lemon/cost_scaling.h
author Peter Kovacs <kpeter@inf.elte.hu>
Sun, 09 Jan 2011 23:20:56 +0100
changeset 1024 745312f9b441
parent 956 141f9c0db4a3
child 1026 9312d6c89d02
permissions -rw-r--r--
Improve the doc of path structures (#406)
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/* -*- mode: C++; indent-tabs-mode: nil; -*-
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 *
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 * This file is a part of LEMON, a generic C++ optimization library.
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 *
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 * Copyright (C) 2003-2010
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 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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 *
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 * Permission to use, modify and distribute this software is granted
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 * provided that this copyright notice appears in all copies. For
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 * precise terms see the accompanying LICENSE file.
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 *
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 * This software is provided "AS IS" with no warranty of any kind,
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 * express or implied, and with no claim as to its suitability for any
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 * purpose.
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 *
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 */
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#ifndef LEMON_COST_SCALING_H
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#define LEMON_COST_SCALING_H
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/// \ingroup min_cost_flow_algs
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/// \file
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/// \brief Cost scaling algorithm for finding a minimum cost flow.
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#include <vector>
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#include <deque>
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#include <limits>
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#include <lemon/core.h>
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#include <lemon/maps.h>
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#include <lemon/math.h>
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#include <lemon/static_graph.h>
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#include <lemon/circulation.h>
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#include <lemon/bellman_ford.h>
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namespace lemon {
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  /// \brief Default traits class of CostScaling algorithm.
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  ///
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  /// Default traits class of CostScaling algorithm.
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  /// \tparam GR Digraph type.
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  /// \tparam V The number type used for flow amounts, capacity bounds
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  /// and supply values. By default it is \c int.
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  /// \tparam C The number type used for costs and potentials.
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  /// By default it is the same as \c V.
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#ifdef DOXYGEN
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  template <typename GR, typename V = int, typename C = V>
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#else
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  template < typename GR, typename V = int, typename C = V,
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             bool integer = std::numeric_limits<C>::is_integer >
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#endif
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  struct CostScalingDefaultTraits
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  {
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    /// The type of the digraph
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    typedef GR Digraph;
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    /// The type of the flow amounts, capacity bounds and supply values
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    typedef V Value;
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    /// The type of the arc costs
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    typedef C Cost;
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    /// \brief The large cost type used for internal computations
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    ///
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    /// The large cost type used for internal computations.
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    /// It is \c long \c long if the \c Cost type is integer,
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    /// otherwise it is \c double.
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    /// \c Cost must be convertible to \c LargeCost.
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    typedef double LargeCost;
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  };
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  // Default traits class for integer cost types
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  template <typename GR, typename V, typename C>
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  struct CostScalingDefaultTraits<GR, V, C, true>
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  {
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    typedef GR Digraph;
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    typedef V Value;
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    typedef C Cost;
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#ifdef LEMON_HAVE_LONG_LONG
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    typedef long long LargeCost;
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#else
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    typedef long LargeCost;
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#endif
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  };
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  /// \addtogroup min_cost_flow_algs
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  /// @{
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  /// \brief Implementation of the Cost Scaling algorithm for
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  /// finding a \ref min_cost_flow "minimum cost flow".
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  ///
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  /// \ref CostScaling implements a cost scaling algorithm that performs
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  /// push/augment and relabel operations for finding a \ref min_cost_flow
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  /// "minimum cost flow" \ref amo93networkflows, \ref goldberg90approximation,
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  /// \ref goldberg97efficient, \ref bunnagel98efficient.
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  /// It is a highly efficient primal-dual solution method, which
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  /// can be viewed as the generalization of the \ref Preflow
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  /// "preflow push-relabel" algorithm for the maximum flow problem.
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  ///
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  /// In general, \ref NetworkSimplex and \ref CostScaling are the fastest
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  /// implementations available in LEMON for this problem.
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  ///
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  /// Most of the parameters of the problem (except for the digraph)
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  /// can be given using separate functions, and the algorithm can be
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  /// executed using the \ref run() function. If some parameters are not
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  /// specified, then default values will be used.
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  ///
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  /// \tparam GR The digraph type the algorithm runs on.
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  /// \tparam V The number type used for flow amounts, capacity bounds
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  /// and supply values in the algorithm. By default, it is \c int.
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  /// \tparam C The number type used for costs and potentials in the
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  /// algorithm. By default, it is the same as \c V.
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  /// \tparam TR The traits class that defines various types used by the
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  /// algorithm. By default, it is \ref CostScalingDefaultTraits
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  /// "CostScalingDefaultTraits<GR, V, C>".
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  /// In most cases, this parameter should not be set directly,
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  /// consider to use the named template parameters instead.
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  ///
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  /// \warning Both number types must be signed and all input data must
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  /// be integer.
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  /// \warning This algorithm does not support negative costs for
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  /// arcs having infinite upper bound.
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  ///
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  /// \note %CostScaling provides three different internal methods,
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  /// from which the most efficient one is used by default.
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  /// For more information, see \ref Method.
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#ifdef DOXYGEN
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  template <typename GR, typename V, typename C, typename TR>
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#else
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  template < typename GR, typename V = int, typename C = V,
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             typename TR = CostScalingDefaultTraits<GR, V, C> >
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#endif
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  class CostScaling
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  {
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  public:
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    /// The type of the digraph
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    typedef typename TR::Digraph Digraph;
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    /// The type of the flow amounts, capacity bounds and supply values
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    typedef typename TR::Value Value;
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    /// The type of the arc costs
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    typedef typename TR::Cost Cost;
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    /// \brief The large cost type
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    ///
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    /// The large cost type used for internal computations.
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    /// By default, it is \c long \c long if the \c Cost type is integer,
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    /// otherwise it is \c double.
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    typedef typename TR::LargeCost LargeCost;
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    /// The \ref CostScalingDefaultTraits "traits class" of the algorithm
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    typedef TR Traits;
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  public:
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    /// \brief Problem type constants for the \c run() function.
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    ///
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    /// Enum type containing the problem type constants that can be
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    /// returned by the \ref run() function of the algorithm.
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    enum ProblemType {
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      /// The problem has no feasible solution (flow).
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      INFEASIBLE,
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      /// The problem has optimal solution (i.e. it is feasible and
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      /// bounded), and the algorithm has found optimal flow and node
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      /// potentials (primal and dual solutions).
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      OPTIMAL,
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      /// The digraph contains an arc of negative cost and infinite
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      /// upper bound. It means that the objective function is unbounded
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      /// on that arc, however, note that it could actually be bounded
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      /// over the feasible flows, but this algroithm cannot handle
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      /// these cases.
