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@2575: 
kpeter@2509: #include <lemon/graph_adaptor.h>
kpeter@2509: #include <lemon/graph_utils.h>
deba@2440: #include <lemon/smart_graph.h>
kpeter@2575: #include <lemon/math.h>
deba@2440: 
kpeter@2619: #define _DEBUG_
kpeter@2619: 
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:   {
deba@2440:     typedef typename CapacityMap::Value Capacity;
deba@2440:     typedef typename CostMap::Value Cost;
deba@2440:     typedef typename SupplyMap::Value Supply;
deba@2440: 
deba@2440:     typedef SmartGraph SGraph;
kpeter@2556:     GRAPH_TYPEDEFS(typename SGraph);
deba@2440: 
deba@2440:     typedef typename SGraph::template EdgeMap<Capacity> SCapacityMap;
deba@2440:     typedef typename SGraph::template EdgeMap<Cost> SCostMap;
deba@2440:     typedef typename SGraph::template NodeMap<Supply> SSupplyMap;
deba@2440:     typedef typename SGraph::template NodeMap<Cost> SPotentialMap;
deba@2440: 
deba@2440:     typedef typename SGraph::template NodeMap<int> IntNodeMap;
deba@2440:     typedef typename SGraph::template NodeMap<bool> BoolNodeMap;
deba@2440:     typedef typename SGraph::template NodeMap<Node> NodeNodeMap;
deba@2440:     typedef typename SGraph::template NodeMap<Edge> EdgeNodeMap;
deba@2440:     typedef typename SGraph::template EdgeMap<int> IntEdgeMap;
kpeter@2619:     typedef typename SGraph::template EdgeMap<bool> BoolEdgeMap;
deba@2440: 
deba@2440:     typedef typename Graph::template NodeMap<Node> NodeRefMap;
deba@2440:     typedef typename Graph::template EdgeMap<Edge> EdgeRefMap;
deba@2440: 
kpeter@2619:     typedef std::vector<Edge> EdgeVector;
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 Map adaptor class for handling reduced edge costs.
kpeter@2575:     ///
kpeter@2556:     /// Map adaptor class for handling reduced edge costs.
deba@2440:     class ReducedCostMap : public MapBase<Edge, Cost>
deba@2440:     {
deba@2440:     private:
deba@2440: 
kpeter@2575:       const SGraph &_gr;
kpeter@2575:       const SCostMap &_cost_map;
kpeter@2575:       const SPotentialMap &_pot_map;
deba@2440: 
deba@2440:     public:
deba@2440: 
kpeter@2575:       ///\e
kpeter@2575:       ReducedCostMap( const SGraph &gr,
kpeter@2575:                       const SCostMap &cost_map,
kpeter@2575:                       const SPotentialMap &pot_map ) :
kpeter@2579:         _gr(gr), _cost_map(cost_map), _pot_map(pot_map) {}
deba@2440: 
kpeter@2575:       ///\e
kpeter@2509:       Cost operator[](const Edge &e) const {
kpeter@2575:         return _cost_map[e] + _pot_map[_gr.source(e)]
kpeter@2575:                            - _pot_map[_gr.target(e)];
deba@2440:       }
deba@2440: 
deba@2440:     }; //class ReducedCostMap
deba@2440: 
kpeter@2575:   private:
deba@2440: 
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@2575:       NetworkSimplex &_ns;
kpeter@2619:       EdgeVector &_edges;
kpeter@2619: 
kpeter@2619:       int _next_edge;
deba@2440: 
kpeter@2575:     public:
deba@2440: 
kpeter@2619:       /// Constructor
kpeter@2619:       FirstEligiblePivotRule(NetworkSimplex &ns, EdgeVector &edges) :
kpeter@2619:         _ns(ns), _edges(edges), _next_edge(0) {}
kpeter@2575: 
kpeter@2619:       /// Find next entering edge
kpeter@2619:       inline bool findEnteringEdge() {
kpeter@2619:         Edge e;
kpeter@2619:         for (int i = _next_edge; i < int(_edges.size()); ++i) {
kpeter@2619:           e = _edges[i];
kpeter@2575:           if (_ns._state[e] * _ns._red_cost[e] < 0) {
kpeter@2575:             _ns._in_edge = e;
kpeter@2619:             _next_edge = i + 1;
kpeter@2575:             return true;
kpeter@2575:           }
kpeter@2575:         }
kpeter@2619:         for (int i = 0; i < _next_edge; ++i) {
kpeter@2619:           e = _edges[i];
kpeter@2575:           if (_ns._state[e] * _ns._red_cost[e] < 0) {
kpeter@2575:             _ns._in_edge = e;
kpeter@2619:             _next_edge = i + 1;
kpeter@2575:             return true;
kpeter@2575:           }
kpeter@2575:         }
kpeter@2575:         return false;
kpeter@2575:       }
kpeter@2575:     }; //class FirstEligiblePivotRule
kpeter@2575: 
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@2575:       NetworkSimplex &_ns;
kpeter@2619:       EdgeVector &_edges;
kpeter@2575: 
kpeter@2575:     public:
kpeter@2575: 
kpeter@2619:       /// Constructor
kpeter@2619:       BestEligiblePivotRule(NetworkSimplex &ns, EdgeVector &edges) :
kpeter@2619:         _ns(ns), _edges(edges) {}
kpeter@2575: 
kpeter@2619:       /// Find next entering edge
kpeter@2619:       inline bool findEnteringEdge() {
kpeter@2575:         Cost min = 0;
kpeter@2619:         Edge e;
