RhodeCode

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;

  /// 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

      /// 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:

    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

    /// \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>

    /// \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;

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 >

  /// 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.

      /// 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.

      _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

    /// \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>

    /// \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;

    /// 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);

    ///

  /// 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>

    ///

    /// \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

    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

    /// \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>