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      UNBOUNDED
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    };
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    /// \brief Constants for selecting the internal method.
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    ///
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    /// Enum type containing constants for selecting the internal method
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    /// for the \ref run() function.
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    ///
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    /// \ref CostScaling provides three internal methods that differ mainly
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    /// in their base operations, which are used in conjunction with the
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    /// relabel operation.
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    /// By default, the so called \ref PARTIAL_AUGMENT
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    /// "Partial Augment-Relabel" method is used, which turned out to be
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    /// the most efficient and the most robust on various test inputs.
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    /// However, the other methods can be selected using the \ref run()
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    /// function with the proper parameter.
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    enum Method {
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      /// Local push operations are used, i.e. flow is moved only on one
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      /// admissible arc at once.
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      PUSH,
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      /// Augment operations are used, i.e. flow is moved on admissible
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      /// paths from a node with excess to a node with deficit.
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      AUGMENT,
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      /// Partial augment operations are used, i.e. flow is moved on
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      /// admissible paths started from a node with excess, but the
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      /// lengths of these paths are limited. This method can be viewed
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      /// as a combined version of the previous two operations.
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      PARTIAL_AUGMENT
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    };
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  private:
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    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
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    typedef std::vector<int> IntVector;
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    typedef std::vector<Value> ValueVector;
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    typedef std::vector<Cost> CostVector;
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    typedef std::vector<LargeCost> LargeCostVector;
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    typedef std::vector<char> BoolVector;
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    // Note: vector<char> is used instead of vector<bool> for efficiency reasons
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  private:
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    template <typename KT, typename VT>
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    class StaticVectorMap {
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    public:
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      typedef KT Key;
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      typedef VT Value;
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      StaticVectorMap(std::vector<Value>& v) : _v(v) {}
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      const Value& operator[](const Key& key) const {
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        return _v[StaticDigraph::id(key)];
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      }
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      Value& operator[](const Key& key) {
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        return _v[StaticDigraph::id(key)];
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      }
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      void set(const Key& key, const Value& val) {
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        _v[StaticDigraph::id(key)] = val;
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      }
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    private:
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      std::vector<Value>& _v;
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    };
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    typedef StaticVectorMap<StaticDigraph::Node, LargeCost> LargeCostNodeMap;
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    typedef StaticVectorMap<StaticDigraph::Arc, LargeCost> LargeCostArcMap;
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  private:
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    // Data related to the underlying digraph
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    const GR &_graph;
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    int _node_num;
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    int _arc_num;
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    int _res_node_num;
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    int _res_arc_num;
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    int _root;
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    // Parameters of the problem
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    bool _have_lower;
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    Value _sum_supply;
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    int _sup_node_num;
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    // Data structures for storing the digraph
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    IntNodeMap _node_id;
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    IntArcMap _arc_idf;
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    IntArcMap _arc_idb;
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    IntVector _first_out;
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    BoolVector _forward;
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    IntVector _source;
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    IntVector _target;
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    IntVector _reverse;
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    // Node and arc data
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    ValueVector _lower;
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    ValueVector _upper;
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    CostVector _scost;
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    ValueVector _supply;
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    ValueVector _res_cap;
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    LargeCostVector _cost;
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    LargeCostVector _pi;
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    ValueVector _excess;
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    IntVector _next_out;
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    std::deque<int> _active_nodes;
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    // Data for scaling
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    LargeCost _epsilon;
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    int _alpha;
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    IntVector _buckets;
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    IntVector _bucket_next;
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    IntVector _bucket_prev;
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    IntVector _rank;
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    int _max_rank;
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    // Data for a StaticDigraph structure
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    typedef std::pair<int, int> IntPair;
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    StaticDigraph _sgr;
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    std::vector<IntPair> _arc_vec;
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    std::vector<LargeCost> _cost_vec;
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    LargeCostArcMap _cost_map;
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    LargeCostNodeMap _pi_map;
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  public:
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    /// \brief Constant for infinite upper bounds (capacities).
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    ///
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    /// Constant for infinite upper bounds (capacities).
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    /// It is \c std::numeric_limits<Value>::infinity() if available,
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    /// \c std::numeric_limits<Value>::max() otherwise.
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    const Value INF;
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  public:
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    /// \name Named Template Parameters
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    /// @{
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    template <typename T>
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    struct SetLargeCostTraits : public Traits {
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      typedef T LargeCost;
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    };
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    /// \brief \ref named-templ-param "Named parameter" for setting
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    /// \c LargeCost type.
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    ///
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    /// \ref named-templ-param "Named parameter" for setting \c LargeCost
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    /// type, which is used for internal computations in the algorithm.
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    /// \c Cost must be convertible to \c LargeCost.
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    template <typename T>
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    struct SetLargeCost
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      : public CostScaling<GR, V, C, SetLargeCostTraits<T> > {
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      typedef  CostScaling<GR, V, C, SetLargeCostTraits<T> > Create;
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    };
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    /// @}
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  protected:
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    CostScaling() {}
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  public:
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    /// \brief Constructor.
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    ///
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    /// The constructor of the class.
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    ///
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    /// \param graph The digraph the algorithm runs on.
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    CostScaling(const GR& graph) :
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      _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph),
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      _cost_map(_cost_vec), _pi_map(_pi),
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      INF(std::numeric_limits<Value>::has_infinity ?
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          std::numeric_limits<Value>::infinity() :
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          std::numeric_limits<Value>::max())
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    {
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      // Check the number types
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      LEMON_ASSERT(std::numeric_limits<Value>::is_signed,
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        "The flow type of CostScaling must be signed");
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      LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
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        "The cost type of CostScaling must be signed");
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      // Reset data structures
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      reset();
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    }
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    /// \name Parameters
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    /// The parameters of the algorithm can be specified using these
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    /// functions.
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    /// @{
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    /// \brief Set the lower bounds on the arcs.
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    ///
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    /// This function sets the lower bounds on the arcs.
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    /// If it is not used before calling \ref run(), the lower bounds
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    /// will be set to zero on all arcs.
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    ///
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    /// \param map An arc map storing the lower bounds.
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    /// Its \c Value type must be convertible to the \c Value type
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    /// of the algorithm.
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    ///
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    /// \return <tt>(*this)</tt>
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    template <typename LowerMap>
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    CostScaling& lowerMap(const LowerMap& map) {
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      _have_lower = true;
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      for (ArcIt a(_graph); a != INVALID; ++a) {
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        _lower[_arc_idf[a]] = map[a];
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        _lower[_arc_idb[a]] = map[a];
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      }
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      return *this;
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    }
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    /// \brief Set the upper bounds (capacities) on the arcs.