kpeter@2619:         for (int i = 0; i < int(_edges.size()); ++i) {
kpeter@2619:           e = _edges[i];
kpeter@2575:           if (_ns._state[e] * _ns._red_cost[e] < min) {
kpeter@2575:             min = _ns._state[e] * _ns._red_cost[e];
kpeter@2575:             _ns._in_edge = e;
kpeter@2575:           }
kpeter@2575:         }
kpeter@2575:         return min < 0;
kpeter@2575:       }
kpeter@2575:     }; //class BestEligiblePivotRule
kpeter@2575: 
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@2575:       NetworkSimplex &_ns;
kpeter@2619:       EdgeVector &_edges;
kpeter@2619: 
kpeter@2575:       int _block_size;
kpeter@2619:       int _next_edge, _min_edge;
kpeter@2575: 
kpeter@2575:     public:
kpeter@2575: 
kpeter@2619:       /// Constructor
kpeter@2619:       BlockSearchPivotRule(NetworkSimplex &ns, EdgeVector &edges) :
kpeter@2619:         _ns(ns), _edges(edges), _next_edge(0), _min_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@2619:         _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_edges.size())),
kpeter@2619:                                 MIN_BLOCK_SIZE );
kpeter@2575:       }
kpeter@2575: 
kpeter@2619:       /// Find next entering edge
kpeter@2619:       inline bool findEnteringEdge() {
kpeter@2575:         Cost curr, min = 0;
kpeter@2619:         Edge e;
kpeter@2619:         int cnt = _block_size;
kpeter@2619:         int i;
kpeter@2619:         for (i = _next_edge; i < int(_edges.size()); ++i) {
kpeter@2619:           e = _edges[i];
kpeter@2575:           if ((curr = _ns._state[e] * _ns._red_cost[e]) < min) {
kpeter@2575:             min = curr;
kpeter@2619:             _min_edge = i;
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@2619:           for (i = 0; i < _next_edge; ++i) {
kpeter@2619:             e = _edges[i];
kpeter@2575:             if ((curr = _ns._state[e] * _ns._red_cost[e]) < min) {
kpeter@2575:               min = curr;
kpeter@2619:               _min_edge = i;
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@2619:         _ns._in_edge = _edges[_min_edge];
kpeter@2619:         _next_edge = i;
kpeter@2619:         return true;
kpeter@2575:       }
kpeter@2575:     }; //class BlockSearchPivotRule
kpeter@2575: 
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@2575:       NetworkSimplex &_ns;
kpeter@2619:       EdgeVector &_edges;
kpeter@2575: 
kpeter@2619:       EdgeVector _candidates;
kpeter@2619:       int _list_length, _minor_limit;
kpeter@2619:       int _curr_length, _minor_count;
kpeter@2619:       int _next_edge, _min_edge;
kpeter@2575: 
kpeter@2575:     public:
kpeter@2575: 
kpeter@2619:       /// Constructor
kpeter@2619:       CandidateListPivotRule(NetworkSimplex &ns, EdgeVector &edges) :
kpeter@2619:         _ns(ns), _edges(edges), _next_edge(0), _min_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@2619:         _list_length = std::max( int(LIST_LENGTH_FACTOR * sqrt(_edges.size())),
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@2619:       inline bool findEnteringEdge() {
kpeter@2575:         Cost min, curr;
kpeter@2619:         if (_curr_length > 0 && _minor_count < _minor_limit) {
kpeter@2619:           // Minor iteration: selecting the best eligible edge from
kpeter@2619:           // the current candidate list
kpeter@2575:           ++_minor_count;
kpeter@2575:           Edge e;
kpeter@2575:           min = 0;
kpeter@2619:           for (int i = 0; i < _curr_length; ++i) {
kpeter@2575:             e = _candidates[i];
kpeter@2619:             curr = _ns._state[e] * _ns._red_cost[e];
kpeter@2619:             if (curr < min) {
kpeter@2575:               min = curr;
kpeter@2575:               _ns._in_edge = e;
kpeter@2575:             }
kpeter@2619:             if (curr >= 0) {
kpeter@2619:               _candidates[i--] = _candidates[--_curr_length];
kpeter@2619:             }
kpeter@2575:           }
kpeter@2575:           if (min < 0) return true;
kpeter@2575:         }
kpeter@2575: 
kpeter@2619:         // Major iteration: building a new candidate list
kpeter@2619:         Edge e;
kpeter@2575:         min = 0;
kpeter@2619:         _curr_length = 0;
kpeter@2619:         int i;
kpeter@2619:         for (i = _next_edge; i < int(_edges.size()); ++i) {
kpeter@2619:           e = _edges[i];
kpeter@2575:           if ((curr = _ns._state[e] * _ns._red_cost[e]) < 0) {
kpeter@2619:             _candidates[_curr_length++] = e;
kpeter@2575:             if (curr < min) {
kpeter@2575:               min = curr;
kpeter@2619:               _min_edge = i;
kpeter@2575:             }
kpeter@2619:             if (_curr_length == _list_length) break;
kpeter@2575:           }
kpeter@2575:         }
