RhodeCode

/* -*- 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.

 *

 */

/// \ingroup demos

/// \file

/// \brief Demo of the graph drawing function \ref graphToEps()

///

/// This demo program shows examples how to use the function \ref

/// graphToEps(). It takes no input but simply creates seven

/// <tt>.eps</tt> files demonstrating the capability of \ref

/// graphToEps(), and showing how to draw directed graphs,

/// how to handle parallel egdes, how to change the properties (like

/// color, shape, size, title etc.) of nodes and arcs individually

/// using appropriate graph maps.

///

/// \include graph_to_eps_demo.cc

#include<lemon/list_graph.h>

#include<lemon/graph_to_eps.h>

#include<lemon/math.h>

using namespace std;

using namespace lemon;

int main()

{

  Palette palette;

  Palette paletteW(true);

  // Create a small digraph

  ListDigraph g;

  typedef ListDigraph::Node Node;

  typedef ListDigraph::NodeIt NodeIt;

  typedef ListDigraph::Arc Arc;

  typedef dim2::Point<int> Point;

  Node n1=g.addNode();

  Node n2=g.addNode();

  Node n3=g.addNode();

  Node n4=g.addNode();

  Node n5=g.addNode();

  ListDigraph::NodeMap<Point> coords(g);

  ListDigraph::NodeMap<double> sizes(g);

  ListDigraph::NodeMap<int> colors(g);

  ListDigraph::NodeMap<int> shapes(g);

  ListDigraph::ArcMap<int> acolors(g);

  ListDigraph::ArcMap<int> widths(g);

  coords[n1]=Point(50,50);  sizes[n1]=1; colors[n1]=1; shapes[n1]=0;

  coords[n2]=Point(50,70);  sizes[n2]=2; colors[n2]=2; shapes[n2]=2;

  coords[n3]=Point(70,70);  sizes[n3]=1; colors[n3]=3; shapes[n3]=0;

  coords[n4]=Point(70,50);  sizes[n4]=2; colors[n4]=4; shapes[n4]=1;

  coords[n5]=Point(85,60);  sizes[n5]=3; colors[n5]=5; shapes[n5]=2;

  Arc a;

  a=g.addArc(n1,n2); acolors[a]=0; widths[a]=1;

  a=g.addArc(n2,n3); acolors[a]=0; widths[a]=1;

  a=g.addArc(n3,n5); acolors[a]=0; widths[a]=3;

  a=g.addArc(n5,n4); acolors[a]=0; widths[a]=1;

  a=g.addArc(n4,n1); acolors[a]=0; widths[a]=1;

  a=g.addArc(n2,n4); acolors[a]=1; widths[a]=2;

  a=g.addArc(n3,n4); acolors[a]=2; widths[a]=1;

  IdMap<ListDigraph,Node> id(g);

  // Create .eps files showing the digraph with different options

  cout << "Create 'graph_to_eps_demo_out_1_pure.eps'" << endl;

  graphToEps(g,"graph_to_eps_demo_out_1_pure.eps").

    coords(coords).

    title("Sample .eps figure").

    copyright("(C) 2003-2009 LEMON Project").

    run();

  cout << "Create 'graph_to_eps_demo_out_2.eps'" << endl;

  graphToEps(g,"graph_to_eps_demo_out_2.eps").

    coords(coords).

    title("Sample .eps figure").

    copyright("(C) 2003-2009 LEMON Project").

    absoluteNodeSizes().absoluteArcWidths().

    nodeScale(2).nodeSizes(sizes).

    nodeShapes(shapes).

    nodeColors(composeMap(palette,colors)).

    arcColors(composeMap(palette,acolors)).

    arcWidthScale(.4).arcWidths(widths).

    nodeTexts(id).nodeTextSize(3).

    run();

  cout << "Create 'graph_to_eps_demo_out_3_arr.eps'" << endl;

  graphToEps(g,"graph_to_eps_demo_out_3_arr.eps").