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    ///
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    /// This function sets the upper bounds (capacities) on the arcs.
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    /// If it is not used before calling \ref run(), the upper bounds
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    /// will be set to \ref INF on all arcs (i.e. the flow value will be
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    /// unbounded from above).
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    ///
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    /// \param map An arc map storing the upper bounds.
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    /// Its \c Value type must be convertible to the \c Value type
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    /// of the algorithm.
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    ///
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    /// \return <tt>(*this)</tt>
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    template<typename UpperMap>
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    CostScaling& upperMap(const UpperMap& map) {
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      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@875
   401
        _upper[_arc_idf[a]] = map[a];
kpeter@874
   402
      }
kpeter@874
   403
      return *this;
kpeter@874
   404
    }
kpeter@874
   405
kpeter@875
   406
    /// \brief Set the costs of the arcs.
kpeter@875
   407
    ///
kpeter@875
   408
    /// This function sets the costs of the arcs.
kpeter@875
   409
    /// If it is not used before calling \ref run(), the costs
kpeter@875
   410
    /// will be set to \c 1 on all arcs.
kpeter@875
   411
    ///
kpeter@875
   412
    /// \param map An arc map storing the costs.
kpeter@875
   413
    /// Its \c Value type must be convertible to the \c Cost type
kpeter@875
   414
    /// of the algorithm.
kpeter@875
   415
    ///
kpeter@875
   416
    /// \return <tt>(*this)</tt>
kpeter@875
   417
    template<typename CostMap>
kpeter@875
   418
    CostScaling& costMap(const CostMap& map) {
kpeter@875
   419
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@875
   420
        _scost[_arc_idf[a]] =  map[a];
kpeter@875
   421
        _scost[_arc_idb[a]] = -map[a];
kpeter@875
   422
      }
kpeter@875
   423
      return *this;
kpeter@875
   424
    }
kpeter@875
   425
kpeter@875
   426
    /// \brief Set the supply values of the nodes.
kpeter@875
   427
    ///
kpeter@875
   428
    /// This function sets the supply values of the nodes.
kpeter@875
   429
    /// If neither this function nor \ref stSupply() is used before
kpeter@875
   430
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@875
   431
    ///
kpeter@875
   432
    /// \param map A node map storing the supply values.
kpeter@875
   433
    /// Its \c Value type must be convertible to the \c Value type
kpeter@875
   434
    /// of the algorithm.
kpeter@875
   435
    ///
kpeter@875
   436
    /// \return <tt>(*this)</tt>
kpeter@875
   437
    template<typename SupplyMap>
kpeter@875
   438
    CostScaling& supplyMap(const SupplyMap& map) {
kpeter@875
   439
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@875
   440
        _supply[_node_id[n]] = map[n];
kpeter@875
   441
      }
kpeter@875
   442
      return *this;
kpeter@875
   443
    }
kpeter@875
   444
kpeter@875
   445
    /// \brief Set single source and target nodes and a supply value.
kpeter@875
   446
    ///
kpeter@875
   447
    /// This function sets a single source node and a single target node
kpeter@875
   448
    /// and the required flow value.
kpeter@875
   449
    /// If neither this function nor \ref supplyMap() is used before
kpeter@875
   450
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@875
   451
    ///
kpeter@875
   452
    /// Using this function has the same effect as using \ref supplyMap()
kpeter@1023
   453
    /// with a map in which \c k is assigned to \c s, \c -k is
kpeter@875
   454
    /// assigned to \c t and all other nodes have zero supply value.
kpeter@875
   455
    ///
kpeter@875
   456
    /// \param s The source node.
kpeter@875
   457
    /// \param t The target node.
kpeter@875
   458
    /// \param k The required amount of flow from node \c s to node \c t
kpeter@875
   459
    /// (i.e. the supply of \c s and the demand of \c t).
kpeter@875
   460
    ///
kpeter@875
   461
    /// \return <tt>(*this)</tt>
kpeter@875
   462
    CostScaling& stSupply(const Node& s, const Node& t, Value k) {
kpeter@875
   463
      for (int i = 0; i != _res_node_num; ++i) {
kpeter@875
   464
        _supply[i] = 0;
kpeter@875
   465
      }
kpeter@875
   466
      _supply[_node_id[s]] =  k;
kpeter@875
   467
      _supply[_node_id[t]] = -k;
kpeter@875
   468
      return *this;
kpeter@875
   469
    }
alpar@956
   470
kpeter@875
   471
    /// @}
kpeter@875
   472
kpeter@874
   473
    /// \name Execution control
kpeter@875
   474
    /// The algorithm can be executed using \ref run().
kpeter@874
   475
kpeter@874
   476
    /// @{
kpeter@874
   477
kpeter@874
   478
    /// \brief Run the algorithm.
kpeter@874
   479
    ///
kpeter@875
   480
    /// This function runs the algorithm.
kpeter@875
   481
    /// The paramters can be specified using functions \ref lowerMap(),
kpeter@875
   482
    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@875
   483
    /// For example,
kpeter@875
   484
    /// \code
kpeter@875
   485
    ///   CostScaling<ListDigraph> cs(graph);
kpeter@875
   486
    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@875
   487
    ///     .supplyMap(sup).run();
kpeter@875
   488
    /// \endcode
kpeter@875
   489
    ///
kpeter@898
   490
    /// This function can be called more than once. All the given parameters
kpeter@898
   491
    /// are kept for the next call, unless \ref resetParams() or \ref reset()
kpeter@898
   492
    /// is used, thus only the modified parameters have to be set again.
kpeter@898
   493
    /// If the underlying digraph was also modified after the construction
kpeter@898
   494
    /// of the class (or the last \ref reset() call), then the \ref reset()
kpeter@898
   495
    /// function must be called.
kpeter@874
   496
    ///
kpeter@876
   497
    /// \param method The internal method that will be used in the
kpeter@876
   498
    /// algorithm. For more information, see \ref Method.
kpeter@876
   499
    /// \param factor The cost scaling factor. It must be larger than one.
kpeter@874
   500
    ///
kpeter@875
   501
    /// \return \c INFEASIBLE if no feasible flow exists,
kpeter@875
   502
    /// \n \c OPTIMAL if the problem has optimal solution
kpeter@875
   503
    /// (i.e. it is feasible and bounded), and the algorithm has found
kpeter@875
   504
    /// optimal flow and node potentials (primal and dual solutions),
kpeter@875
   505
    /// \n \c UNBOUNDED if the digraph contains an arc of negative cost
kpeter@875
   506
    /// and infinite upper bound. It means that the objective function
kpeter@878
   507
    /// is unbounded on that arc, however, note that it could actually be
kpeter@875
   508
    /// bounded over the feasible flows, but this algroithm cannot handle
kpeter@875
   509
    /// these cases.
