RhodeCode

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#ifndef LEMON_CAPACITY_SCALING_H

#define LEMON_CAPACITY_SCALING_H

/// \ingroup min_cost_flow_algs

///

/// \file

/// \brief Capacity Scaling algorithm for finding a minimum cost flow.

#include <vector>

#include <limits>

#include <lemon/core.h>

#include <lemon/bin_heap.h>

namespace lemon {

  /// \brief Default traits class of CapacityScaling algorithm.

  ///

  /// Default traits class of CapacityScaling algorithm.

  /// \tparam GR Digraph type.

  /// and supply values. By default it is \c int.

  /// By default it is the same as \c V.

  template <typename GR, typename V = int, typename C = V>

  struct CapacityScalingDefaultTraits

  {

    /// The type of the digraph

    typedef GR Digraph;

    /// The type of the flow amounts, capacity bounds and supply values

    typedef V Value;

    /// The type of the arc costs

    typedef C Cost;

    /// \brief The type of the heap used for internal Dijkstra computations.

    ///

    /// The type of the heap used for internal Dijkstra computations.

    /// It must conform to the \ref lemon::concepts::Heap "Heap" concept,

    /// its priority type must be \c Cost and its cross reference type

    /// must be \ref RangeMap "RangeMap<int>".

    typedef BinHeap<Cost, RangeMap<int> > Heap;

  };

  /// \addtogroup min_cost_flow_algs

  /// @{

  /// \brief Implementation of the Capacity Scaling algorithm for

  /// finding a \ref min_cost_flow "minimum cost flow".

  ///

  /// \ref CapacityScaling implements the capacity scaling version

  /// of the successive shortest path algorithm for finding a

  /// \ref min_cost_flow "minimum cost flow". It is an efficient dual

  /// solution method.

  ///

  /// 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.

  /// and supply values in the algorithm. By default it is \c int.

  /// algorithm. By default it is the same as \c V.

  ///

  /// be integer.

  /// \warning This algorithm does not support negative costs for such

  /// arcs that have infinite upper bound.

#ifdef DOXYGEN

  template <typename GR, typename V, typename C, typename TR>

#else

  template < typename GR, typename V = int, typename C = V,

             typename TR = CapacityScalingDefaultTraits<GR, V, C> >

#endif

  class CapacityScaling

  {

  public:

    /// The type of the digraph

    typedef typename TR::Digraph Digraph;

    /// The type of the flow amounts, capacity bounds and supply values

    typedef typename TR::Value Value;

    /// The type of the arc costs

    typedef typename TR::Cost Cost;

    /// The type of the heap used for internal Dijkstra computations

    typedef typename TR::Heap Heap;

    /// The \ref CapacityScalingDefaultTraits "traits class" of the algorithm

    typedef TR Traits;

  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 digraph contains an arc of negative cost and infinite

      /// upper bound. It means that the objective function is unbounded

      /// over the feasible flows, but this algroithm cannot handle

      /// these cases.

      UNBOUNDED

    };

  private:

    TEMPLATE_DIGRAPH_TYPEDEFS(GR);

    typedef std::vector<int> IntVector;

    typedef std::vector<char> BoolVector;

    typedef std::vector<Value> ValueVector;

    typedef std::vector<Cost> CostVector;

  private:

    // Data related to the underlying digraph

    const GR &_graph;

    int _node_num;

    int _arc_num;

    int _res_arc_num;

    int _root;

    // Parameters of the problem

    /// It must conform to the \ref lemon::concepts::Heap "Heap" concept,

    /// its priority type must be \c Cost and its cross reference type

    /// must be \ref RangeMap "RangeMap<int>".

    template <typename T>

    struct SetHeap

      : public CapacityScaling<GR, V, C, SetHeapTraits<T> > {

      typedef  CapacityScaling<GR, V, C, SetHeapTraits<T> > Create;

    };

    /// @}

  public:

    /// \brief Constructor.

    ///

    /// The constructor of the class.

    ///

    /// \param graph The digraph the algorithm runs on.

    CapacityScaling(const GR& graph) :

      _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph),

      INF(std::numeric_limits<Value>::has_infinity ?

          std::numeric_limits<Value>::infinity() :

          std::numeric_limits<Value>::max())

    {

      LEMON_ASSERT(std::numeric_limits<Value>::is_signed,

        "The flow type of CapacityScaling must be signed");

      LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,

        "The cost type of CapacityScaling must be signed");

      // Resize vectors

      _node_num = countNodes(_graph);

      _arc_num = countArcs(_graph);

      _res_arc_num = 2 * (_arc_num + _node_num);

      _root = _node_num;

      ++_node_num;

      _first_out.resize(_node_num + 1);

      _forward.resize(_res_arc_num);

      _source.resize(_res_arc_num);

      _target.resize(_res_arc_num);

      _reverse.resize(_res_arc_num);

      _lower.resize(_res_arc_num);

      _upper.resize(_res_arc_num);

      _cost.resize(_res_arc_num);

      _supply.resize(_node_num);

      _res_cap.resize(_res_arc_num);

    /// 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>

    CapacityScaling& lowerMap(const LowerMap& map) {

      _have_lower = true;

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

        _lower[_arc_idf[a]] = map[a];

        _lower[_arc_idb[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

    ///

    /// \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>

    CapacityScaling& upperMap(const UpperMap& map) {

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

        _upper[_arc_idf[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.