    title("Sample .eps figure (with arrowheads)").

    copyright("(C) 2003-2009 LEMON Project").

    absoluteNodeSizes().absoluteArcWidths().

    nodeColors(composeMap(palette,colors)).

    coords(coords).

    nodeScale(2).nodeSizes(sizes).

    nodeShapes(shapes).

    arcColors(composeMap(palette,acolors)).

    arcWidthScale(.4).arcWidths(widths).

    nodeTexts(id).nodeTextSize(3).

    drawArrows().arrowWidth(2).arrowLength(2).

    run();

  // Add more arcs to the digraph

  a=g.addArc(n1,n4); acolors[a]=2; widths[a]=1;

  a=g.addArc(n4,n1); acolors[a]=1; widths[a]=2;

  a=g.addArc(n1,n2); acolors[a]=1; widths[a]=1;

  a=g.addArc(n1,n2); acolors[a]=2; widths[a]=1;

  a=g.addArc(n1,n2); acolors[a]=3; widths[a]=1;

  a=g.addArc(n1,n2); acolors[a]=4; widths[a]=1;

  a=g.addArc(n1,n2); acolors[a]=5; widths[a]=1;

  a=g.addArc(n1,n2); acolors[a]=6; widths[a]=1;

  a=g.addArc(n1,n2); acolors[a]=7; widths[a]=1;

  cout << "Create 'graph_to_eps_demo_out_4_par.eps'" << endl;

  graphToEps(g,"graph_to_eps_demo_out_4_par.eps").

    title("Sample .eps figure (parallel arcs)").

    copyright("(C) 2003-2009 LEMON Project").

    absoluteNodeSizes().absoluteArcWidths().

    nodeShapes(shapes).

    coords(coords).

    nodeScale(2).nodeSizes(sizes).

    nodeColors(composeMap(palette,colors)).

    arcColors(composeMap(palette,acolors)).

    arcWidthScale(.4).arcWidths(widths).

    nodeTexts(id).nodeTextSize(3).

    enableParallel().parArcDist(1.5).

    run();

  cout << "Create 'graph_to_eps_demo_out_5_par_arr.eps'" << endl;

  graphToEps(g,"graph_to_eps_demo_out_5_par_arr.eps").

    title("Sample .eps figure (parallel arcs and arrowheads)").

    copyright("(C) 2003-2009 LEMON Project").

    absoluteNodeSizes().absoluteArcWidths().

    nodeScale(2).nodeSizes(sizes).

    coords(coords).

    nodeShapes(shapes).

    nodeColors(composeMap(palette,colors)).

    arcColors(composeMap(palette,acolors)).

    arcWidthScale(.3).arcWidths(widths).

    nodeTexts(id).nodeTextSize(3).

    enableParallel().parArcDist(1).

    drawArrows().arrowWidth(1).arrowLength(1).

    run();

  cout << "Create 'graph_to_eps_demo_out_6_par_arr_a4.eps'" << endl;

  graphToEps(g,"graph_to_eps_demo_out_6_par_arr_a4.eps").

    title("Sample .eps figure (fits to A4)").

    copyright("(C) 2003-2009 LEMON Project").

    scaleToA4().

    absoluteNodeSizes().absoluteArcWidths().

    nodeScale(2).nodeSizes(sizes).

    coords(coords).

    nodeShapes(shapes).

    nodeColors(composeMap(palette,colors)).

    arcColors(composeMap(palette,acolors)).

    arcWidthScale(.3).arcWidths(widths).

    nodeTexts(id).nodeTextSize(3).

    enableParallel().parArcDist(1).

    drawArrows().arrowWidth(1).arrowLength(1).

    run();

  // Create an .eps file showing the colors of a default Palette

  ListDigraph h;

  ListDigraph::NodeMap<int> hcolors(h);

  ListDigraph::NodeMap<Point> hcoords(h);

  for(int i=0;i<int(paletteW.size());i++) {

    Node n=h.addNode();

    hcoords[n]=Point(1+i%cols,1+i/cols);

    hcolors[n]=i;