kpeter@875
   510
    ///
kpeter@876
   511
    /// \see ProblemType, Method
kpeter@898
   512
    /// \see resetParams(), reset()
kpeter@876
   513
    ProblemType run(Method method = PARTIAL_AUGMENT, int factor = 8) {
kpeter@876
   514
      _alpha = factor;
kpeter@875
   515
      ProblemType pt = init();
kpeter@875
   516
      if (pt != OPTIMAL) return pt;
kpeter@876
   517
      start(method);
kpeter@875
   518
      return OPTIMAL;
kpeter@875
   519
    }
kpeter@875
   520
kpeter@875
   521
    /// \brief Reset all the parameters that have been given before.
kpeter@875
   522
    ///
kpeter@875
   523
    /// This function resets all the paramaters that have been given
kpeter@875
   524
    /// before using functions \ref lowerMap(), \ref upperMap(),
kpeter@875
   525
    /// \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@875
   526
    ///
kpeter@898
   527
    /// It is useful for multiple \ref run() calls. Basically, all the given
kpeter@898
   528
    /// parameters are kept for the next \ref run() call, unless
kpeter@898
   529
    /// \ref resetParams() or \ref reset() is used.
kpeter@898
   530
    /// If the underlying digraph was also modified after the construction
kpeter@898
   531
    /// of the class or the last \ref reset() call, then the \ref reset()
kpeter@898
   532
    /// function must be used, otherwise \ref resetParams() is sufficient.
kpeter@875
   533
    ///
kpeter@875
   534
    /// For example,
kpeter@875
   535
    /// \code
kpeter@875
   536
    ///   CostScaling<ListDigraph> cs(graph);
kpeter@875
   537
    ///
kpeter@875
   538
    ///   // First run
kpeter@875
   539
    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@875
   540
    ///     .supplyMap(sup).run();
kpeter@875
   541
    ///
kpeter@898
   542
    ///   // Run again with modified cost map (resetParams() is not called,
kpeter@875
   543
    ///   // so only the cost map have to be set again)
kpeter@875
   544
    ///   cost[e] += 100;
kpeter@875
   545
    ///   cs.costMap(cost).run();
kpeter@875
   546
    ///
kpeter@898
   547
    ///   // Run again from scratch using resetParams()
kpeter@875
   548
    ///   // (the lower bounds will be set to zero on all arcs)
kpeter@898
   549
    ///   cs.resetParams();
kpeter@875
   550
    ///   cs.upperMap(capacity).costMap(cost)
kpeter@875
   551
    ///     .supplyMap(sup).run();
kpeter@875
   552
    /// \endcode
kpeter@875
   553
    ///
kpeter@875
   554
    /// \return <tt>(*this)</tt>
kpeter@898
   555
    ///
kpeter@898
   556
    /// \see reset(), run()
kpeter@898
   557
    CostScaling& resetParams() {
kpeter@875
   558
      for (int i = 0; i != _res_node_num; ++i) {
kpeter@875
   559
        _supply[i] = 0;
kpeter@874
   560
      }
kpeter@875
   561
      int limit = _first_out[_root];
kpeter@875
   562
      for (int j = 0; j != limit; ++j) {
kpeter@875
   563
        _lower[j] = 0;
kpeter@875
   564
        _upper[j] = INF;
kpeter@875
   565
        _scost[j] = _forward[j] ? 1 : -1;
kpeter@875
   566
      }
kpeter@875
   567
      for (int j = limit; j != _res_arc_num; ++j) {
kpeter@875
   568
        _lower[j] = 0;
kpeter@875
   569
        _upper[j] = INF;
kpeter@875
   570
        _scost[j] = 0;
kpeter@875
   571
        _scost[_reverse[j]] = 0;
alpar@956
   572
      }
kpeter@875
   573
      _have_lower = false;
kpeter@875
   574
      return *this;
kpeter@874
   575
    }
kpeter@874
   576
kpeter@898
   577
    /// \brief Reset all the parameters that have been given before.
kpeter@898
   578
    ///
kpeter@898
   579
    /// This function resets all the paramaters that have been given
kpeter@898
   580
    /// before using functions \ref lowerMap(), \ref upperMap(),
kpeter@898
   581
    /// \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@898
   582
    ///
kpeter@898
   583
    /// It is useful for multiple run() calls. If this function is not
kpeter@898
   584
    /// used, all the parameters given before are kept for the next
kpeter@898
   585
    /// \ref run() call.
kpeter@898
   586
    /// However, the underlying digraph must not be modified after this
kpeter@898
   587
    /// class have been constructed, since it copies and extends the graph.