kpeter@2619:         if (_curr_length < _list_length) {
kpeter@2619:           for (i = 0; i < _next_edge; ++i) {
kpeter@2619:             e = _edges[i];
kpeter@2575:             if ((curr = _ns._state[e] * _ns._red_cost[e]) < 0) {
kpeter@2619:               _candidates[_curr_length++] = e;
kpeter@2575:               if (curr < min) {
kpeter@2575:                 min = curr;
kpeter@2619:                 _min_edge = i;
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@2619:         _ns._in_edge = _edges[_min_edge];
kpeter@2619:         _next_edge = i;
kpeter@2575:         return true;
kpeter@2575:       }
kpeter@2575:     }; //class CandidateListPivotRule
kpeter@2575: 
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@2619:       NetworkSimplex &_ns;
kpeter@2619:       EdgeVector &_edges;
kpeter@2619: 
kpeter@2619:       EdgeVector _candidates;
kpeter@2619:       SCostMap _cand_cost;
kpeter@2619:       int _block_size, _head_length, _curr_length;
kpeter@2619:       int _next_edge;
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@2619:         const SCostMap &_map;
kpeter@2619:       public:
kpeter@2619:         SortFunc(const SCostMap &map) : _map(map) {}
kpeter@2619:         bool operator()(const Edge &e1, const Edge &e2) {
kpeter@2619: 	  return _map[e1] < _map[e2];
kpeter@2619:         }
kpeter@2619:       };
kpeter@2619: 
kpeter@2619:       SortFunc _sort_func;
kpeter@2619: 
kpeter@2619:     public:
kpeter@2619: 
kpeter@2619:       /// Constructor
kpeter@2619:       AlteringListPivotRule(NetworkSimplex &ns, EdgeVector &edges) :
kpeter@2619:         _ns(ns), _edges(edges), _cand_cost(_ns._graph),
kpeter@2619:         _next_edge(0), _sort_func(_cand_cost)
kpeter@2619:       {
kpeter@2619:         // The main parameters of the pivot rule
kpeter@2619:         const double BLOCK_SIZE_FACTOR = 1.0;
kpeter@2619:         const int MIN_BLOCK_SIZE = 10;
kpeter@2619:         const double HEAD_LENGTH_FACTOR = 0.1;
kpeter@2619:         const int MIN_HEAD_LENGTH = 5;
kpeter@2619: 
kpeter@2619:         _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_edges.size())),
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@2619:       inline bool findEnteringEdge() {
kpeter@2619:         // Checking the current candidate list
kpeter@2619:         Edge e;
kpeter@2619:         for (int idx = 0; idx < _curr_length; ++idx) {
kpeter@2619:           e = _candidates[idx];
kpeter@2619:           if ((_cand_cost[e] = _ns._state[e] * _ns._red_cost[e]) >= 0) {
kpeter@2619:             _candidates[idx--] = _candidates[--_curr_length];
kpeter@2619:           }
kpeter@2619:         }
kpeter@2619: 
kpeter@2619:         // Extending the list
kpeter@2619:         int cnt = _block_size;
kpeter@2619:         int last_edge = 0;
kpeter@2619:         int limit = _head_length;
kpeter@2619:         for (int i = _next_edge; i < int(_edges.size()); ++i) {
kpeter@2619:           e = _edges[i];
kpeter@2619:           if ((_cand_cost[e] = _ns._state[e] * _ns._red_cost[e]) < 0) {
kpeter@2619:             _candidates[_curr_length++] = e;
kpeter@2619:             last_edge = i;
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@2619:           for (int i = 0; i < _next_edge; ++i) {
kpeter@2619:             e = _edges[i];
kpeter@2619:             if ((_cand_cost[e] = _ns._state[e] * _ns._red_cost[e]) < 0) {
kpeter@2619:               _candidates[_curr_length++] = e;
kpeter@2619:               last_edge = i;
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@2619:         // Sorting the list partially
kpeter@2619:         EdgeVector::iterator sort_end = _candidates.begin();
kpeter@2619:         EdgeVector::iterator vector_end = _candidates.begin();
kpeter@2619:         for (int idx = 0; idx < _curr_length; ++idx) {
kpeter@2619:           ++vector_end;
kpeter@2619:           if (idx <= _head_length) ++sort_end;
kpeter@2619:         }
kpeter@2619:         partial_sort(_candidates.begin(), sort_end, vector_end, _sort_func);
kpeter@2619: 
kpeter@2619:         _ns._in_edge = _candidates[0];
kpeter@2619:         if (_curr_length > _head_length) {
kpeter@2619:           _candidates[0] = _candidates[_head_length - 1];
kpeter@2619:           _curr_length = _head_length - 1;
kpeter@2619:         } else {
kpeter@2619:           _candidates[0] = _candidates[_curr_length - 1];
kpeter@2619:           --_curr_length;
kpeter@2619:         }
kpeter@2619: 
kpeter@2619:         return true;
kpeter@2619:       }
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 directed graph the algorithm runs on
kpeter@2575:     SGraph _graph;
kpeter@2575:     // The original graph
kpeter@2575:     const Graph &_graph_ref;
