diff -r e9c203fb003d -r 994c7df296c9 lemon/network_simplex.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/network_simplex.h	Thu Dec 10 17:05:35 2009 +0100
@@ -0,0 +1,1489 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2009
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#ifndef LEMON_NETWORK_SIMPLEX_H
+#define LEMON_NETWORK_SIMPLEX_H
+
+/// \ingroup min_cost_flow_algs
+///
+/// \file
+/// \brief Network Simplex algorithm for finding a minimum cost flow.
+
+#include <vector>
+#include <limits>
+#include <algorithm>
+
+#include <lemon/core.h>
+#include <lemon/math.h>
+
+namespace lemon {
+
+  /// \addtogroup min_cost_flow_algs
+  /// @{
+
+  /// \brief Implementation of the primal Network Simplex algorithm
+  /// for finding a \ref min_cost_flow "minimum cost flow".
+  ///
+  /// \ref NetworkSimplex implements the primal Network Simplex algorithm
+  /// for finding a \ref min_cost_flow "minimum cost flow".
+  /// This algorithm is a specialized version of the linear programming
+  /// simplex method directly for the minimum cost flow problem.
+  /// It is one of the most efficient solution methods.
+  ///
+  /// In general this class is the fastest implementation available
+  /// in LEMON for the minimum cost flow problem.
+  /// Moreover it supports both directions of the supply/demand inequality
+  /// constraints. For more information see \ref SupplyType.
+  ///
+  /// Most of the parameters of the problem (except for the digraph)
+  /// can be given using separate functions, and the algorithm can be
+  /// executed using the \ref run() function. If some parameters are not
+  /// specified, then default values will be used.
+  ///
+  /// \tparam GR The digraph type the algorithm runs on.
+  /// \tparam V The value type used for flow amounts, capacity bounds
+  /// and supply values in the algorithm. By default it is \c int.
+  /// \tparam C The value type used for costs and potentials in the
+  /// algorithm. By default it is the same as \c V.
+  ///
+  /// \warning Both value types must be signed and all input data must
+  /// be integer.
+  ///
+  /// \note %NetworkSimplex provides five different pivot rule
+  /// implementations, from which the most efficient one is used
+  /// by default. For more information see \ref PivotRule.
+  template <typename GR, typename V = int, typename C = V>
+  class NetworkSimplex
+  {
+  public:
+
+    /// The type of the flow amounts, capacity bounds and supply values
+    typedef V Value;
+    /// The type of the arc costs
+    typedef C Cost;
+
+  public:
+
+    /// \brief Problem type constants for the \c run() function.
+    ///
+    /// Enum type containing the problem type constants that can be
+    /// returned by the \ref run() function of the algorithm.
+    enum ProblemType {
+      /// The problem has no feasible solution (flow).
+      INFEASIBLE,
+      /// The problem has optimal solution (i.e. it is feasible and
+      /// bounded), and the algorithm has found optimal flow and node
+      /// potentials (primal and dual solutions).
+      OPTIMAL,
+      /// The objective function of the problem is unbounded, i.e.
+      /// there is a directed cycle having negative total cost and
+      /// infinite upper bound.
+      UNBOUNDED
+    };
+    
+    /// \brief Constants for selecting the type of the supply constraints.
+    ///
+    /// Enum type containing constants for selecting the supply type,
+    /// i.e. the direction of the inequalities in the supply/demand
+    /// constraints of the \ref min_cost_flow "minimum cost flow problem".
+    ///
+    /// The default supply type is \c GEQ, the \c LEQ type can be
+    /// selected using \ref supplyType().
+    /// The equality form is a special case of both supply types.
+    enum SupplyType {
+      /// This option means that there are <em>"greater or equal"</em>
+      /// supply/demand constraints in the definition of the problem.
+      GEQ,
+      /// This option means that there are <em>"less or equal"</em>
+      /// supply/demand constraints in the definition of the problem.
+      LEQ
+    };
+    
+    /// \brief Constants for selecting the pivot rule.
+    ///
+    /// Enum type containing constants for selecting the pivot rule for
+    /// the \ref run() function.
+    ///
+    /// \ref NetworkSimplex provides five different pivot rule
+    /// implementations that significantly affect the running time
+    /// of the algorithm.
+    /// By default \ref BLOCK_SEARCH "Block Search" is used, which
+    /// proved to be the most efficient and the most robust on various
+    /// test inputs according to our benchmark tests.
+    /// However another pivot rule can be selected using the \ref run()
+    /// function with the proper parameter.
+    enum PivotRule {
+
+      /// The First Eligible pivot rule.
+      /// The next eligible arc is selected in a wraparound fashion
+      /// in every iteration.
+      FIRST_ELIGIBLE,
+
+      /// The Best Eligible pivot rule.
+      /// The best eligible arc is selected in every iteration.
+      BEST_ELIGIBLE,
+
+      /// The Block Search pivot rule.
+      /// A specified number of arcs are examined in every iteration
+      /// in a wraparound fashion and the best eligible arc is selected
+      /// from this block.
+      BLOCK_SEARCH,
+
+      /// The Candidate List pivot rule.
+      /// In a major iteration a candidate list is built from eligible arcs
+      /// in a wraparound fashion and in the following minor iterations
+      /// the best eligible arc is selected from this list.
+      CANDIDATE_LIST,
+
+      /// The Altering Candidate List pivot rule.
+      /// It is a modified version of the Candidate List method.
+      /// It keeps only the several best eligible arcs from the former
+      /// candidate list and extends this list in every iteration.
