:       delta = _cap[_in_arc];
kpeter@593:       int result = 0;
kpeter@593:       Capacity d;
kpeter@593:       int e;
kpeter@593: 
kpeter@593:       // Search the cycle along the path form the first node to the root
kpeter@593:       for (int u = first; u != join; u = _parent[u]) {
kpeter@593:         e = _pred[u];
kpeter@593:         d = _forward[u] ? _flow[e] : _cap[e] - _flow[e];
kpeter@593:         if (d < delta) {
kpeter@593:           delta = d;
kpeter@593:           u_out = u;
kpeter@593:           result = 1;
kpeter@593:         }
kpeter@593:       }
kpeter@593:       // Search the cycle along the path form the second node to the root
kpeter@593:       for (int u = second; u != join; u = _parent[u]) {
kpeter@593:         e = _pred[u];
kpeter@593:         d = _forward[u] ? _cap[e] - _flow[e] : _flow[e];
kpeter@593:         if (d <= delta) {
kpeter@593:           delta = d;
kpeter@593:           u_out = u;
kpeter@593:           result = 2;
kpeter@593:         }
kpeter@593:       }
kpeter@593: 
kpeter@593:       if (result == 1) {
kpeter@593:         u_in = first;
kpeter@593:         v_in = second;
kpeter@593:       } else {
kpeter@593:         u_in = second;
kpeter@593:         v_in = first;
kpeter@593:       }
kpeter@593:       return result != 0;
kpeter@593:     }
kpeter@593: 
kpeter@593:     // Change _flow and _state vectors
kpeter@593:     void changeFlow(bool change) {
kpeter@593:       // Augment along the cycle
kpeter@593:       if (delta > 0) {
kpeter@593:         Capacity val = _state[_in_arc] * delta;
kpeter@593:         _flow[_in_arc] += val;
kpeter@593:         for (int u = _source[_in_arc]; u != join; u = _parent[u]) {
kpeter@593:           _flow[_pred[u]] += _forward[u] ? -val : val;
kpeter@593:         }
kpeter@593:         for (int u = _target[_in_arc]; u != join; u = _parent[u]) {
kpeter@593:           _flow[_pred[u]] += _forward[u] ? val : -val;
kpeter@593:         }
kpeter@593:       }
kpeter@593:       // Update the state of the entering and leaving arcs
kpeter@593:       if (change) {
kpeter@593:         _state[_in_arc] = STATE_TREE;
kpeter@593:         _state[_pred[u_out]] =
kpeter@593:           (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER;
kpeter@593:       } else {
kpeter@593:         _state[_in_arc] = -_state[_in_arc];
kpeter@593:       }
kpeter@593:     }
kpeter@593: 
kpeter@593:     // Update _thread and _parent vectors
kpeter@593:     void updateThreadParent() {
kpeter@593:       int u;
kpeter@593:       v_out = _parent[u_out];
kpeter@593: 
kpeter@593:       // Handle the case when join and v_out coincide
kpeter@593:       bool par_first = false;
kpeter@593:       if (join == v_out) {
kpeter@593:         for (u = join; u != u_in && u != v_in; u = _thread[u]) ;
kpeter@593:         if (u == v_in) {
kpeter@593:           par_first = true;
kpeter@593:           while (_thread[u] != u_out) u = _thread[u];
kpeter@593:           first = u;
kpeter@593:         }
kpeter@593:       }
kpeter@593: 
kpeter@593:       // Find the last successor of u_in (u) and the node after it (right)
kpeter@593:       // according to the thread index
kpeter@593:       for (u = u_in; _depth[_thread[u]] > _depth[u_in]; u = _thread[u]) ;
kpeter@593:       right = _thread[u];
kpeter@593:       if (_thread[v_in] == u_out) {
kpeter@593:         for (last = u; _depth[last] > _depth[u_out]; last = _thread[last]) ;
kpeter@593:         if (last == u_out) last = _thread[last];
kpeter@593:       }
kpeter@593:       else last = _thread[v_in];
kpeter@593: 
kpeter@593:       // Update stem nodes
kpeter@593:       _thread[v_in] = stem = u_in;
kpeter@593:       par_stem = v_in;
kpeter@593:       while (stem != u_out) {
kpeter@593:         _thread[u] = new_stem = _parent[stem];
kpeter@593: 
kpeter@593:         // Find the node just before the stem node (u) according to
kpeter@593:         // the original thread index
kpeter@593:         for (u = new_stem; _thread[u] != stem; u = _thread[u]) ;
kpeter@593:         _thread[u] = right;
kpeter@593: 
kpeter@593:         // Change the parent node of stem and shift stem and par_stem nodes
kpeter@593:         _parent[stem] = par_stem;
kpeter@593:         par_stem = stem;
kpeter@593:         stem = new_stem;
kpeter@593: 
kpeter@593:         // Find the last successor of stem (u) and the node after it (right)
kpeter@593:         // according to the thread index
kpeter@593:         for (u = stem; _depth[_thread[u]] > _depth[stem]; u = _thread[u]) ;
kpeter@593:         right = _thread[u];
kpeter@593:       }
kpeter@593:       _parent[u_out] = par_stem;
kpeter@593:       _thread[u] = last;
kpeter@593: 
kpeter@593:       if (join == v_out && par_first) {
kpeter@593:         if (first != v_in) _thread[first] = right;
kpeter@593:       } else {
kpeter@593:         for (u = v_out; _thread[u] != u_out; u = _thread[u]) ;
kpeter@593:         _thread[u] = right;
kpeter@593:       }
kpeter@593:     }
kpeter@593: 
kpeter@593:     // Update _pred and _forward vectors
kpeter@593:     void updatePredArc() {
kpeter@593:       int u = u_out, v;
kpeter@593:       while (u != u_in) {
kpeter@593:         v = _parent[u];
kpeter@593:         _pred[u] = _pred[v];
kpeter@593:         _forward[u] = !_forward[v];
kpeter@593:         u = v;
kpeter@593:       }
kpeter@593:       _pred[u_in] = _in_arc;
kpeter@593:       _forward[u_in] = (u_in == _source[_in_arc]);
kpeter@593:     }
kpeter@593: 
kpeter@593:     // Update _depth and _potential vectors
kpeter@593:     void updateDepthPotential() {
kpeter@593:       _depth[u_in] = _depth[v_in] + 1;
kpeter@593:       Cost sigma = _forward[u_in] ?