kpeter@2575:     // The original lower bound map
kpeter@2575:     const LowerMap *_lower;
kpeter@2575:     // The capacity map
kpeter@2575:     SCapacityMap _capacity;
kpeter@2575:     // The cost map
kpeter@2575:     SCostMap _cost;
kpeter@2575:     // The supply map
kpeter@2575:     SSupplyMap _supply;
kpeter@2575:     bool _valid_supply;
kpeter@2575: 
kpeter@2575:     // Edge map of the current flow
kpeter@2575:     SCapacityMap _flow;
kpeter@2575:     // Node map of the current potentials
kpeter@2575:     SPotentialMap _potential;
kpeter@2575: 
kpeter@2575:     // The depth node map of the spanning tree structure
kpeter@2575:     IntNodeMap _depth;
kpeter@2575:     // The parent node map of the spanning tree structure
kpeter@2575:     NodeNodeMap _parent;
kpeter@2575:     // The pred_edge node map of the spanning tree structure
kpeter@2575:     EdgeNodeMap _pred_edge;
kpeter@2575:     // The thread node map of the spanning tree structure
kpeter@2575:     NodeNodeMap _thread;
kpeter@2575:     // The forward node map of the spanning tree structure
kpeter@2575:     BoolNodeMap _forward;
kpeter@2575:     // The state edge map
kpeter@2575:     IntEdgeMap _state;
kpeter@2575:     // The root node of the starting spanning tree
kpeter@2575:     Node _root;
kpeter@2575: 
kpeter@2575:     // The reduced cost map
kpeter@2575:     ReducedCostMap _red_cost;
kpeter@2575: 
kpeter@2619:     // The non-artifical edges
kpeter@2619:     EdgeVector _edges;
kpeter@2619: 
kpeter@2575:     // Members for handling the original graph
kpeter@2581:     FlowMap *_flow_result;
kpeter@2581:     PotentialMap *_potential_result;
kpeter@2581:     bool _local_flow;
kpeter@2581:     bool _local_potential;
kpeter@2575:     NodeRefMap _node_ref;
kpeter@2575:     EdgeRefMap _edge_ref;
deba@2440: 
kpeter@2556:     // The entering edge of the current pivot iteration.
kpeter@2575:     Edge _in_edge;
kpeter@2575: 
kpeter@2556:     // Temporary nodes used in the current pivot iteration.
kpeter@2556:     Node join, u_in, v_in, u_out, v_out;
kpeter@2556:     Node right, first, second, last;
kpeter@2556:     Node stem, par_stem, new_stem;
kpeter@2556:     // The maximum augment amount along the found cycle in the current
kpeter@2556:     // pivot iteration.
kpeter@2556:     Capacity delta;
deba@2440: 
deba@2440:   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@2575:       _graph(), _graph_ref(graph), _lower(&lower), _capacity(_graph),
kpeter@2575:       _cost(_graph), _supply(_graph), _flow(_graph),
kpeter@2575:       _potential(_graph), _depth(_graph), _parent(_graph),
kpeter@2575:       _pred_edge(_graph), _thread(_graph), _forward(_graph),
kpeter@2575:       _state(_graph), _red_cost(_graph, _cost, _potential),
kpeter@2581:       _flow_result(0), _potential_result(0),
kpeter@2581:       _local_flow(false), _local_potential(false),
kpeter@2575:       _node_ref(graph), _edge_ref(graph)
deba@2440:     {
deba@2440:       // Checking the sum of supply values
deba@2440:       Supply sum = 0;
kpeter@2575:       for (typename Graph::NodeIt n(_graph_ref); n != INVALID; ++n)
kpeter@2575:         sum += supply[n];
kpeter@2575:       if (!(_valid_supply = sum == 0)) return;
deba@2440: 
kpeter@2575:       // Copying _graph_ref to _graph
kpeter@2575:       _graph.reserveNode(countNodes(_graph_ref) + 1);
kpeter@2575:       _graph.reserveEdge(countEdges(_graph_ref) + countNodes(_graph_ref));
kpeter@2575:       copyGraph(_graph, _graph_ref)
kpeter@2575:         .edgeMap(_cost, cost)
kpeter@2575:         .nodeRef(_node_ref)
kpeter@2575:         .edgeRef(_edge_ref)
kpeter@2556:         .run();
deba@2440: 
kpeter@2556:       // Removing non-zero lower bounds
kpeter@2575:       for (typename Graph::EdgeIt e(_graph_ref); e != INVALID; ++e) {
kpeter@2575:         _capacity[_edge_ref[e]] = capacity[e] - lower[e];
deba@2440:       }
kpeter@2575:       for (typename Graph::NodeIt n(_graph_ref); n != INVALID; ++n) {
kpeter@2575:         Supply s = supply[n];
kpeter@2575:         for (typename Graph::InEdgeIt e(_graph_ref, n); e != INVALID; ++e)
kpeter@2575:           s += lower[e];
kpeter@2575:         for (typename Graph::OutEdgeIt e(_graph_ref, n); e != INVALID; ++e)
kpeter@2575:           s -= lower[e];
kpeter@2575:         _supply[_node_ref[n]] = s;
deba@2440:       }
deba@2440:     }
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@2575:       _graph(), _graph_ref(graph), _lower(NULL), _capacity(_graph),
kpeter@2575:       _cost(_graph), _supply(_graph), _flow(_graph),
kpeter@2575:       _potential(_graph), _depth(_graph), _parent(_graph),
kpeter@2575:       _pred_edge(_graph), _thread(_graph), _forward(_graph),