+      ALTERING_LIST
+    };
+    
+  private:
+
+    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
+
+    typedef std::vector<Arc> ArcVector;
+    typedef std::vector<Node> NodeVector;
+    typedef std::vector<int> IntVector;
+    typedef std::vector<bool> BoolVector;
+    typedef std::vector<Value> ValueVector;
+    typedef std::vector<Cost> CostVector;
+
+    // State constants for arcs
+    enum ArcStateEnum {
+      STATE_UPPER = -1,
+      STATE_TREE  =  0,
+      STATE_LOWER =  1
+    };
+
+  private:
+
+    // Data related to the underlying digraph
+    const GR &_graph;
+    int _node_num;
+    int _arc_num;
+    int _all_arc_num;
+    int _search_arc_num;
+
+    // Parameters of the problem
+    bool _have_lower;
+    SupplyType _stype;
+    Value _sum_supply;
+
+    // Data structures for storing the digraph
+    IntNodeMap _node_id;
+    IntArcMap _arc_id;
+    IntVector _source;
+    IntVector _target;
+
+    // Node and arc data
+    ValueVector _lower;
+    ValueVector _upper;
+    ValueVector _cap;
+    CostVector _cost;
+    ValueVector _supply;
+    ValueVector _flow;
+    CostVector _pi;
+
+    // Data for storing the spanning tree structure
+    IntVector _parent;
+    IntVector _pred;
+    IntVector _thread;
+    IntVector _rev_thread;
+    IntVector _succ_num;
+    IntVector _last_succ;
+    IntVector _dirty_revs;
+    BoolVector _forward;
+    IntVector _state;
+    int _root;
+
+    // Temporary data used in the current pivot iteration
+    int in_arc, join, u_in, v_in, u_out, v_out;
+    int first, second, right, last;
+    int stem, par_stem, new_stem;
+    Value delta;
+
+  public:
+  
+    /// \brief Constant for infinite upper bounds (capacities).
+    ///
+    /// Constant for infinite upper bounds (capacities).
+    /// It is \c std::numeric_limits<Value>::infinity() if available,
+    /// \c std::numeric_limits<Value>::max() otherwise.
+    const Value INF;
+
+  private:
+
+    // Implementation of the First Eligible pivot rule
+    class FirstEligiblePivotRule
+    {
+    private:
+
+      // References to the NetworkSimplex class
+      const IntVector  &_source;
+      const IntVector  &_target;
+      const CostVector &_cost;
+      const IntVector  &_state;
+      const CostVector &_pi;
+      int &_in_arc;
+      int _search_arc_num;
+
+      // Pivot rule data
+      int _next_arc;
+
+    public:
+
+      // Constructor
+      FirstEligiblePivotRule(NetworkSimplex &ns) :
+        _source(ns._source), _target(ns._target),
+        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
+        _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
+        _next_arc(0)
+      {}
+
+      // Find next entering arc
+      bool findEnteringArc() {
+        Cost c;
+        for (int e = _next_arc; e < _search_arc_num; ++e) {
+          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+          if (c < 0) {
+            _in_arc = e;
+            _next_arc = e + 1;
+            return true;
+          }
+        }
+        for (int e = 0; e < _next_arc; ++e) {
+          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+          if (c < 0) {
+            _in_arc = e;
+            _next_arc = e + 1;
+            return true;
+          }
+        }
+        return false;
+      }
+
+    }; //class FirstEligiblePivotRule
+
+
+    // Implementation of the Best Eligible pivot rule
+    class BestEligiblePivotRule
+    {
+    private:
+
+      // References to the NetworkSimplex class
+      const IntVector  &_source;
+      const IntVector  &_target;
+      const CostVector &_cost;
+      const IntVector  &_state;
+      const CostVector &_pi;
+      int &_in_arc;
+      int _search_arc_num;
+
+    public:
+
+      // Constructor
+      BestEligiblePivotRule(NetworkSimplex &ns) :
+        _source(ns._source), _target(ns._target),
+        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
+        _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num)
+      {}
+
+      // Find next entering arc
+      bool findEnteringArc() {
+        Cost c, min = 0;
+        for (int e = 0; e < _search_arc_num; ++e) {
+          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+          if (c < min) {
+            min = c;
+            _in_arc = e;
+          }
+        }
+        return min < 0;
+      }
+
+    }; //class BestEligiblePivotRule
+
+
+    // Implementation of the Block Search pivot rule
+    class BlockSearchPivotRule
+    {
+    private:
+
+      // References to the NetworkSimplex class
+      const IntVector  &_source;
+      const IntVector  &_target;
+      const CostVector &_cost;
+      const IntVector  &_state;
+      const CostVector &_pi;
+      int &_in_arc;
+      int _search_arc_num;
+
+      // Pivot rule data
+      int _block_size;
+      int _next_arc;
+
+    public:
+
+      // Constructor
+      BlockSearchPivotRule(NetworkSimplex &ns) :
+        _source(ns._source), _target(ns._target),
+        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
+        _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
+        _next_arc(0)
+      {
+        // The main parameters of the pivot rule
+        const double BLOCK_SIZE_FACTOR = 0.5;
+        const int MIN_BLOCK_SIZE = 10;
+
+        _block_size = std::max( int(BLOCK_SIZE_FACTOR *
+                                    std::sqrt(double(_search_arc_num))),
+                                MIN_BLOCK_SIZE );
+      }
+
+      // Find next entering arc
+      bool findEnteringArc() {
+        Cost c, min = 0;
+        int cnt = _block_size;
+        int e, min_arc = _next_arc;
+        for (e = _next_arc; e < _search_arc_num; ++e) {
+          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+          if (c < min) {
+            min = c;
+            min_arc = e;
+          }
+          if (--cnt == 0) {
+            if (min < 0) break;
+            cnt = _block_size;
+          }
+        }
+        if (min == 0 || cnt > 0) {
+          for (e = 0; e < _next_arc; ++e) {
+            c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+            if (c < min) {
+              min = c;
+              min_arc = e;
+            }
+            if (--cnt == 0) {
+              if (min < 0) break;
+              cnt = _block_size;
+            }
+          }
+        }
+        if (min >= 0) return false;
+        _in_arc = min_arc;
+        _next_arc = e;
+        return true;
+      }
+
+    }; //class BlockSearchPivotRule
+
+
+    // Implementation of the Candidate List pivot rule
+    class CandidateListPivotRule
+    {
+    private:
+
+      // References to the NetworkSimplex class
+      const IntVector  &_source;
+      const IntVector  &_target;
+      const CostVector &_cost;
+      const IntVector  &_state;
+      const CostVector &_pi;
+      int &_in_arc;
+      int _search_arc_num;
+
+      // Pivot rule data
+      IntVector _candidates;
+      int _list_length, _minor_limit;