  }

  cout << "Create 'graph_to_eps_demo_out_7_colors.eps'" << endl;

  graphToEps(h,"graph_to_eps_demo_out_7_colors.eps").

    scale(60).

    title("Sample .eps figure (Palette demo)").

    copyright("(C) 2003-2009 LEMON Project").

    coords(hcoords).

    absoluteNodeSizes().absoluteArcWidths().

    nodeScale(.45).

    distantColorNodeTexts().

    nodeTexts(hcolors).nodeTextSize(.6).

    nodeColors(composeMap(paletteW,hcolors)).

    run();

  return 0;

}

/* -*- 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

///

/// \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>

#include <lemon/maps.h>

#include <lemon/circulation.h>

#include <lemon/adaptors.h>

namespace lemon {

  /// \addtogroup min_cost_flow

  /// @{

  /// \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 direction of the supply/demand inequality

  /// constraints. For more information see \ref ProblemType.

  ///

  /// \tparam GR The digraph type the algorithm runs on.

  /// \tparam F 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 F.

  ///

  /// \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 F = int, typename C = F>

  class NetworkSimplex

  {

  public:

    /// The flow type of the algorithm

    typedef F Flow;

    /// The cost type of the algorithm

    typedef C Cost;

#ifdef DOXYGEN

    /// The type of the flow map

    typedef GR::ArcMap<Flow> FlowMap;

    /// The type of the potential map

    typedef GR::NodeMap<Cost> PotentialMap;

#else

    /// The type of the flow map

    typedef typename GR::template ArcMap<Flow> FlowMap;

    /// The type of the potential map

    typedef typename GR::template NodeMap<Cost> PotentialMap;

#endif

  public:

    /// \brief Enum type for selecting the pivot rule.

    ///

    /// Enum type 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

    };

    /// \brief Enum type for selecting the problem type.

    ///

    /// Enum type for selecting the problem 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 problem type is \c GEQ, since this form is supported

    /// by other minimum cost flow algorithms and the \ref Circulation

    /// algorithm as well.

    /// The \c LEQ problem type can be selected using the \ref problemType()

    /// function.

    ///

    /// Note that the equality form is a special case of both problem type.

    enum ProblemType {

      /// This option means that there are "<em>greater or equal</em>"

      /// constraints in the defintion, i.e. the exact formulation of the

      /// problem is the following.

      /**

          \f[ \min\sum_{uv\in A} f(uv) \cdot cost(uv) \f]

          \f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \geq

              sup(u) \quad \forall u\in V \f]

          \f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f]

      */

      /// It means that the total demand must be greater or equal to the 

      /// total supply (i.e. \f$\sum_{u\in V} sup(u)\f$ must be zero or

      /// negative) and all the supplies have to be carried out from 

      /// the supply nodes, but there could be demands that are not 

      /// satisfied.

      GEQ,

      /// It is just an alias for the \c GEQ option.

      CARRY_SUPPLIES = GEQ,

      /// This option means that there are "<em>less or equal</em>"

      /// constraints in the defintion, i.e. the exact formulation of the

      /// problem is the following.

      /**

          \f[ \min\sum_{uv\in A} f(uv) \cdot cost(uv) \f]

          \f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \leq

              sup(u) \quad \forall u\in V \f]

          \f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f]

      */

      /// It means that the total demand must be less or equal to the 

      /// total supply (i.e. \f$\sum_{u\in V} sup(u)\f$ must be zero or

      /// positive) and all the demands have to be satisfied, but there

      /// could be supplies that are not carried out from the supply

      /// nodes.

      LEQ,

      /// It is just an alias for the \c LEQ option.