kpeter@2575:       _state(_graph), _red_cost(_graph, _cost, _potential),
kpeter@2581:       _flow_result(0), _potential_result(0),
kpeter@2581:       _local_flow(false), _local_potential(false),
kpeter@2575:       _node_ref(graph), _edge_ref(graph)
deba@2440:     {
deba@2440:       // Checking the sum of supply values
deba@2440:       Supply sum = 0;
kpeter@2575:       for (typename Graph::NodeIt n(_graph_ref); n != INVALID; ++n)
kpeter@2575:         sum += supply[n];
kpeter@2575:       if (!(_valid_supply = sum == 0)) return;
deba@2440: 
kpeter@2575:       // Copying _graph_ref to graph
kpeter@2575:       copyGraph(_graph, _graph_ref)
kpeter@2575:         .edgeMap(_capacity, capacity)
kpeter@2575:         .edgeMap(_cost, cost)
kpeter@2575:         .nodeMap(_supply, supply)
kpeter@2575:         .nodeRef(_node_ref)
kpeter@2575:         .edgeRef(_edge_ref)
kpeter@2556:         .run();
deba@2440:     }
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@2575:                     typename Graph::Node s,
kpeter@2575:                     typename Graph::Node t,
kpeter@2575:                     typename SupplyMap::Value flow_value ) :
kpeter@2575:       _graph(), _graph_ref(graph), _lower(&lower), _capacity(_graph),
kpeter@2575:       _cost(_graph), _supply(_graph), _flow(_graph),
kpeter@2575:       _potential(_graph), _depth(_graph), _parent(_graph),
kpeter@2575:       _pred_edge(_graph), _thread(_graph), _forward(_graph),
kpeter@2575:       _state(_graph), _red_cost(_graph, _cost, _potential),
kpeter@2581:       _flow_result(0), _potential_result(0),
kpeter@2581:       _local_flow(false), _local_potential(false),
kpeter@2575:       _node_ref(graph), _edge_ref(graph)
deba@2440:     {
kpeter@2575:       // Copying _graph_ref to graph
kpeter@2575:       copyGraph(_graph, _graph_ref)
kpeter@2575:         .edgeMap(_cost, cost)
kpeter@2575:         .nodeRef(_node_ref)
kpeter@2575:         .edgeRef(_edge_ref)
kpeter@2556:         .run();
deba@2440: 
kpeter@2556:       // Removing non-zero lower bounds
kpeter@2575:       for (typename Graph::EdgeIt e(_graph_ref); e != INVALID; ++e) {
kpeter@2575:         _capacity[_edge_ref[e]] = capacity[e] - lower[e];
deba@2440:       }
kpeter@2575:       for (typename Graph::NodeIt n(_graph_ref); n != INVALID; ++n) {
kpeter@2575:         Supply sum = 0;
kpeter@2575:         if (n == s) sum =  flow_value;
kpeter@2575:         if (n == t) sum = -flow_value;
kpeter@2575:         for (typename Graph::InEdgeIt e(_graph_ref, n); e != INVALID; ++e)
kpeter@2575:           sum += lower[e];
kpeter@2575:         for (typename Graph::OutEdgeIt e(_graph_ref, n); e != INVALID; ++e)
kpeter@2575:           sum -= lower[e];
kpeter@2575:         _supply[_node_ref[n]] = sum;
deba@2440:       }
kpeter@2575:       _valid_supply = true;
deba@2440:     }
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@2575:                     typename Graph::Node s,
kpeter@2575:                     typename Graph::Node t,
kpeter@2575:                     typename SupplyMap::Value flow_value ) :
kpeter@2575:       _graph(), _graph_ref(graph), _lower(NULL), _capacity(_graph),
kpeter@2575:       _cost(_graph), _supply(_graph, 0), _flow(_graph),
kpeter@2575:       _potential(_graph), _depth(_graph), _parent(_graph),
kpeter@2575:       _pred_edge(_graph), _thread(_graph), _forward(_graph),
kpeter@2575:       _state(_graph), _red_cost(_graph, _cost, _potential),
kpeter@2581:       _flow_result(0), _potential_result(0),
kpeter@2581:       _local_flow(false), _local_potential(false),
kpeter@2575:       _node_ref(graph), _edge_ref(graph)
deba@2440:     {
kpeter@2575:       // Copying _graph_ref to graph
kpeter@2575:       copyGraph(_graph, _graph_ref)
kpeter@2575:         .edgeMap(_capacity, capacity)
kpeter@2575:         .edgeMap(_cost, cost)
kpeter@2575:         .nodeRef(_node_ref)
kpeter@2575:         .edgeRef(_edge_ref)
kpeter@2556:         .run();
kpeter@2575:       _supply[_node_ref[s]] =  flow_value;
kpeter@2575:       _supply[_node_ref[t]] = -flow_value;
kpeter@2575:       _valid_supply = true;
deba@2440:     }
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@2619:     /// pivot rule proved to be by far the fastest and the most robust
kpeter@2619:     /// on 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@2575:       for (typename Graph::EdgeIt e(_graph_ref); e != INVALID; ++e)
kpeter@2581:         c += (*_flow_result)[e] * _cost[_edge_ref[e]];
deba@2440:       return c;
deba@2440:     }
deba@2440: 
kpeter@2581:     /// @}
kpeter@2581: 
kpeter@2575:   private:
deba@2440: 
kpeter@2619:     /// \brief Extend the underlying graph and initialize all the
deba@2440:     /// node and edge maps.