+      int _curr_length, _minor_count;
+      int _next_arc;
+
+    public:
+
+      /// Constructor
+      CandidateListPivotRule(NetworkSimplex &ns) :
+        _source(ns._source), _target(ns._target),
+        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
+        _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
+        _next_arc(0)
+      {
+        // The main parameters of the pivot rule
+        const double LIST_LENGTH_FACTOR = 1.0;
+        const int MIN_LIST_LENGTH = 10;
+        const double MINOR_LIMIT_FACTOR = 0.1;
+        const int MIN_MINOR_LIMIT = 3;
+
+        _list_length = std::max( int(LIST_LENGTH_FACTOR *
+                                     std::sqrt(double(_search_arc_num))),
+                                 MIN_LIST_LENGTH );
+        _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length),
+                                 MIN_MINOR_LIMIT );
+        _curr_length = _minor_count = 0;
+        _candidates.resize(_list_length);
+      }
+
+      /// Find next entering arc
+      bool findEnteringArc() {
+        Cost min, c;
+        int e, min_arc = _next_arc;
+        if (_curr_length > 0 && _minor_count < _minor_limit) {
+          // Minor iteration: select the best eligible arc from the
+          // current candidate list
+          ++_minor_count;
+          min = 0;
+          for (int i = 0; i < _curr_length; ++i) {
+            e = _candidates[i];
+            c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+            if (c < min) {
+              min = c;
+              min_arc = e;
+            }
+            if (c >= 0) {
+              _candidates[i--] = _candidates[--_curr_length];
+            }
+          }
+          if (min < 0) {
+            _in_arc = min_arc;
+            return true;
+          }
+        }
+
+        // Major iteration: build a new candidate list
+        min = 0;
+        _curr_length = 0;
+        for (e = _next_arc; e < _search_arc_num; ++e) {
+          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+          if (c < 0) {
+            _candidates[_curr_length++] = e;
+            if (c < min) {
+              min = c;
+              min_arc = e;
+            }
+            if (_curr_length == _list_length) break;
+          }
+        }
+        if (_curr_length < _list_length) {
+          for (e = 0; e < _next_arc; ++e) {
+            c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+            if (c < 0) {
+              _candidates[_curr_length++] = e;
+              if (c < min) {
+                min = c;
+                min_arc = e;
+              }
+              if (_curr_length == _list_length) break;
+            }
+          }
+        }
+        if (_curr_length == 0) return false;
+        _minor_count = 1;
+        _in_arc = min_arc;
+        _next_arc = e;
+        return true;
+      }
+
+    }; //class CandidateListPivotRule
+
+
+    // Implementation of the Altering Candidate List pivot rule
+    class AlteringListPivotRule
+    {
+    private:
+
+      // References to the NetworkSimplex class
+      const IntVector  &_source;
+      const IntVector  &_target;
+      const CostVector &_cost;
+      const IntVector  &_state;
+      const CostVector &_pi;
+      int &_in_arc;
+      int _search_arc_num;
+
+      // Pivot rule data
+      int _block_size, _head_length, _curr_length;
+      int _next_arc;
+      IntVector _candidates;
+      CostVector _cand_cost;
+
+      // Functor class to compare arcs during sort of the candidate list
+      class SortFunc
+      {
+      private:
+        const CostVector &_map;
+      public:
+        SortFunc(const CostVector &map) : _map(map) {}
+        bool operator()(int left, int right) {
+          return _map[left] > _map[right];
+        }
+      };
+
+      SortFunc _sort_func;
+
+    public:
+
+      // Constructor
+      AlteringListPivotRule(NetworkSimplex &ns) :
+        _source(ns._source), _target(ns._target),
+        _cost(ns._cost), _state(ns._state), _pi(ns._pi),
+        _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num),
+        _next_arc(0), _cand_cost(ns._search_arc_num), _sort_func(_cand_cost)
+      {
+        // The main parameters of the pivot rule
+        const double BLOCK_SIZE_FACTOR = 1.5;
+        const int MIN_BLOCK_SIZE = 10;
+        const double HEAD_LENGTH_FACTOR = 0.1;
+        const int MIN_HEAD_LENGTH = 3;
+
+        _block_size = std::max( int(BLOCK_SIZE_FACTOR *
+                                    std::sqrt(double(_search_arc_num))),
+                                MIN_BLOCK_SIZE );
+        _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size),
+                                 MIN_HEAD_LENGTH );
+        _candidates.resize(_head_length + _block_size);
+        _curr_length = 0;
+      }
+
+      // Find next entering arc
+      bool findEnteringArc() {
+        // Check the current candidate list
+        int e;
+        for (int i = 0; i < _curr_length; ++i) {
+          e = _candidates[i];
+          _cand_cost[e] = _state[e] *
+            (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+          if (_cand_cost[e] >= 0) {
+            _candidates[i--] = _candidates[--_curr_length];
+          }
+        }
+
+        // Extend the list
+        int cnt = _block_size;
+        int last_arc = 0;
+        int limit = _head_length;
+
+        for (int e = _next_arc; e < _search_arc_num; ++e) {
+          _cand_cost[e] = _state[e] *
+            (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+          if (_cand_cost[e] < 0) {
+            _candidates[_curr_length++] = e;
+            last_arc = e;
+          }
+          if (--cnt == 0) {
+            if (_curr_length > limit) break;
+            limit = 0;
+            cnt = _block_size;
+          }
+        }
+        if (_curr_length <= limit) {
+          for (int e = 0; e < _next_arc; ++e) {
+            _cand_cost[e] = _state[e] *
+              (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+            if (_cand_cost[e] < 0) {
+              _candidates[_curr_length++] = e;
+              last_arc = e;
+            }
+            if (--cnt == 0) {
+              if (_curr_length > limit) break;
+              limit = 0;
+              cnt = _block_size;
+            }
+          }
+        }
+        if (_curr_length == 0) return false;
+        _next_arc = last_arc + 1;
+
+        // Make heap of the candidate list (approximating a partial sort)
+        make_heap( _candidates.begin(), _candidates.begin() + _curr_length,
+                   _sort_func );
+
+        // Pop the first element of the heap
+        _in_arc = _candidates[0];
+        pop_heap( _candidates.begin(), _candidates.begin() + _curr_length,
+                  _sort_func );
+        _curr_length = std::min(_head_length, _curr_length - 1);
+        return true;
+      }
+
+    }; //class AlteringListPivotRule
+
+  public:
+
+    /// \brief Constructor.