kpeter@898
   588
    /// \return <tt>(*this)</tt>
kpeter@898
   589
    CostScaling& reset() {
kpeter@898
   590
      // Resize vectors
kpeter@898
   591
      _node_num = countNodes(_graph);
kpeter@898
   592
      _arc_num = countArcs(_graph);
kpeter@898
   593
      _res_node_num = _node_num + 1;
kpeter@898
   594
      _res_arc_num = 2 * (_arc_num + _node_num);
kpeter@898
   595
      _root = _node_num;
kpeter@898
   596
kpeter@898
   597
      _first_out.resize(_res_node_num + 1);
kpeter@898
   598
      _forward.resize(_res_arc_num);
kpeter@898
   599
      _source.resize(_res_arc_num);
kpeter@898
   600
      _target.resize(_res_arc_num);
kpeter@898
   601
      _reverse.resize(_res_arc_num);
kpeter@898
   602
kpeter@898
   603
      _lower.resize(_res_arc_num);
kpeter@898
   604
      _upper.resize(_res_arc_num);
kpeter@898
   605
      _scost.resize(_res_arc_num);
kpeter@898
   606
      _supply.resize(_res_node_num);
alpar@956
   607
kpeter@898
   608
      _res_cap.resize(_res_arc_num);
kpeter@898
   609
      _cost.resize(_res_arc_num);
kpeter@898
   610
      _pi.resize(_res_node_num);
kpeter@898
   611
      _excess.resize(_res_node_num);
kpeter@898
   612
      _next_out.resize(_res_node_num);
kpeter@898
   613
kpeter@898
   614
      _arc_vec.reserve(_res_arc_num);
kpeter@898
   615
      _cost_vec.reserve(_res_arc_num);
kpeter@898
   616
kpeter@898
   617
      // Copy the graph
kpeter@898
   618
      int i = 0, j = 0, k = 2 * _arc_num + _node_num;
kpeter@898
   619
      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@898
   620
        _node_id[n] = i;
kpeter@898
   621
      }
kpeter@898
   622
      i = 0;
kpeter@898
   623
      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@898
   624
        _first_out[i] = j;
kpeter@898
   625
        for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) {
kpeter@898
   626
          _arc_idf[a] = j;
kpeter@898
   627
          _forward[j] = true;
kpeter@898
   628
          _source[j] = i;
kpeter@898
   629
          _target[j] = _node_id[_graph.runningNode(a)];
kpeter@898
   630
        }
kpeter@898
   631
        for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) {
kpeter@898
   632
          _arc_idb[a] = j;
kpeter@898
   633
          _forward[j] = false;
kpeter@898
   634
          _source[j] = i;
kpeter@898
   635
          _target[j] = _node_id[_graph.runningNode(a)];
kpeter@898
   636
        }
kpeter@898
   637
        _forward[j] = false;
kpeter@898
   638
        _source[j] = i;
kpeter@898
   639
        _target[j] = _root;
kpeter@898
   640
        _reverse[j] = k;
kpeter@898
   641
        _forward[k] = true;
kpeter@898
   642
        _source[k] = _root;
kpeter@898
   643
        _target[k] = i;
kpeter@898
   644
        _reverse[k] = j;
kpeter@898
   645
        ++j; ++k;
kpeter@898
   646
      }
kpeter@898
   647
      _first_out[i] = j;
kpeter@898
   648
      _first_out[_res_node_num] = k;
kpeter@898
   649
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@898
   650
        int fi = _arc_idf[a];
kpeter@898
   651
        int bi = _arc_idb[a];
kpeter@898
   652
        _reverse[fi] = bi;
kpeter@898
   653
        _reverse[bi] = fi;
kpeter@898
   654
      }
alpar@956
   655
kpeter@898
   656
      // Reset parameters
kpeter@898
   657
      resetParams();
kpeter@898
   658
      return *this;
kpeter@898
   659
    }
kpeter@898
   660
kpeter@874
   661
    /// @}
kpeter@874
   662
kpeter@874
   663
    /// \name Query Functions
kpeter@875
   664
    /// The results of the algorithm can be obtained using these
kpeter@874
   665
    /// functions.\n
kpeter@875
   666
    /// The \ref run() function must be called before using them.
kpeter@874
   667
kpeter@874
   668
    /// @{
kpeter@874
   669
kpeter@875
   670
    /// \brief Return the total cost of the found flow.
kpeter@874
   671
    ///
kpeter@875
   672
    /// This function returns the total cost of the found flow.
kpeter@875
   673
    /// Its complexity is O(e).
kpeter@875
   674
    ///
kpeter@875
   675
    /// \note The return type of the function can be specified as a
kpeter@875
   676
    /// template parameter. For example,
kpeter@875
   677
    /// \code
kpeter@875
   678
    ///   cs.totalCost<double>();
kpeter@875
   679
    /// \endcode
kpeter@875
   680
    /// It is useful if the total cost cannot be stored in the \c Cost
kpeter@875
   681
    /// type of the algorithm, which is the default return type of the
kpeter@875
   682
    /// function.
kpeter@874
   683
    ///
kpeter@874
   684
    /// \pre \ref run() must be called before using this function.
kpeter@875
   685
    template <typename Number>
kpeter@875
   686
    Number totalCost() const {
kpeter@875
   687
      Number c = 0;
kpeter@875
   688
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@875
   689
        int i = _arc_idb[a];
kpeter@875
   690
        c += static_cast<Number>(_res_cap[i]) *
kpeter@875
   691
             (-static_cast<Number>(_scost[i]));
kpeter@875
   692
      }
kpeter@875
   693
      return c;
kpeter@874
   694
    }
kpeter@874
   695
kpeter@875
   696
#ifndef DOXYGEN
kpeter@875
   697
    Cost totalCost() const {
kpeter@875
   698
      return totalCost<Cost>();
kpeter@874
   699
    }
kpeter@875
   700
#endif
kpeter@874
   701
kpeter@874
   702
    /// \brief Return the flow on the given arc.
kpeter@874
   703
    ///
kpeter@875
   704
    /// This function returns the flow on the given arc.
kpeter@874
   705
    ///
kpeter@874
   706
    /// \pre \ref run() must be called before using this function.
kpeter@875
   707
    Value flow(const Arc& a) const {
kpeter@875
   708
      return _res_cap[_arc_idb[a]];
kpeter@874
   709
    }
kpeter@874
   710
kpeter@875
   711
    /// \brief Return the flow map (the primal solution).
kpeter@874
   712
    ///
kpeter@875
   713
    /// This function copies the flow value on each arc into the given
kpeter@875
   714
    /// map. The \c Value type of the algorithm must be convertible to
kpeter@875
   715
    /// the \c Value type of the map.
kpeter@874
   716
    ///
kpeter@874
   717
    /// \pre \ref run() must be called before using this function.
kpeter@875
   718
    template <typename FlowMap>
kpeter@875
   719
    void flowMap(FlowMap &map) const {
kpeter@875
   720
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@875
   721
        map.set(a, _res_cap[_arc_idb[a]]);
kpeter@875
   722
      }
kpeter@874
   723
    }
kpeter@874
   724
kpeter@875
   725
    /// \brief Return the potential (dual value) of the given node.
kpeter@874
   726
    ///
kpeter@875
   727
    /// This function returns the potential (dual value) of the
kpeter@875
   728
    /// given node.
kpeter@874
   729
    ///
kpeter@874
   730
    /// \pre \ref run() must be called before using this function.
kpeter@875
   731
    Cost potential(const Node& n) const {
kpeter@875
   732
      return static_cast<Cost>(_pi[_node_id[n]]);
kpeter@875
   733
    }
kpeter@875
   734
kpeter@875
   735
    /// \brief Return the potential map (the dual solution).
kpeter@875
   736
    ///
kpeter@875
   737
    /// This function copies the potential (dual value) of each node
kpeter@875
   738
    /// into the given map.
kpeter@875
   739
    /// The \c Cost type of the algorithm must be convertible to the
kpeter@875
   740
    /// \c Value type of the map.
kpeter@875
   741
    ///
kpeter@875
   742
    /// \pre \ref run() must be called before using this function.