deba@2440:     bool init() {
kpeter@2575:       if (!_valid_supply) return false;
deba@2440: 
kpeter@2581:       // Initializing result maps
kpeter@2581:       if (!_flow_result) {
kpeter@2581:         _flow_result = new FlowMap(_graph_ref);
kpeter@2581:         _local_flow = true;
kpeter@2581:       }
kpeter@2581:       if (!_potential_result) {
kpeter@2581:         _potential_result = new PotentialMap(_graph_ref);
kpeter@2581:         _local_potential = true;
kpeter@2581:       }
kpeter@2581: 
kpeter@2619:       // Initializing the edge vector and the edge maps
kpeter@2619:       _edges.reserve(countEdges(_graph));
kpeter@2575:       for (EdgeIt e(_graph); e != INVALID; ++e) {
kpeter@2619:         _edges.push_back(e);
kpeter@2575:         _flow[e] = 0;
kpeter@2575:         _state[e] = STATE_LOWER;
deba@2440:       }
deba@2440: 
deba@2440:       // Adding an artificial root node to the graph
kpeter@2575:       _root = _graph.addNode();
kpeter@2575:       _parent[_root] = INVALID;
kpeter@2575:       _pred_edge[_root] = INVALID;
kpeter@2575:       _depth[_root] = 0;
kpeter@2575:       _supply[_root] = 0;
kpeter@2575:       _potential[_root] = 0;
deba@2440: 
deba@2440:       // Adding artificial edges to the graph and initializing the node
deba@2440:       // maps of the spanning tree data structure
kpeter@2575:       Node last = _root;
deba@2440:       Edge e;
deba@2440:       Cost max_cost = std::numeric_limits<Cost>::max() / 4;
kpeter@2575:       for (NodeIt u(_graph); u != INVALID; ++u) {
kpeter@2575:         if (u == _root) continue;
kpeter@2575:         _thread[last] = u;
kpeter@2556:         last = u;
kpeter@2575:         _parent[u] = _root;
kpeter@2575:         _depth[u] = 1;
kpeter@2575:         if (_supply[u] >= 0) {
kpeter@2575:           e = _graph.addEdge(u, _root);
kpeter@2575:           _flow[e] = _supply[u];
kpeter@2575:           _forward[u] = true;
kpeter@2575:           _potential[u] = -max_cost;
kpeter@2556:         } else {
kpeter@2575:           e = _graph.addEdge(_root, u);
kpeter@2575:           _flow[e] = -_supply[u];
kpeter@2575:           _forward[u] = false;
kpeter@2575:           _potential[u] = max_cost;
kpeter@2556:         }
kpeter@2575:         _cost[e] = max_cost;
kpeter@2575:         _capacity[e] = std::numeric_limits<Capacity>::max();
kpeter@2575:         _state[e] = STATE_TREE;
kpeter@2575:         _pred_edge[u] = e;
deba@2440:       }
kpeter@2575:       _thread[last] = _root;
deba@2440: 
kpeter@2575:       return true;
deba@2440:     }
deba@2440: 
kpeter@2619:     /// Find the join node.
kpeter@2619:     inline Node findJoinNode() {
kpeter@2575:       Node u = _graph.source(_in_edge);
kpeter@2575:       Node v = _graph.target(_in_edge);
kpeter@2575:       while (u != v) {
kpeter@2575:         if (_depth[u] == _depth[v]) {
kpeter@2575:           u = _parent[u];
kpeter@2575:           v = _parent[v];
kpeter@2556:         }
kpeter@2575:         else if (_depth[u] > _depth[v]) u = _parent[u];
kpeter@2575:         else v = _parent[v];
deba@2440:       }
deba@2440:       return u;
deba@2440:     }
deba@2440: 
kpeter@2619:     /// \brief Find the leaving edge of the cycle.
kpeter@2619:     /// \return \c true if the leaving edge is not the same as the
kpeter@2619:     /// entering edge.