+    ///
+    /// The constructor of the class.
+    ///
+    /// \param graph The digraph the algorithm runs on.
+    NetworkSimplex(const GR& graph) :
+      _graph(graph), _node_id(graph), _arc_id(graph),
+      INF(std::numeric_limits<Value>::has_infinity ?
+          std::numeric_limits<Value>::infinity() :
+          std::numeric_limits<Value>::max())
+    {
+      // Check the value types
+      LEMON_ASSERT(std::numeric_limits<Value>::is_signed,
+        "The flow type of NetworkSimplex must be signed");
+      LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
+        "The cost type of NetworkSimplex must be signed");
+        
+      // Resize vectors
+      _node_num = countNodes(_graph);
+      _arc_num = countArcs(_graph);
+      int all_node_num = _node_num + 1;
+      int max_arc_num = _arc_num + 2 * _node_num;
+
+      _source.resize(max_arc_num);
+      _target.resize(max_arc_num);
+
+      _lower.resize(_arc_num);
+      _upper.resize(_arc_num);
+      _cap.resize(max_arc_num);
+      _cost.resize(max_arc_num);
+      _supply.resize(all_node_num);
+      _flow.resize(max_arc_num);
+      _pi.resize(all_node_num);
+
+      _parent.resize(all_node_num);
+      _pred.resize(all_node_num);
+      _forward.resize(all_node_num);
+      _thread.resize(all_node_num);
+      _rev_thread.resize(all_node_num);
+      _succ_num.resize(all_node_num);
+      _last_succ.resize(all_node_num);
+      _state.resize(max_arc_num);
+
+      // Copy the graph (store the arcs in a mixed order)
+      int i = 0;
+      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
+        _node_id[n] = i;
+      }
+      int k = std::max(int(std::sqrt(double(_arc_num))), 10);
+      i = 0;
+      for (ArcIt a(_graph); a != INVALID; ++a) {
+        _arc_id[a] = i;
+        _source[i] = _node_id[_graph.source(a)];
+        _target[i] = _node_id[_graph.target(a)];
+        if ((i += k) >= _arc_num) i = (i % k) + 1;
+      }
+      
+      // Initialize maps
+      for (int i = 0; i != _node_num; ++i) {
+        _supply[i] = 0;
+      }
+      for (int i = 0; i != _arc_num; ++i) {
+        _lower[i] = 0;
+        _upper[i] = INF;
+        _cost[i] = 1;
+      }
+      _have_lower = false;
+      _stype = GEQ;
+    }
+
+    /// \name Parameters
+    /// The parameters of the algorithm can be specified using these
+    /// functions.
+
+    /// @{
+
+    /// \brief Set the lower bounds on the arcs.
+    ///
+    /// This function sets the lower bounds on the arcs.
+    /// If it is not used before calling \ref run(), the lower bounds
+    /// will be set to zero on all arcs.
+    ///
+    /// \param map An arc map storing the lower bounds.
+    /// Its \c Value type must be convertible to the \c Value type
+    /// of the algorithm.
+    ///
+    /// \return <tt>(*this)</tt>
+    template <typename LowerMap>
+    NetworkSimplex& lowerMap(const LowerMap& map) {
+      _have_lower = true;
+      for (ArcIt a(_graph); a != INVALID; ++a) {
+        _lower[_arc_id[a]] = map[a];
+      }
+      return *this;
+    }
+
+    /// \brief Set the upper bounds (capacities) on the arcs.
+    ///
+    /// This function sets the upper bounds (capacities) on the arcs.
+    /// If it is not used before calling \ref run(), the upper bounds
+    /// will be set to \ref INF on all arcs (i.e. the flow value will be
+    /// unbounded from above on each arc).
+    ///
+    /// \param map An arc map storing the upper bounds.
+    /// Its \c Value type must be convertible to the \c Value type
+    /// of the algorithm.
+    ///
+    /// \return <tt>(*this)</tt>
+    template<typename UpperMap>
+    NetworkSimplex& upperMap(const UpperMap& map) {
+      for (ArcIt a(_graph); a != INVALID; ++a) {
+        _upper[_arc_id[a]] = map[a];
+      }
+      return *this;
+    }
+
+    /// \brief Set the costs of the arcs.
+    ///
+    /// This function sets the costs of the arcs.
+    /// If it is not used before calling \ref run(), the costs
+    /// will be set to \c 1 on all arcs.
+    ///
+    /// \param map An arc map storing the costs.
+    /// Its \c Value type must be convertible to the \c Cost type
+    /// of the algorithm.
+    ///
+    /// \return <tt>(*this)</tt>
+    template<typename CostMap>
+    NetworkSimplex& costMap(const CostMap& map) {
+      for (ArcIt a(_graph); a != INVALID; ++a) {
+        _cost[_arc_id[a]] = map[a];
+      }
+      return *this;
+    }
+
+    /// \brief Set the supply values of the nodes.
+    ///
+    /// This function sets the supply values of the nodes.
+    /// If neither this function nor \ref stSupply() is used before
+    /// calling \ref run(), the supply of each node will be set to zero.
+    /// (It makes sense only if non-zero lower bounds are given.)
+    ///
+    /// \param map A node map storing the supply values.