kpeter@875
   743
    template <typename PotentialMap>
kpeter@875
   744
    void potentialMap(PotentialMap &map) const {
kpeter@875
   745
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@875
   746
        map.set(n, static_cast<Cost>(_pi[_node_id[n]]));
kpeter@875
   747
      }
kpeter@874
   748
    }
kpeter@874
   749
kpeter@874
   750
    /// @}
kpeter@874
   751
kpeter@874
   752
  private:
kpeter@874
   753
kpeter@875
   754
    // Initialize the algorithm
kpeter@875
   755
    ProblemType init() {
kpeter@887
   756
      if (_res_node_num <= 1) return INFEASIBLE;
kpeter@875
   757
kpeter@875
   758
      // Check the sum of supply values
kpeter@875
   759
      _sum_supply = 0;
kpeter@875
   760
      for (int i = 0; i != _root; ++i) {
kpeter@875
   761
        _sum_supply += _supply[i];
kpeter@874
   762
      }
kpeter@875
   763
      if (_sum_supply > 0) return INFEASIBLE;
alpar@956
   764
kpeter@875
   765
kpeter@875
   766
      // Initialize vectors
kpeter@875
   767
      for (int i = 0; i != _res_node_num; ++i) {
kpeter@875
   768
        _pi[i] = 0;
kpeter@875
   769
        _excess[i] = _supply[i];
kpeter@875
   770
      }
alpar@956
   771
kpeter@875
   772
      // Remove infinite upper bounds and check negative arcs
kpeter@875
   773
      const Value MAX = std::numeric_limits<Value>::max();
kpeter@875
   774
      int last_out;
kpeter@875
   775
      if (_have_lower) {
kpeter@875
   776
        for (int i = 0; i != _root; ++i) {
kpeter@875
   777
          last_out = _first_out[i+1];
kpeter@875
   778
          for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@875
   779
            if (_forward[j]) {
kpeter@875
   780
              Value c = _scost[j] < 0 ? _upper[j] : _lower[j];
kpeter@875
   781
              if (c >= MAX) return UNBOUNDED;
kpeter@875
   782
              _excess[i] -= c;
kpeter@875
   783
              _excess[_target[j]] += c;
kpeter@875
   784
            }
kpeter@875
   785
          }
kpeter@875
   786
        }
kpeter@875
   787
      } else {
kpeter@875
   788
        for (int i = 0; i != _root; ++i) {
kpeter@875
   789
          last_out = _first_out[i+1];
kpeter@875
   790
          for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@875
   791
            if (_forward[j] && _scost[j] < 0) {
kpeter@875
   792
              Value c = _upper[j];
kpeter@875
   793
              if (c >= MAX) return UNBOUNDED;
kpeter@875
   794
              _excess[i] -= c;
kpeter@875
   795
              _excess[_target[j]] += c;
kpeter@875
   796
            }
kpeter@875
   797
          }
kpeter@875
   798
        }
kpeter@875
   799
      }
kpeter@875
   800
      Value ex, max_cap = 0;
kpeter@875
   801
      for (int i = 0; i != _res_node_num; ++i) {
kpeter@875
   802
        ex = _excess[i];
kpeter@875
   803
        _excess[i] = 0;
kpeter@875
   804
        if (ex < 0) max_cap -= ex;
kpeter@875
   805
      }
kpeter@875
   806
      for (int j = 0; j != _res_arc_num; ++j) {
kpeter@875
   807
        if (_upper[j] >= MAX) _upper[j] = max_cap;
kpeter@874
   808
      }
kpeter@874
   809
kpeter@875
   810
      // Initialize the large cost vector and the epsilon parameter
kpeter@875
   811
      _epsilon = 0;
kpeter@875
   812
      LargeCost lc;
kpeter@875
   813
      for (int i = 0; i != _root; ++i) {
kpeter@875
   814
        last_out = _first_out[i+1];
kpeter@875
   815
        for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@875
   816
          lc = static_cast<LargeCost>(_scost[j]) * _res_node_num * _alpha;
kpeter@875
   817
          _cost[j] = lc;
kpeter@875
   818
          if (lc > _epsilon) _epsilon = lc;
kpeter@875
   819
        }
kpeter@875
   820
      }
kpeter@875
   821
      _epsilon /= _alpha;
kpeter@874
   822
kpeter@875
   823
      // Initialize maps for Circulation and remove non-zero lower bounds
kpeter@875
   824
      ConstMap<Arc, Value> low(0);
kpeter@875
   825
      typedef typename Digraph::template ArcMap<Value> ValueArcMap;
kpeter@875
   826
      typedef typename Digraph::template NodeMap<Value> ValueNodeMap;
kpeter@875
   827
      ValueArcMap cap(_graph), flow(_graph);
kpeter@875
   828
      ValueNodeMap sup(_graph);
kpeter@875
   829
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@875
   830
        sup[n] = _supply[_node_id[n]];
kpeter@874
   831
      }
kpeter@875
   832
      if (_have_lower) {
kpeter@875
   833
        for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@875
   834
          int j = _arc_idf[a];
kpeter@875
   835
          Value c = _lower[j];
kpeter@875
   836
          cap[a] = _upper[j] - c;
kpeter@875
   837
          sup[_graph.source(a)] -= c;
kpeter@875
   838
          sup[_graph.target(a)] += c;
kpeter@875
   839
        }
kpeter@875
   840
      } else {
kpeter@875
   841
        for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@875
   842
          cap[a] = _upper[_arc_idf[a]];
kpeter@875
   843
        }
kpeter@875
   844
      }
kpeter@874
   845
kpeter@910
   846
      _sup_node_num = 0;
kpeter@910
   847
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@910
   848
        if (sup[n] > 0) ++_sup_node_num;
kpeter@910
   849
      }
kpeter@910
   850
kpeter@874
   851
      // Find a feasible flow using Circulation
kpeter@875
   852
      Circulation<Digraph, ConstMap<Arc, Value>, ValueArcMap, ValueNodeMap>
kpeter@875
   853
        circ(_graph, low, cap, sup);
kpeter@875
   854
      if (!circ.flowMap(flow).run()) return INFEASIBLE;
kpeter@875
   855
kpeter@875
   856
      // Set residual capacities and handle GEQ supply type
kpeter@875
   857
      if (_sum_supply < 0) {
kpeter@875
   858
        for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@875
   859
          Value fa = flow[a];
kpeter@875
   860
          _res_cap[_arc_idf[a]] = cap[a] - fa;