kpeter@593:         _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] :
kpeter@593:         _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]];
kpeter@593:       _pi[u_in] += sigma;
kpeter@593:       for(int u = _thread[u_in]; _parent[u] != -1; u = _thread[u]) {
kpeter@593:         _depth[u] = _depth[_parent[u]] + 1;
kpeter@593:         if (_depth[u] <= _depth[u_in]) break;
kpeter@593:         _pi[u] += sigma;
kpeter@593:       }
kpeter@593:     }
kpeter@593: 
kpeter@593:     // Execute the algorithm
kpeter@593:     bool start(PivotRuleEnum pivot_rule) {
kpeter@593:       // Select the pivot rule implementation
kpeter@593:       switch (pivot_rule) {
kpeter@593:         case FIRST_ELIGIBLE_PIVOT:
kpeter@593:           return start<FirstEligiblePivotRule>();
kpeter@593:         case BEST_ELIGIBLE_PIVOT:
kpeter@593:           return start<BestEligiblePivotRule>();
kpeter@593:         case BLOCK_SEARCH_PIVOT:
kpeter@593:           return start<BlockSearchPivotRule>();
kpeter@593:         case CANDIDATE_LIST_PIVOT:
kpeter@593:           return start<CandidateListPivotRule>();
kpeter@593:         case ALTERING_LIST_PIVOT:
kpeter@593:           return start<AlteringListPivotRule>();
kpeter@593:       }
kpeter@593:       return false;
kpeter@593:     }
kpeter@593: 
kpeter@593:     template<class PivotRuleImplementation>
kpeter@593:     bool start() {
kpeter@593:       PivotRuleImplementation pivot(*this);
kpeter@593: 
kpeter@593:       // Execute the network simplex algorithm
kpeter@593:       while (pivot.findEnteringArc()) {
kpeter@593:         findJoinNode();
kpeter@593:         bool change = findLeavingArc();
kpeter@593:         changeFlow(change);
kpeter@593:         if (change) {
kpeter@593:           updateThreadParent();
kpeter@593:           updatePredArc();
kpeter@593:           updateDepthPotential();
kpeter@593:         }
kpeter@593:       }
kpeter@593: 
kpeter@593:       // Check if the flow amount equals zero on all the artificial arcs
kpeter@593:       for (int e = _arc_num; e != _arc_num + _node_num; ++e) {
kpeter@593:         if (_flow[e] > 0) return false;
kpeter@593:       }
kpeter@593: 
kpeter@593:       // Copy flow values to _flow_result
kpeter@593:       if (_orig_lower) {
kpeter@593:         for (int i = 0; i != _arc_num; ++i) {
kpeter@593:           Arc e = _arc[i];
kpeter@593:           (*_flow_result)[e] = (*_orig_lower)[e] + _flow[i];
kpeter@593:         }
kpeter@593:       } else {
kpeter@593:         for (int i = 0; i != _arc_num; ++i) {
kpeter@593:           (*_flow_result)[_arc[i]] = _flow[i];
kpeter@593:         }
kpeter@593:       }
kpeter@593:       // Copy potential values to _potential_result
kpeter@593:       for (int i = 0; i != _node_num; ++i) {
kpeter@593:         (*_potential_result)[_node[i]] = _pi[i];
kpeter@593:       }
kpeter@593: 
kpeter@593:       return true;
kpeter@593:     }
kpeter@593: 
kpeter@593:   }; //class NetworkSimplex
kpeter@593: 
kpeter@593:   ///@}
kpeter@593: 
kpeter@593: } //namespace lemon
kpeter@593: 
kpeter@593: #endif //LEMON_NETWORK_SIMPLEX_H