+    /// Its \c Value type must be convertible to the \c Value type
+    /// of the algorithm.
+    ///
+    /// \return <tt>(*this)</tt>
+    template<typename SupplyMap>
+    NetworkSimplex& supplyMap(const SupplyMap& map) {
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+        _supply[_node_id[n]] = map[n];
+      }
+      return *this;
+    }
+
+    /// \brief Set single source and target nodes and a supply value.
+    ///
+    /// This function sets a single source node and a single target node
+    /// and the required flow value.
+    /// If neither this function nor \ref supplyMap() is used before
+    /// calling \ref run(), the supply of each node will be set to zero.
+    /// (It makes sense only if non-zero lower bounds are given.)
+    ///
+    /// Using this function has the same effect as using \ref supplyMap()
+    /// with such a map in which \c k is assigned to \c s, \c -k is
+    /// assigned to \c t and all other nodes have zero supply value.
+    ///
+    /// \param s The source node.
+    /// \param t The target node.
+    /// \param k The required amount of flow from node \c s to node \c t
+    /// (i.e. the supply of \c s and the demand of \c t).
+    ///
+    /// \return <tt>(*this)</tt>
+    NetworkSimplex& stSupply(const Node& s, const Node& t, Value k) {
+      for (int i = 0; i != _node_num; ++i) {
+        _supply[i] = 0;
+      }
+      _supply[_node_id[s]] =  k;
+      _supply[_node_id[t]] = -k;
+      return *this;
+    }
+    
+    /// \brief Set the type of the supply constraints.
+    ///
+    /// This function sets the type of the supply/demand constraints.
+    /// If it is not used before calling \ref run(), the \ref GEQ supply
+    /// type will be used.
+    ///
+    /// For more information see \ref SupplyType.
+    ///
+    /// \return <tt>(*this)</tt>
+    NetworkSimplex& supplyType(SupplyType supply_type) {
+      _stype = supply_type;
+      return *this;
+    }
+
+    /// @}
+
+    /// \name Execution Control
+    /// The algorithm can be executed using \ref run().
+
+    /// @{
+
+    /// \brief Run the algorithm.
+    ///
+    /// This function runs the algorithm.
+    /// The paramters can be specified using functions \ref lowerMap(),
+    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(), 
+    /// \ref supplyType().
+    /// For example,
+    /// \code
+    ///   NetworkSimplex<ListDigraph> ns(graph);
+    ///   ns.lowerMap(lower).upperMap(upper).costMap(cost)
+    ///     .supplyMap(sup).run();
+    /// \endcode
+    ///
+    /// This function can be called more than once. All the parameters
+    /// that have been given are kept for the next call, unless
+    /// \ref reset() is called, thus only the modified parameters
+    /// have to be set again. See \ref reset() for examples.
+    /// However the underlying digraph must not be modified after this
+    /// class have been constructed, since it copies and extends the graph.
+    ///
+    /// \param pivot_rule The pivot rule that will be used during the
+    /// algorithm. For more information see \ref PivotRule.
+    ///
+    /// \return \c INFEASIBLE if no feasible flow exists,
+    /// \n \c OPTIMAL if the problem has optimal solution
+    /// (i.e. it is feasible and bounded), and the algorithm has found
+    /// optimal flow and node potentials (primal and dual solutions),
+    /// \n \c UNBOUNDED if the objective function of the problem is
+    /// unbounded, i.e. there is a directed cycle having negative total
+    /// cost and infinite upper bound.
+    ///
+    /// \see ProblemType, PivotRule
+    ProblemType run(PivotRule pivot_rule = BLOCK_SEARCH) {
+      if (!init()) return INFEASIBLE;
+      return start(pivot_rule);
+    }
+
+    /// \brief Reset all the parameters that have been given before.
+    ///
+    /// This function resets all the paramaters that have been given
+    /// before using functions \ref lowerMap(), \ref upperMap(),
+    /// \ref costMap(), \ref supplyMap(), \ref stSupply(), \ref supplyType().
+    ///
+    /// It is useful for multiple run() calls. If this function is not
+    /// used, all the parameters given before are kept for the next
+    /// \ref run() call.
+    /// However the underlying digraph must not be modified after this
+    /// class have been constructed, since it copies and extends the graph.
+    ///
+    /// For example,
+    /// \code
+    ///   NetworkSimplex<ListDigraph> ns(graph);
+    ///
+    ///   // First run
+    ///   ns.lowerMap(lower).upperMap(upper).costMap(cost)
+    ///     .supplyMap(sup).run();
+    ///
+    ///   // Run again with modified cost map (reset() is not called,
+    ///   // so only the cost map have to be set again)
+    ///   cost[e] += 100;
+    ///   ns.costMap(cost).run();
+    ///
+    ///   // Run again from scratch using reset()
+    ///   // (the lower bounds will be set to zero on all arcs)
+    ///   ns.reset();
+    ///   ns.upperMap(capacity).costMap(cost)
+    ///     .supplyMap(sup).run();
+    /// \endcode
+    ///
+    /// \return <tt>(*this)</tt>
+    NetworkSimplex& reset() {
+      for (int i = 0; i != _node_num; ++i) {
+        _supply[i] = 0;
+      }
+      for (int i = 0; i != _arc_num; ++i) {
+        _lower[i] = 0;
+        _upper[i] = INF;
+        _cost[i] = 1;
+      }
+      _have_lower = false;
+      _stype = GEQ;
+      return *this;
+    }
+
+    /// @}
+
+    /// \name Query Functions
+    /// The results of the algorithm can be obtained using these
+    /// functions.\n
+    /// The \ref run() function must be called before using them.
+
+    /// @{
+
+    /// \brief Return the total cost of the found flow.
+    ///
+    /// This function returns the total cost of the found flow.
+    /// Its complexity is O(e).
+    ///
+    /// \note The return type of the function can be specified as a
+    /// template parameter. For example,
+    /// \code
+    ///   ns.totalCost<double>();
+    /// \endcode
+    /// It is useful if the total cost cannot be stored in the \c Cost
+    /// type of the algorithm, which is the default return type of the
+    /// function.