      SATISFY_DEMANDS = LEQ

    };

  private:

    TEMPLATE_DIGRAPH_TYPEDEFS(GR);

    typedef typename GR::template ArcMap<Flow> FlowArcMap;

    typedef typename GR::template ArcMap<Cost> CostArcMap;

    typedef typename GR::template NodeMap<Flow> FlowNodeMap;

    typedef std::vector<Arc> ArcVector;

    typedef std::vector<Node> NodeVector;

    typedef std::vector<int> IntVector;

    typedef std::vector<bool> BoolVector;

    typedef std::vector<Flow> FlowVector;

    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;

    // Parameters of the problem

    FlowArcMap *_plower;

    FlowArcMap *_pupper;

    CostArcMap *_pcost;

    FlowNodeMap *_psupply;

    bool _pstsup;

    Node _psource, _ptarget;

    Flow _pstflow;

    ProblemType _ptype;

    // Result maps

    FlowMap *_flow_map;

    PotentialMap *_potential_map;

    bool _local_flow;

    bool _local_potential;

    // Data structures for storing the digraph

    IntNodeMap _node_id;

    ArcVector _arc_ref;

    IntVector _source;

    IntVector _target;

    // Node and arc data

    FlowVector _cap;

    CostVector _cost;

    FlowVector _supply;

    FlowVector _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;

    Flow delta;

  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 _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), _arc_num(ns._arc_num), _next_arc(0)

      {}

      // Find next entering arc

      bool findEnteringArc() {

        Cost c;

        for (int e = _next_arc; e < _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 _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), _arc_num(ns._arc_num)

      {}

      // Find next entering arc

      bool findEnteringArc() {

        Cost c, min = 0;

        for (int e = 0; e < _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 _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), _arc_num(ns._arc_num), _next_arc(0)

      {

        // The main parameters of the pivot rule

        const double BLOCK_SIZE_FACTOR = 2.0;

        const int MIN_BLOCK_SIZE = 10;

                                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 < _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 _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), _arc_num(ns._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;

                                 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 < _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 _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), _arc_num(ns._arc_num),

        _next_arc(0), _cand_cost(ns._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;

                                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 < _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),

      _plower(NULL), _pupper(NULL), _pcost(NULL),

      _psupply(NULL), _pstsup(false), _ptype(GEQ),

      _flow_map(NULL), _potential_map(NULL),

      _local_flow(false), _local_potential(false),

      _node_id(graph)

    {

      LEMON_ASSERT(std::numeric_limits<Flow>::is_integer &&

                   std::numeric_limits<Flow>::is_signed,

        "The flow type of NetworkSimplex must be signed integer");

      LEMON_ASSERT(std::numeric_limits<Cost>::is_integer &&

                   std::numeric_limits<Cost>::is_signed,

        "The cost type of NetworkSimplex must be signed integer");

    }

    /// Destructor.

    ~NetworkSimplex() {

      if (_local_flow) delete _flow_map;

      if (_local_potential) delete _potential_map;

    }

    /// \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 neither this function nor \ref boundMaps() is 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 Flow type

    /// of the algorithm.

    ///

    /// \return <tt>(*this)</tt>

    template <typename LOWER>

    NetworkSimplex& lowerMap(const LOWER& map) {

      delete _plower;

      _plower = new FlowArcMap(_graph);

      for (ArcIt a(_graph); a != INVALID; ++a) {

        (*_plower)[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 none of the functions \ref upperMap(), \ref capacityMap()

    /// and \ref boundMaps() is used before calling \ref run(),

    /// the upper bounds (capacities) will be set to

    /// \c std::numeric_limits<Flow>::max() on all arcs.

    ///

    /// \param map An arc map storing the upper bounds.

    /// Its \c Value type must be convertible to the \c Flow type

    /// of the algorithm.

    ///

    /// \return <tt>(*this)</tt>

    template<typename UPPER>

    NetworkSimplex& upperMap(const UPPER& map) {

      delete _pupper;

      _pupper = new FlowArcMap(_graph);

      for (ArcIt a(_graph); a != INVALID; ++a) {

        (*_pupper)[a] = map[a];

      }

      return *this;

    }

    /// \brief Set the upper bounds (capacities) on the arcs.