kpeter@2619:     inline bool findLeavingEdge() {
deba@2440:       // Initializing first and second nodes according to the direction
deba@2440:       // of the cycle
kpeter@2575:       if (_state[_in_edge] == STATE_LOWER) {
kpeter@2575:         first  = _graph.source(_in_edge);
kpeter@2575:         second = _graph.target(_in_edge);
deba@2440:       } else {
kpeter@2575:         first  = _graph.target(_in_edge);
kpeter@2575:         second = _graph.source(_in_edge);
deba@2440:       }
kpeter@2575:       delta = _capacity[_in_edge];
deba@2440:       bool result = false;
deba@2440:       Capacity d;
deba@2440:       Edge e;
deba@2440: 
deba@2440:       // Searching the cycle along the path form the first node to the
deba@2440:       // root node
kpeter@2575:       for (Node u = first; u != join; u = _parent[u]) {
kpeter@2575:         e = _pred_edge[u];
kpeter@2575:         d = _forward[u] ? _flow[e] : _capacity[e] - _flow[e];
kpeter@2556:         if (d < delta) {
kpeter@2556:           delta = d;
kpeter@2556:           u_out = u;
kpeter@2556:           u_in = first;
kpeter@2556:           v_in = second;
kpeter@2556:           result = true;
kpeter@2556:         }
deba@2440:       }
deba@2440:       // Searching the cycle along the path form the second node to the
deba@2440:       // root node
kpeter@2575:       for (Node u = second; u != join; u = _parent[u]) {
kpeter@2575:         e = _pred_edge[u];
kpeter@2575:         d = _forward[u] ? _capacity[e] - _flow[e] : _flow[e];
kpeter@2556:         if (d <= delta) {
kpeter@2556:           delta = d;
kpeter@2556:           u_out = u;
kpeter@2556:           u_in = second;
kpeter@2556:           v_in = first;
kpeter@2556:           result = true;
kpeter@2556:         }
deba@2440:       }
deba@2440:       return result;
deba@2440:     }
deba@2440: 
kpeter@2619:     /// Change \c flow and \c state edge maps.
kpeter@2619:     inline void changeFlows(bool change) {
deba@2440:       // Augmenting along the cycle
deba@2440:       if (delta > 0) {
kpeter@2575:         Capacity val = _state[_in_edge] * delta;
kpeter@2575:         _flow[_in_edge] += val;
kpeter@2575:         for (Node u = _graph.source(_in_edge); u != join; u = _parent[u]) {
kpeter@2575:           _flow[_pred_edge[u]] += _forward[u] ? -val : val;
kpeter@2556:         }
kpeter@2575:         for (Node u = _graph.target(_in_edge); u != join; u = _parent[u]) {
kpeter@2575:           _flow[_pred_edge[u]] += _forward[u] ? val : -val;
kpeter@2556:         }
deba@2440:       }
deba@2440:       // Updating the state of the entering and leaving edges
deba@2440:       if (change) {
kpeter@2575:         _state[_in_edge] = STATE_TREE;
kpeter@2575:         _state[_pred_edge[u_out]] =
kpeter@2575:           (_flow[_pred_edge[u_out]] == 0) ? STATE_LOWER : STATE_UPPER;
deba@2440:       } else {
kpeter@2575:         _state[_in_edge] = -_state[_in_edge];
deba@2440:       }
deba@2440:     }
deba@2440: 
kpeter@2619:     /// Update \c thread and \c parent node maps.
kpeter@2619:     inline void updateThreadParent() {
deba@2440:       Node u;
kpeter@2575:       v_out = _parent[u_out];
deba@2440: 
deba@2440:       // Handling the case when join and v_out coincide
deba@2440:       bool par_first = false;
deba@2440:       if (join == v_out) {
kpeter@2575:         for (u = join; u != u_in && u != v_in; u = _thread[u]) ;
kpeter@2556:         if (u == v_in) {
kpeter@2556:           par_first = true;
kpeter@2575:           while (_thread[u] != u_out) u = _thread[u];
kpeter@2556:           first = u;
kpeter@2556:         }
deba@2440:       }
deba@2440: 
deba@2440:       // Finding the last successor of u_in (u) and the node after it
deba@2440:       // (right) according to the thread index
kpeter@2575:       for (u = u_in; _depth[_thread[u]] > _depth[u_in]; u = _thread[u]) ;
kpeter@2575:       right = _thread[u];
kpeter@2575:       if (_thread[v_in] == u_out) {
kpeter@2575:         for (last = u; _depth[last] > _depth[u_out]; last = _thread[last]) ;
kpeter@2575:         if (last == u_out) last = _thread[last];
deba@2440:       }
kpeter@2575:       else last = _thread[v_in];
deba@2440: 
deba@2440:       // Updating stem nodes
kpeter@2575:       _thread[v_in] = stem = u_in;
deba@2440:       par_stem = v_in;
deba@2440:       while (stem != u_out) {
kpeter@2575:         _thread[u] = new_stem = _parent[stem];
deba@2440: 
kpeter@2556:         // Finding the node just before the stem node (u) according to
kpeter@2556:         // the original thread index
kpeter@2575:         for (u = new_stem; _thread[u] != stem; u = _thread[u]) ;
kpeter@2575:         _thread[u] = right;
deba@2440: 
kpeter@2556:         // Changing the parent node of stem and shifting stem and
kpeter@2556:         // par_stem nodes
kpeter@2575:         _parent[stem] = par_stem;
kpeter@2556:         par_stem = stem;
kpeter@2556:         stem = new_stem;
deba@2440: 
kpeter@2556:         // Finding the last successor of stem (u) and the node after it
kpeter@2556:         // (right) according to the thread index
kpeter@2575:         for (u = stem; _depth[_thread[u]] > _depth[stem]; u = _thread[u]) ;
kpeter@2575:         right = _thread[u];
deba@2440:       }
kpeter@2575:       _parent[u_out] = par_stem;
kpeter@2575:       _thread[u] = last;
deba@2440: 
deba@2440:       if (join == v_out && par_first) {
kpeter@2575:         if (first != v_in) _thread[first] = right;
deba@2440:       } else {
kpeter@2575:         for (u = v_out; _thread[u] != u_out; u = _thread[u]) ;
kpeter@2575:         _thread[u] = right;
deba@2440:       }
deba@2440:     }
deba@2440: 
kpeter@2619:     /// Update \c pred_edge and \c forward node maps.