kpeter@875
   861
          _res_cap[_arc_idb[a]] = fa;
kpeter@875
   862
          sup[_graph.source(a)] -= fa;
kpeter@875
   863
          sup[_graph.target(a)] += fa;
kpeter@875
   864
        }
kpeter@875
   865
        for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@875
   866
          _excess[_node_id[n]] = sup[n];
kpeter@875
   867
        }
kpeter@875
   868
        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
kpeter@875
   869
          int u = _target[a];
kpeter@875
   870
          int ra = _reverse[a];
kpeter@875
   871
          _res_cap[a] = -_sum_supply + 1;
kpeter@875
   872
          _res_cap[ra] = -_excess[u];
kpeter@875
   873
          _cost[a] = 0;
kpeter@875
   874
          _cost[ra] = 0;
kpeter@875
   875
          _excess[u] = 0;
kpeter@875
   876
        }
kpeter@875
   877
      } else {
kpeter@875
   878
        for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@875
   879
          Value fa = flow[a];
kpeter@875
   880
          _res_cap[_arc_idf[a]] = cap[a] - fa;
kpeter@875
   881
          _res_cap[_arc_idb[a]] = fa;
kpeter@875
   882
        }
kpeter@875
   883
        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
kpeter@875
   884
          int ra = _reverse[a];
kpeter@910
   885
          _res_cap[a] = 0;
kpeter@875
   886
          _res_cap[ra] = 0;
kpeter@875
   887
          _cost[a] = 0;
kpeter@875
   888
          _cost[ra] = 0;
kpeter@875
   889
        }
kpeter@875
   890
      }
alpar@956
   891
kpeter@875
   892
      return OPTIMAL;
kpeter@875
   893
    }
kpeter@875
   894
kpeter@875
   895
    // Execute the algorithm and transform the results
kpeter@876
   896
    void start(Method method) {
kpeter@876
   897
      // Maximum path length for partial augment
kpeter@876
   898
      const int MAX_PATH_LENGTH = 4;
kpeter@910
   899
alpar@956
   900
      // Initialize data structures for buckets
kpeter@910
   901
      _max_rank = _alpha * _res_node_num;
kpeter@910
   902
      _buckets.resize(_max_rank);
kpeter@910
   903
      _bucket_next.resize(_res_node_num + 1);
kpeter@910
   904
      _bucket_prev.resize(_res_node_num + 1);
kpeter@910
   905
      _rank.resize(_res_node_num + 1);
alpar@956
   906
kpeter@875
   907
      // Execute the algorithm
kpeter@876
   908
      switch (method) {
kpeter@876
   909
        case PUSH:
kpeter@876
   910
          startPush();
kpeter@876
   911
          break;
kpeter@876
   912
        case AUGMENT:
kpeter@876
   913
          startAugment();
kpeter@876
   914
          break;
kpeter@876
   915
        case PARTIAL_AUGMENT:
kpeter@876
   916
          startAugment(MAX_PATH_LENGTH);
kpeter@876
   917
          break;
kpeter@875
   918
      }
kpeter@875
   919
kpeter@875
   920
      // Compute node potentials for the original costs
kpeter@875
   921
      _arc_vec.clear();
kpeter@875
   922
      _cost_vec.clear();
kpeter@875
   923
      for (int j = 0; j != _res_arc_num; ++j) {
kpeter@875
   924
        if (_res_cap[j] > 0) {
kpeter@875
   925
          _arc_vec.push_back(IntPair(_source[j], _target[j]));
kpeter@875
   926
          _cost_vec.push_back(_scost[j]);
kpeter@875
   927
        }
kpeter@875
   928
      }
kpeter@875
   929
      _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end());
kpeter@875
   930
kpeter@875
   931
      typename BellmanFord<StaticDigraph, LargeCostArcMap>
kpeter@875
   932
        ::template SetDistMap<LargeCostNodeMap>::Create bf(_sgr, _cost_map);
kpeter@875
   933
      bf.distMap(_pi_map);
kpeter@875
   934
      bf.init(0);
kpeter@875
   935
      bf.start();
kpeter@875
   936
kpeter@875
   937
      // Handle non-zero lower bounds
kpeter@875
   938
      if (_have_lower) {
kpeter@875
   939
        int limit = _first_out[_root];
kpeter@875
   940
        for (int j = 0; j != limit; ++j) {
kpeter@875
   941
          if (!_forward[j]) _res_cap[j] += _lower[j];
kpeter@875
   942
        }
kpeter@875
   943
      }
kpeter@874
   944
    }
alpar@956
   945
kpeter@910
   946
    // Initialize a cost scaling phase
kpeter@910
   947
    void initPhase() {
kpeter@910
   948
      // Saturate arcs not satisfying the optimality condition
kpeter@910
   949
      for (int u = 0; u != _res_node_num; ++u) {
kpeter@910
   950
        int last_out = _first_out[u+1];
kpeter@910
   951
        LargeCost pi_u = _pi[u];
kpeter@910
   952
        for (int a = _first_out[u]; a != last_out; ++a) {
kpeter@910
   953
          int v = _target[a];
kpeter@910
   954
          if (_res_cap[a] > 0 && _cost[a] + pi_u - _pi[v] < 0) {
kpeter@910
   955
            Value delta = _res_cap[a];
kpeter@910
   956
            _excess[u] -= delta;
kpeter@910
   957
            _excess[v] += delta;
kpeter@910
   958
            _res_cap[a] = 0;
kpeter@910
   959
            _res_cap[_reverse[a]] += delta;
kpeter@910
   960
          }
kpeter@910
   961
        }
kpeter@910
   962
      }
alpar@956
   963
kpeter@910
   964
      // Find active nodes (i.e. nodes with positive excess)
kpeter@910
   965
      for (int u = 0; u != _res_node_num; ++u) {
kpeter@910
   966
        if (_excess[u] > 0) _active_nodes.push_back(u);
kpeter@910
   967
      }
kpeter@910
   968
kpeter@910
   969
      // Initialize the next arcs
kpeter@910
   970
      for (int u = 0; u != _res_node_num; ++u) {
kpeter@910
   971
        _next_out[u] = _first_out[u];
kpeter@910
   972
      }
kpeter@910
   973
    }
alpar@956
   974
kpeter@910
   975
    // Early termination heuristic
kpeter@910
   976
    bool earlyTermination() {
kpeter@910
   977
      const double EARLY_TERM_FACTOR = 3.0;
kpeter@910
   978
kpeter@910
   979
      // Build a static residual graph
kpeter@910
   980
      _arc_vec.clear();
kpeter@910
   981
      _cost_vec.clear();
kpeter@910
   982