+    ///
+    /// \pre \ref run() must be called before using this function.
+    template <typename Number>
+    Number totalCost() const {
+      Number c = 0;
+      for (ArcIt a(_graph); a != INVALID; ++a) {
+        int i = _arc_id[a];
+        c += Number(_flow[i]) * Number(_cost[i]);
+      }
+      return c;
+    }
+
+#ifndef DOXYGEN
+    Cost totalCost() const {
+      return totalCost<Cost>();
+    }
+#endif
+
+    /// \brief Return the flow on the given arc.
+    ///
+    /// This function returns the flow on the given arc.
+    ///
+    /// \pre \ref run() must be called before using this function.
+    Value flow(const Arc& a) const {
+      return _flow[_arc_id[a]];
+    }
+
+    /// \brief Return the flow map (the primal solution).
+    ///
+    /// This function copies the flow value on each arc into the given
+    /// map. The \c Value type of the algorithm must be convertible to
+    /// the \c Value type of the map.
+    ///
+    /// \pre \ref run() must be called before using this function.
+    template <typename FlowMap>
+    void flowMap(FlowMap &map) const {
+      for (ArcIt a(_graph); a != INVALID; ++a) {
+        map.set(a, _flow[_arc_id[a]]);
+      }
+    }
+
+    /// \brief Return the potential (dual value) of the given node.
+    ///
+    /// This function returns the potential (dual value) of the
+    /// given node.
+    ///
+    /// \pre \ref run() must be called before using this function.
+    Cost potential(const Node& n) const {
+      return _pi[_node_id[n]];
+    }
+
+    /// \brief Return the potential map (the dual solution).
+    ///
+    /// This function copies the potential (dual value) of each node
+    /// into the given map.
+    /// The \c Cost type of the algorithm must be convertible to the
+    /// \c Value type of the map.
+    ///
+    /// \pre \ref run() must be called before using this function.
+    template <typename PotentialMap>
+    void potentialMap(PotentialMap &map) const {
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+        map.set(n, _pi[_node_id[n]]);
+      }
+    }
+
+    /// @}
+
+  private:
+
+    // Initialize internal data structures
+    bool init() {
+      if (_node_num == 0) return false;
+
+      // Check the sum of supply values
+      _sum_supply = 0;
+      for (int i = 0; i != _node_num; ++i) {
+        _sum_supply += _supply[i];
+      }
+      if ( !((_stype == GEQ && _sum_supply <= 0) ||
+             (_stype == LEQ && _sum_supply >= 0)) ) return false;
+
+      // Remove non-zero lower bounds
+      if (_have_lower) {
+        for (int i = 0; i != _arc_num; ++i) {
+          Value c = _lower[i];
+          if (c >= 0) {
+            _cap[i] = _upper[i] < INF ? _upper[i] - c : INF;
+          } else {
+            _cap[i] = _upper[i] < INF + c ? _upper[i] - c : INF;
+          }
+          _supply[_source[i]] -= c;
+          _supply[_target[i]] += c;
+        }
+      } else {
+        for (int i = 0; i != _arc_num; ++i) {
+          _cap[i] = _upper[i];
+        }
+      }
+
+      // Initialize artifical cost
+      Cost ART_COST;
+      if (std::numeric_limits<Cost>::is_exact) {
+        ART_COST = std::numeric_limits<Cost>::max() / 2 + 1;
+      } else {
+        ART_COST = std::numeric_limits<Cost>::min();
+        for (int i = 0; i != _arc_num; ++i) {
+          if (_cost[i] > ART_COST) ART_COST = _cost[i];
+        }
+        ART_COST = (ART_COST + 1) * _node_num;
+      }
+
+      // Initialize arc maps
+      for (int i = 0; i != _arc_num; ++i) {
+        _flow[i] = 0;
+        _state[i] = STATE_LOWER;
+      }
+      
+      // Set data for the artificial root node
+      _root = _node_num;
+      _parent[_root] = -1;
+      _pred[_root] = -1;
+      _thread[_root] = 0;
+      _rev_thread[0] = _root;
+      _succ_num[_root] = _node_num + 1;
+      _last_succ[_root] = _root - 1;
+      _supply[_root] = -_sum_supply;
+      _pi[_root] = 0;
+
+      // Add artificial arcs and initialize the spanning tree data structure
+      if (_sum_supply == 0) {
+        // EQ supply constraints
+        _search_arc_num = _arc_num;
+        _all_arc_num = _arc_num + _node_num;
+        for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
+          _parent[u] = _root;
+          _pred[u] = e;
+          _thread[u] = u + 1;
+          _rev_thread[u + 1] = u;
+          _succ_num[u] = 1;
+          _last_succ[u] = u;
+          _cap[e] = INF;
+          _state[e] = STATE_TREE;
+          if (_supply[u] >= 0) {
+            _forward[u] = true;
+            _pi[u] = 0;
+            _source[e] = u;
+            _target[e] = _root;
+            _flow[e] = _supply[u];
+            _cost[e] = 0;
+          } else {
+            _forward[u] = false;
+            _pi[u] = ART_COST;
+            _source[e] = _root;
+            _target[e] = u;
+            _flow[e] = -_supply[u];
+            _cost[e] = ART_COST;
+          }
+        }
+      }
+      else if (_sum_supply > 0) {
+        // LEQ supply constraints
+        _search_arc_num = _arc_num + _node_num;
+        int f = _arc_num + _node_num;
+        for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
+          _parent[u] = _root;
+          _thread[u] = u + 1;
+          _rev_thread[u + 1] = u;
+          _succ_num[u] = 1;
+          _last_succ[u] = u;
+          if (_supply[u] >= 0) {
+            _forward[u] = true;
+            _pi[u] = 0;
+            _pred[u] = e;
+            _source[e] = u;
+            _target[e] = _root;
+            _cap[e] = INF;
+            _flow[e] = _supply[u];
+            _cost[e] = 0;
+            _state[e] = STATE_TREE;
+          } else {
+            _forward[u] = false;
+            _pi[u] = ART_COST;
+            _pred[u] = f;