    ///

    /// @}

    /// \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().

    /// For example,

    /// \code

    ///   CapacityScaling<ListDigraph> cs(graph);

    ///   cs.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.

    /// class have been constructed, since it copies and extends the graph.

    ///

    /// \param factor The capacity scaling factor. It must be larger than

    /// one to use scaling. If it is less or equal to one, then scaling

    /// will be disabled.

    ///

    /// \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 digraph contains an arc of negative cost

    /// and infinite upper bound. It means that the objective function

    /// bounded over the feasible flows, but this algroithm cannot handle

    /// these cases.

    ///

    /// \see ProblemType

    ProblemType run(int factor = 4) {

      _factor = factor;

      ProblemType pt = init();

      if (pt != OPTIMAL) return pt;

      return start();

    }

    /// \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().

    ///

    /// 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,

#ifndef LEMON_COST_SCALING_H

#define LEMON_COST_SCALING_H

/// \ingroup min_cost_flow_algs

/// \file

/// \brief Cost scaling algorithm for finding a minimum cost flow.

#include <vector>

#include <deque>

#include <limits>

#include <lemon/core.h>

#include <lemon/maps.h>

#include <lemon/math.h>

#include <lemon/static_graph.h>

#include <lemon/circulation.h>

#include <lemon/bellman_ford.h>

namespace lemon {

  /// \brief Default traits class of CostScaling algorithm.

  ///

  /// Default traits class of CostScaling algorithm.

  /// \tparam GR Digraph type.

  /// and supply values. By default it is \c int.

  /// By default it is the same as \c V.

#ifdef DOXYGEN

  template <typename GR, typename V = int, typename C = V>

#else

  template < typename GR, typename V = int, typename C = V,

             bool integer = std::numeric_limits<C>::is_integer >

#endif

  struct CostScalingDefaultTraits

  {

    /// The type of the digraph

    typedef GR Digraph;

    /// The type of the flow amounts, capacity bounds and supply values

    typedef V Value;

    /// The type of the arc costs

    typedef C Cost;

    /// \brief The large cost type used for internal computations

    ///

    /// The large cost type used for internal computations.

    /// It is \c long \c long if the \c Cost type is integer,

    /// otherwise it is \c double.

    /// \c Cost must be convertible to \c LargeCost.

    typedef double LargeCost;

  };

#else

    typedef long LargeCost;

#endif

  };

  /// \addtogroup min_cost_flow_algs

  /// @{

  /// \brief Implementation of the Cost Scaling algorithm for

  /// finding a \ref min_cost_flow "minimum cost flow".

  ///

  /// \ref CostScaling implements a cost scaling algorithm that performs

  /// push/augment and relabel operations for finding a minimum cost

  /// flow. It is an efficient primal-dual solution method, which

  /// can be viewed as the generalization of the \ref Preflow

  /// "preflow push-relabel" algorithm for the maximum flow problem.

  ///

  /// 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.

  /// and supply values in the algorithm. By default it is \c int.

  /// algorithm. By default it is the same as \c V.

  ///

  /// be integer.

  /// \warning This algorithm does not support negative costs for such

  /// arcs that have infinite upper bound.

  ///

  /// \note %CostScaling provides three different internal methods,

  /// from which the most efficient one is used by default.

  /// For more information, see \ref Method.

#ifdef DOXYGEN

  template <typename GR, typename V, typename C, typename TR>

#else

  template < typename GR, typename V = int, typename C = V,

             typename TR = CostScalingDefaultTraits<GR, V, C> >

#endif

  class CostScaling

  {

  public:

    /// The type of the digraph

    typedef typename TR::Digraph Digraph;

    /// The type of the flow amounts, capacity bounds and supply values

    typedef typename TR::Value Value;

    /// The type of the arc costs

    typedef typename TR::Cost Cost;

    /// The large cost type used for internal computations.

    /// Using the \ref CostScalingDefaultTraits "default traits class",

    /// it is \c long \c long if the \c Cost type is integer,

    /// otherwise it is \c double.

    typedef typename TR::LargeCost LargeCost;

    /// The \ref CostScalingDefaultTraits "traits class" of the algorithm

    typedef TR Traits;

  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 digraph contains an arc of negative cost and infinite

      /// upper bound. It means that the objective function is unbounded

      /// over the feasible flows, but this algroithm cannot handle

      /// these cases.

      UNBOUNDED

    };

    /// \brief Constants for selecting the internal method.

    ///

    /// Enum type containing constants for selecting the internal method

    /// for the \ref run() function.

    ///

    /// \ref CostScaling provides three internal methods that differ mainly

    /// in their base operations, which are used in conjunction with the

    /// relabel operation.

    /// By default, the so called \ref PARTIAL_AUGMENT

    /// "Partial Augment-Relabel" method is used, which proved to be

    /// the most efficient and the most robust on various test inputs.