    ///

    /// This function sets the upper bounds (capacities) on the arcs.

    /// It is just an alias for \ref upperMap().

    ///

    /// \return <tt>(*this)</tt>

    template<typename CAP>

    NetworkSimplex& capacityMap(const CAP& map) {

      return upperMap(map);

    }

    /// \brief Set the lower and upper bounds on the arcs.

    ///

    /// This function sets the lower and upper bounds on the arcs.

    /// If neither this function nor \ref lowerMap() is used before

    /// calling \ref run(), the lower bounds will be set to zero

    /// on all arcs.

    /// If none of the functions \ref upperMap(), \ref capacityMap()

    /// and \ref boundMaps() is used before calling \ref run(),

    /// the upper bounds (capacities) will be set to

    /// \c std::numeric_limits<Flow>::max() on all arcs.

    ///

    /// \param lower An arc map storing the lower bounds.

    /// \param upper An arc map storing the upper bounds.

    ///

    /// The \c Value type of the maps must be convertible to the

    /// \c Flow type of the algorithm.

    ///

    /// \note This function is just a shortcut of calling \ref lowerMap()

    /// and \ref upperMap() separately.

    ///

    /// \return <tt>(*this)</tt>

    template <typename LOWER, typename UPPER>

    NetworkSimplex& boundMaps(const LOWER& lower, const UPPER& upper) {

      return lowerMap(lower).upperMap(upper);

    }

    /// \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 COST>

    NetworkSimplex& costMap(const COST& map) {

      delete _pcost;

      _pcost = new CostArcMap(_graph);

      for (ArcIt a(_graph); a != INVALID; ++a) {

        (*_pcost)[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 Flow type

    /// of the algorithm.

    ///

    /// \return <tt>(*this)</tt>

    template<typename SUP>

    NetworkSimplex& supplyMap(const SUP& map) {

      delete _psupply;

      _pstsup = false;

      _psupply = new FlowNodeMap(_graph);

      for (NodeIt n(_graph); n != INVALID; ++n) {

        (*_psupply)[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.)

    ///

    /// \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, Flow k) {

      delete _psupply;

      _psupply = NULL;

      _pstsup = true;

      _psource = s;

      _ptarget = t;

      _pstflow = k;

      return *this;

    }

    /// \brief Set the problem type.

    ///

    /// This function sets the problem type for the algorithm.

    /// If it is not used before calling \ref run(), the \ref GEQ problem

    /// type will be used.

    ///

    /// For more information see \ref ProblemType.

    ///

    /// \return <tt>(*this)</tt>

    NetworkSimplex& problemType(ProblemType problem_type) {

      _ptype = problem_type;

      return *this;

    }

    /// \brief Set the flow map.

    ///

    /// This function sets the flow map.

    /// If it is not used before calling \ref run(), an instance will

    /// be allocated automatically. The destructor deallocates this

    /// automatically allocated map, of course.

    ///

    /// \return <tt>(*this)</tt>

    NetworkSimplex& flowMap(FlowMap& map) {

      if (_local_flow) {

        delete _flow_map;

        _local_flow = false;

      }

      _flow_map = ↦

      return *this;

    }

    /// \brief Set the potential map.

    ///

    /// This function sets the potential map, which is used for storing

    /// the dual solution.

    /// If it is not used before calling \ref run(), an instance will

    /// be allocated automatically. The destructor deallocates this

    /// automatically allocated map, of course.

    ///

    /// \return <tt>(*this)</tt>

    NetworkSimplex& potentialMap(PotentialMap& map) {

      if (_local_potential) {

        delete _potential_map;

        _local_potential = false;

      }

      _potential_map = ↦

      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 capacityMap(), \ref boundMaps(),

    /// \ref costMap(), \ref supplyMap(), \ref stSupply(), 

    /// \ref problemType(), \ref flowMap() and \ref potentialMap().

    /// For example,

    /// \code