+            _source[f] = _root;
+            _target[f] = u;
+            _cap[f] = INF;
+            _flow[f] = -_supply[u];
+            _cost[f] = ART_COST;
+            _state[f] = STATE_TREE;
+            _source[e] = u;
+            _target[e] = _root;
+            _cap[e] = INF;
+            _flow[e] = 0;
+            _cost[e] = 0;
+            _state[e] = STATE_LOWER;
+            ++f;
+          }
+        }
+        _all_arc_num = f;
+      }
+      else {
+        // GEQ supply constraints
+        _search_arc_num = _arc_num + _node_num;
+        int f = _arc_num + _node_num;
+        for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {
+          _parent[u] = _root;
+          _thread[u] = u + 1;
+          _rev_thread[u + 1] = u;
+          _succ_num[u] = 1;
+          _last_succ[u] = u;
+          if (_supply[u] <= 0) {
+            _forward[u] = false;
+            _pi[u] = 0;
+            _pred[u] = e;
+            _source[e] = _root;
+            _target[e] = u;
+            _cap[e] = INF;
+            _flow[e] = -_supply[u];
+            _cost[e] = 0;
+            _state[e] = STATE_TREE;
+          } else {
+            _forward[u] = true;
+            _pi[u] = -ART_COST;
+            _pred[u] = f;
+            _source[f] = u;
+            _target[f] = _root;
+            _cap[f] = INF;
+            _flow[f] = _supply[u];
+            _state[f] = STATE_TREE;
+            _cost[f] = ART_COST;
+            _source[e] = _root;
+            _target[e] = u;
+            _cap[e] = INF;
+            _flow[e] = 0;
+            _cost[e] = 0;
+            _state[e] = STATE_LOWER;
+            ++f;
+          }
+        }
+        _all_arc_num = f;
+      }
+
+      return true;
+    }
+
+    // Find the join node
+    void findJoinNode() {
+      int u = _source[in_arc];
+      int v = _target[in_arc];
+      while (u != v) {
+        if (_succ_num[u] < _succ_num[v]) {
+          u = _parent[u];
+        } else {
+          v = _parent[v];
+        }
+      }
+      join = u;
+    }
+
+    // Find the leaving arc of the cycle and returns true if the
+    // leaving arc is not the same as the entering arc
+    bool findLeavingArc() {
+      // Initialize first and second nodes according to the direction
+      // of the cycle
+      if (_state[in_arc] == STATE_LOWER) {
+        first  = _source[in_arc];
+        second = _target[in_arc];
+      } else {
+        first  = _target[in_arc];
+        second = _source[in_arc];
+      }
+      delta = _cap[in_arc];
+      int result = 0;
+      Value d;
+      int e;
+
+      // Search the cycle along the path form the first node to the root
+      for (int u = first; u != join; u = _parent[u]) {
+        e = _pred[u];
+        d = _forward[u] ?
+          _flow[e] : (_cap[e] == INF ? INF : _cap[e] - _flow[e]);
+        if (d < delta) {
+          delta = d;
+          u_out = u;
+          result = 1;
+        }
+      }
+      // Search the cycle along the path form the second node to the root
+      for (int u = second; u != join; u = _parent[u]) {
+        e = _pred[u];
+        d = _forward[u] ? 
+          (_cap[e] == INF ? INF : _cap[e] - _flow[e]) : _flow[e];
+        if (d <= delta) {
+          delta = d;
+          u_out = u;
+          result = 2;
+        }
+      }
+
+      if (result == 1) {
+        u_in = first;
+        v_in = second;
+      } else {
+        u_in = second;
+        v_in = first;
+      }
+      return result != 0;
+    }
+
+    // Change _flow and _state vectors
+    void changeFlow(bool change) {
+      // Augment along the cycle
+      if (delta > 0) {
+        Value val = _state[in_arc] * delta;
+        _flow[in_arc] += val;
+        for (int u = _source[in_arc]; u != join; u = _parent[u]) {
+          _flow[_pred[u]] += _forward[u] ? -val : val;
+        }
+        for (int u = _target[in_arc]; u != join; u = _parent[u]) {
+          _flow[_pred[u]] += _forward[u] ? val : -val;
+        }
+      }
+      // Update the state of the entering and leaving arcs
+      if (change) {
+        _state[in_arc] = STATE_TREE;
+        _state[_pred[u_out]] =
+          (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER;
+      } else {
+        _state[in_arc] = -_state[in_arc];
+      }
+    }
+
+    // Update the tree structure
+    void updateTreeStructure() {
+      int u, w;
+      int old_rev_thread = _rev_thread[u_out];
+      int old_succ_num = _succ_num[u_out];
+      int old_last_succ = _last_succ[u_out];
+      v_out = _parent[u_out];
+
+      u = _last_succ[u_in];  // the last successor of u_in
+      right = _thread[u];    // the node after it
+
+      // Handle the case when old_rev_thread equals to v_in
+      // (it also means that join and v_out coincide)
+      if (old_rev_thread == v_in) {
+        last = _thread[_last_succ[u_out]];
+      } else {
+        last = _thread[v_in];
+      }
+
+      // Update _thread and _parent along the stem nodes (i.e. the nodes
+      // between u_in and u_out, whose parent have to be changed)
+      _thread[v_in] = stem = u_in;
+      _dirty_revs.clear();
+      _dirty_revs.push_back(v_in);
+      par_stem = v_in;
+      while (stem != u_out) {
+        // Insert the next stem node into the thread list
+        new_stem = _parent[stem];
+        _thread[u] = new_stem;
+        _dirty_revs.push_back(u);
+
+        // Remove the subtree of stem from the thread list
+        w = _rev_thread[stem];
+        _thread[w] = right;
+        _rev_thread[right] = w;
+
+        // Change the parent node and shift stem nodes
+        _parent[stem] = par_stem;
+        par_stem = stem;
+        stem = new_stem;
+
+        // Update u and right
+        u = _last_succ[stem] == _last_succ[par_stem] ?