kpeter@2619:     inline void updatePredEdge() {
deba@2440:       Node u = u_out, v;
deba@2440:       while (u != u_in) {
kpeter@2575:         v = _parent[u];
kpeter@2575:         _pred_edge[u] = _pred_edge[v];
kpeter@2575:         _forward[u] = !_forward[v];
kpeter@2556:         u = v;
deba@2440:       }
kpeter@2575:       _pred_edge[u_in] = _in_edge;
kpeter@2575:       _forward[u_in] = (u_in == _graph.source(_in_edge));
deba@2440:     }
deba@2440: 
kpeter@2619:     /// Update \c depth and \c potential node maps.
kpeter@2619:     inline void updateDepthPotential() {
kpeter@2575:       _depth[u_in] = _depth[v_in] + 1;
kpeter@2575:       _potential[u_in] = _forward[u_in] ?
kpeter@2575:         _potential[v_in] - _cost[_pred_edge[u_in]] :
kpeter@2575:         _potential[v_in] + _cost[_pred_edge[u_in]];
deba@2440: 
kpeter@2575:       Node u = _thread[u_in], v;
deba@2440:       while (true) {
kpeter@2575:         v = _parent[u];
kpeter@2556:         if (v == INVALID) break;
kpeter@2575:         _depth[u] = _depth[v] + 1;
kpeter@2575:         _potential[u] = _forward[u] ?
kpeter@2575:           _potential[v] - _cost[_pred_edge[u]] :
kpeter@2575:           _potential[v] + _cost[_pred_edge[u]];
kpeter@2575:         if (_depth[u] <= _depth[v_in]) break;
kpeter@2575:         u = _thread[u];
deba@2440:       }
deba@2440:     }
deba@2440: 
kpeter@2619:     /// Execute the algorithm.
kpeter@2575:     bool start(PivotRuleEnum pivot_rule) {
kpeter@2619:       // Selecting 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@2619:       PivotRuleImplementation pivot(*this, _edges);
kpeter@2575: 
kpeter@2575:       // Executing the network simplex algorithm
kpeter@2575:       while (pivot.findEnteringEdge()) {
kpeter@2556:         join = findJoinNode();
kpeter@2556:         bool change = findLeavingEdge();
kpeter@2556:         changeFlows(change);
kpeter@2556:         if (change) {
kpeter@2556:           updateThreadParent();
kpeter@2556:           updatePredEdge();
kpeter@2556:           updateDepthPotential();
kpeter@2556:         }
deba@2440:       }
deba@2440: 
kpeter@2575:       // Checking if the flow amount equals zero on all the artificial
kpeter@2575:       // edges
kpeter@2575:       for (InEdgeIt e(_graph, _root); e != INVALID; ++e)
kpeter@2575:         if (_flow[e] > 0) return false;
kpeter@2575:       for (OutEdgeIt e(_graph, _root); e != INVALID; ++e)
kpeter@2575:         if (_flow[e] > 0) return false;
deba@2440: 
kpeter@2575:       // Copying flow values to _flow_result
kpeter@2575:       if (_lower) {
kpeter@2575:         for (typename Graph::EdgeIt e(_graph_ref); e != INVALID; ++e)
kpeter@2581:           (*_flow_result)[e] = (*_lower)[e] + _flow[_edge_ref[e]];
deba@2440:       } else {
kpeter@2575:         for (typename Graph::EdgeIt e(_graph_ref); e != INVALID; ++e)
kpeter@2581:           (*_flow_result)[e] = _flow[_edge_ref[e]];
deba@2440:       }
kpeter@2575:       // Copying potential values to _potential_result
kpeter@2575:       for (typename Graph::NodeIt n(_graph_ref); n != INVALID; ++n)
kpeter@2581:         (*_potential_result)[n] = _potential[_node_ref[n]];
deba@2440: 
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