    /// However, the other methods can be selected using the \ref run()

    /// function with the proper parameter.

    enum Method {

      /// Local push operations are used, i.e. flow is moved only on one

      /// admissible arc at once.

      PUSH,

      /// Augment operations are used, i.e. flow is moved on admissible

      /// paths from a node with excess to a node with deficit.

    /// type, which is used for internal computations in the algorithm.

    /// \c Cost must be convertible to \c LargeCost.

    template <typename T>

    struct SetLargeCost

      : public CostScaling<GR, V, C, SetLargeCostTraits<T> > {

      typedef  CostScaling<GR, V, C, SetLargeCostTraits<T> > Create;

    };

    /// @}

  public:

    /// \brief Constructor.

    ///

    /// The constructor of the class.

    ///

    /// \param graph The digraph the algorithm runs on.

    CostScaling(const GR& graph) :

      _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph),

      _cost_map(_cost_vec), _pi_map(_pi),

      INF(std::numeric_limits<Value>::has_infinity ?

          std::numeric_limits<Value>::infinity() :

          std::numeric_limits<Value>::max())

    {

      LEMON_ASSERT(std::numeric_limits<Value>::is_signed,

        "The flow type of CostScaling must be signed");

      LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,

        "The cost type of CostScaling must be signed");

      // Resize vectors

      _node_num = countNodes(_graph);

      _arc_num = countArcs(_graph);

      _res_node_num = _node_num + 1;

      _res_arc_num = 2 * (_arc_num + _node_num);

      _root = _node_num;

      _first_out.resize(_res_node_num + 1);

      _forward.resize(_res_arc_num);

      _source.resize(_res_arc_num);

      _target.resize(_res_arc_num);

      _reverse.resize(_res_arc_num);

      _lower.resize(_res_arc_num);

      _upper.resize(_res_arc_num);

      _scost.resize(_res_arc_num);

      _supply.resize(_res_node_num);

      _res_cap.resize(_res_arc_num);

    /// 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>

    CostScaling& lowerMap(const LowerMap& map) {

      _have_lower = true;

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

        _lower[_arc_idf[a]] = map[a];

        _lower[_arc_idb[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

    ///

    /// \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>

    CostScaling& upperMap(const UpperMap& map) {

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

        _upper[_arc_idf[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.

    ///

    /// For example,

    /// \code

    ///   CostScaling<ListDigraph> cs(graph);

    ///   cs.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 method The internal method that will be used in the

    /// algorithm. For more information, see \ref Method.

    /// \param factor The cost scaling factor. It must be larger than one.

    ///

    /// \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 digraph contains an arc of negative cost

    /// and infinite upper bound. It means that the objective function

    /// bounded over the feasible flows, but this algroithm cannot handle

    /// these cases.

    ///

    /// \see ProblemType, Method

    ProblemType run(Method method = PARTIAL_AUGMENT, int factor = 8) {

      _alpha = factor;

      ProblemType pt = init();

      if (pt != OPTIMAL) return pt;

      start(method);

      return OPTIMAL;

    }

    /// \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().

    ///

    /// 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.

    /// class have been constructed, since it copies and extends the graph.

    ///

    /// For example,

    /// \code

    ///   CostScaling<ListDigraph> cs(graph);

    ///

    ///   // First run

    ///   cs.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;

    ///   cs.costMap(cost).run();

    ///

    ///   // Run again from scratch using reset()

    ///   // (the lower bounds will be set to zero on all arcs)

    ///   cs.reset();

    ///   cs.upperMap(capacity).costMap(cost)

    ///     .supplyMap(sup).run();

    /// \endcode

    ///

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

    CostScaling& reset() {

/// \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"

  /// \ref amo93networkflows, \ref dantzig63linearprog,

  /// \ref kellyoneill91netsimplex.

  ///

  /// 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.

  /// and supply values in the algorithm. By default, it is \c int.

  /// algorithm. By default, it is the same as \c V.

  ///

  /// 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,

    /// 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

    /// However, another pivot rule can be selected using the \ref run()

    /// function with the proper parameter.

    enum PivotRule {

      /// The \e First \e Eligible pivot rule.

      /// The next eligible arc is selected in a wraparound fashion

      /// in every iteration.

      FIRST_ELIGIBLE,

      /// The \e Best \e Eligible pivot rule.

      /// The best eligible arc is selected in every iteration.

      BEST_ELIGIBLE,

      /// The \e Block \e 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 \e Candidate \e 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,

                  _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.

    /// \param arc_mixing Indicate if the arcs have to be stored in a

    /// mixed order in the internal data structure. 

    /// In special cases, it could lead to better overall performance,

    /// but it is usually slower. Therefore it is disabled by default.

    NetworkSimplex(const GR& graph, bool arc_mixing = false) :

      _graph(graph), _node_id(graph), _arc_id(graph),

      MAX(std::numeric_limits<Value>::max()),

      INF(std::numeric_limits<Value>::has_infinity ?

          std::numeric_limits<Value>::infinity() : MAX)

    {

      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);

    ///

    /// 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

    ///

    /// \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.

    ///