+          _rev_thread[par_stem] : _last_succ[stem];
+        right = _thread[u];
+      }
+      _parent[u_out] = par_stem;
+      _thread[u] = last;
+      _rev_thread[last] = u;
+      _last_succ[u_out] = u;
+
+      // Remove the subtree of u_out from the thread list except for
+      // the case when old_rev_thread equals to v_in
+      // (it also means that join and v_out coincide)
+      if (old_rev_thread != v_in) {
+        _thread[old_rev_thread] = right;
+        _rev_thread[right] = old_rev_thread;
+      }
+
+      // Update _rev_thread using the new _thread values
+      for (int i = 0; i < int(_dirty_revs.size()); ++i) {
+        u = _dirty_revs[i];
+        _rev_thread[_thread[u]] = u;
+      }
+
+      // Update _pred, _forward, _last_succ and _succ_num for the
+      // stem nodes from u_out to u_in
+      int tmp_sc = 0, tmp_ls = _last_succ[u_out];
+      u = u_out;
+      while (u != u_in) {
+        w = _parent[u];
+        _pred[u] = _pred[w];
+        _forward[u] = !_forward[w];
+        tmp_sc += _succ_num[u] - _succ_num[w];
+        _succ_num[u] = tmp_sc;
+        _last_succ[w] = tmp_ls;
+        u = w;
+      }
+      _pred[u_in] = in_arc;
+      _forward[u_in] = (u_in == _source[in_arc]);
+      _succ_num[u_in] = old_succ_num;
+
+      // Set limits for updating _last_succ form v_in and v_out
+      // towards the root
+      int up_limit_in = -1;
+      int up_limit_out = -1;
+      if (_last_succ[join] == v_in) {
+        up_limit_out = join;
+      } else {
+        up_limit_in = join;
+      }
+
+      // Update _last_succ from v_in towards the root
+      for (u = v_in; u != up_limit_in && _last_succ[u] == v_in;
+           u = _parent[u]) {
+        _last_succ[u] = _last_succ[u_out];
+      }
+      // Update _last_succ from v_out towards the root
+      if (join != old_rev_thread && v_in != old_rev_thread) {
+        for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
+             u = _parent[u]) {
+          _last_succ[u] = old_rev_thread;
+        }
+      } else {
+        for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
+             u = _parent[u]) {
+          _last_succ[u] = _last_succ[u_out];
+        }
+      }
+
+      // Update _succ_num from v_in to join
+      for (u = v_in; u != join; u = _parent[u]) {
+        _succ_num[u] += old_succ_num;
+      }
+      // Update _succ_num from v_out to join
+      for (u = v_out; u != join; u = _parent[u]) {
+        _succ_num[u] -= old_succ_num;
+      }
+    }
+
+    // Update potentials
+    void updatePotential() {
+      Cost sigma = _forward[u_in] ?
+        _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] :
+        _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]];
+      // Update potentials in the subtree, which has been moved
+      int end = _thread[_last_succ[u_in]];
+      for (int u = u_in; u != end; u = _thread[u]) {
+        _pi[u] += sigma;
+      }
+    }
+
+    // Execute the algorithm
+    ProblemType start(PivotRule pivot_rule) {
+      // Select the pivot rule implementation
+      switch (pivot_rule) {
+        case FIRST_ELIGIBLE:
+          return start<FirstEligiblePivotRule>();
+        case BEST_ELIGIBLE:
+          return start<BestEligiblePivotRule>();
+        case BLOCK_SEARCH:
+          return start<BlockSearchPivotRule>();
+        case CANDIDATE_LIST:
+          return start<CandidateListPivotRule>();
+        case ALTERING_LIST:
+          return start<AlteringListPivotRule>();
+      }
+      return INFEASIBLE; // avoid warning
+    }
+
+    template <typename PivotRuleImpl>
+    ProblemType start() {
+      PivotRuleImpl pivot(*this);
+
+      // Execute the Network Simplex algorithm
+      while (pivot.findEnteringArc()) {
+        findJoinNode();
+        bool change = findLeavingArc();
+        if (delta >= INF) return UNBOUNDED;
+        changeFlow(change);
+        if (change) {
+          updateTreeStructure();
+          updatePotential();
+        }
+      }
+      
+      // Check feasibility
+      for (int e = _search_arc_num; e != _all_arc_num; ++e) {
+        if (_flow[e] != 0) return INFEASIBLE;
+      }
+
+      // Transform the solution and the supply map to the original form
+      if (_have_lower) {
+        for (int i = 0; i != _arc_num; ++i) {
+          Value c = _lower[i];
+          if (c != 0) {
+            _flow[i] += c;
+            _supply[_source[i]] += c;
+            _supply[_target[i]] -= c;
+          }
+        }
+      }
+      
+      // Shift potentials to meet the requirements of the GEQ/LEQ type
+      // optimality conditions
+      if (_sum_supply == 0) {
+        if (_stype == GEQ) {
+          Cost max_pot = std::numeric_limits<Cost>::min();
+          for (int i = 0; i != _node_num; ++i) {
+            if (_pi[i] > max_pot) max_pot = _pi[i];
+          }
+          if (max_pot > 0) {
+            for (int i = 0; i != _node_num; ++i)
+              _pi[i] -= max_pot;
+          }
+        } else {
+          Cost min_pot = std::numeric_limits<Cost>::max();
+          for (int i = 0; i != _node_num; ++i) {
+            if (_pi[i] < min_pot) min_pot = _pi[i];
+          }
+          if (min_pot < 0) {
+            for (int i = 0; i != _node_num; ++i)
+              _pi[i] -= min_pot;
+          }
+        }
+      }
+
+      return OPTIMAL;
+    }
+
+  }; //class NetworkSimplex
+
+  ///@}
+
+} //namespace lemon
+
+#endif //LEMON_NETWORK_SIMPLEX_H