      for (int j = 0; j != _res_arc_num; ++j) {
kpeter@910
   983
        if (_res_cap[j] > 0) {
kpeter@910
   984
          _arc_vec.push_back(IntPair(_source[j], _target[j]));
kpeter@910
   985
          _cost_vec.push_back(_cost[j] + 1);
kpeter@910
   986
        }
kpeter@910
   987
      }
kpeter@910
   988
      _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end());
kpeter@910
   989
kpeter@910
   990
      // Run Bellman-Ford algorithm to check if the current flow is optimal
kpeter@910
   991
      BellmanFord<StaticDigraph, LargeCostArcMap> bf(_sgr, _cost_map);
kpeter@910
   992
      bf.init(0);
kpeter@910
   993
      bool done = false;
kpeter@910
   994
      int K = int(EARLY_TERM_FACTOR * std::sqrt(double(_res_node_num)));
kpeter@910
   995
      for (int i = 0; i < K && !done; ++i) {
kpeter@910
   996
        done = bf.processNextWeakRound();
kpeter@910
   997
      }
kpeter@910
   998
      return done;
kpeter@910
   999
    }
kpeter@910
  1000
kpeter@910
  1001
    // Global potential update heuristic
kpeter@910
  1002
    void globalUpdate() {
kpeter@910
  1003
      int bucket_end = _root + 1;
alpar@956
  1004
kpeter@910
  1005
      // Initialize buckets
kpeter@910
  1006
      for (int r = 0; r != _max_rank; ++r) {
kpeter@910
  1007
        _buckets[r] = bucket_end;
kpeter@910
  1008
      }
kpeter@910
  1009
      Value total_excess = 0;
kpeter@910
  1010
      for (int i = 0; i != _res_node_num; ++i) {
kpeter@910
  1011
        if (_excess[i] < 0) {
kpeter@910
  1012
          _rank[i] = 0;
kpeter@910
  1013
          _bucket_next[i] = _buckets[0];
kpeter@910
  1014
          _bucket_prev[_buckets[0]] = i;
kpeter@910
  1015
          _buckets[0] = i;
kpeter@910
  1016
        } else {
kpeter@910
  1017
          total_excess += _excess[i];
kpeter@910
  1018
          _rank[i] = _max_rank;
kpeter@910
  1019
        }
kpeter@910
  1020
      }
kpeter@910
  1021
      if (total_excess == 0) return;
kpeter@910
  1022
kpeter@910
  1023
      // Search the buckets
kpeter@910
  1024
      int r = 0;
kpeter@910
  1025
      for ( ; r != _max_rank; ++r) {
kpeter@910
  1026
        while (_buckets[r] != bucket_end) {
kpeter@910
  1027
          // Remove the first node from the current bucket
kpeter@910
  1028
          int u = _buckets[r];
kpeter@910
  1029
          _buckets[r] = _bucket_next[u];
alpar@956
  1030
kpeter@910
  1031
          // Search the incomming arcs of u
kpeter@910
  1032
          LargeCost pi_u = _pi[u];
kpeter@910
  1033
          int last_out = _first_out[u+1];
kpeter@910
  1034
          for (int a = _first_out[u]; a != last_out; ++a) {
kpeter@910
  1035
            int ra = _reverse[a];
kpeter@910
  1036
            if (_res_cap[ra] > 0) {
kpeter@910
  1037
              int v = _source[ra];
kpeter@910
  1038
              int old_rank_v = _rank[v];
kpeter@910
  1039
              if (r < old_rank_v) {
kpeter@910
  1040
                // Compute the new rank of v
kpeter@910
  1041
                LargeCost nrc = (_cost[ra] + _pi[v] - pi_u) / _epsilon;
kpeter@910
  1042
                int new_rank_v = old_rank_v;
kpeter@910
  1043
                if (nrc < LargeCost(_max_rank))
kpeter@910
  1044
                  new_rank_v = r + 1 + int(nrc);
alpar@956
  1045
kpeter@910
  1046
                // Change the rank of v
kpeter@910
  1047
                if (new_rank_v < old_rank_v) {
kpeter@910
  1048
                  _rank[v] = new_rank_v;
kpeter@910
  1049
                  _next_out[v] = _first_out[v];
alpar@956
  1050
kpeter@910
  1051
                  // Remove v from its old bucket
kpeter@910
  1052
                  if (old_rank_v < _max_rank) {
kpeter@910
  1053
                    if (_buckets[old_rank_v] == v) {
kpeter@910
  1054
                      _buckets[old_rank_v] = _bucket_next[v];
kpeter@910
  1055
                    } else {
kpeter@910
  1056
                      _bucket_next[_bucket_prev[v]] = _bucket_next[v];
kpeter@910
  1057
                      _bucket_prev[_bucket_next[v]] = _bucket_prev[v];
kpeter@910
  1058
                    }
kpeter@910
  1059
                  }
alpar@956
  1060
kpeter@910
  1061
                  // Insert v to its new bucket
kpeter@910
  1062
                  _bucket_next[v] = _buckets[new_rank_v];
kpeter@910
  1063
                  _bucket_prev[_buckets[new_rank_v]] = v;
kpeter@910
  1064
                  _buckets[new_rank_v] = v;
kpeter@910
  1065
                }
kpeter@910
  1066
              }
kpeter@910
  1067
            }
kpeter@910
  1068
          }
kpeter@910
  1069
kpeter@910
  1070
          // Finish search if there are no more active nodes
kpeter@910
  1071
          if (_excess[u] > 0) {
kpeter@910
  1072
            total_excess -= _excess[u];
kpeter@910
  1073
            if (total_excess <= 0) break;
kpeter@910
  1074
          }
kpeter@910
  1075
        }
kpeter@910
  1076
        if (total_excess <= 0) break;
kpeter@910
  1077
      }
alpar@956
  1078
kpeter@910
  1079
      // Relabel nodes
kpeter@910
  1080
      for (int u = 0; u != _res_node_num; ++u) {
kpeter@910
  1081
        int k = std::min(_rank[u], r);
kpeter@910
  1082
        if (k > 0) {
kpeter@910
  1083
          _pi[u] -= _epsilon * k;
kpeter@910
  1084
          _next_out[u] = _first_out[u];
kpeter@910
  1085
        }
kpeter@910
  1086
      }
kpeter@910
  1087
    }
kpeter@874
  1088
kpeter@876
  1089
    /// Execute the algorithm performing augment and relabel operations
kpeter@876
  1090
    void startAugment(int max_length = std::numeric_limits<int>::max()) {
kpeter@874
  1091
      // Paramters for heuristics
kpeter@910
  1092
      const int EARLY_TERM_EPSILON_LIMIT = 1000;
kpeter@910
  1093
      const double GLOBAL_UPDATE_FACTOR = 3.0;
kpeter@874
  1094
kpeter@910
  1095
      const int global_update_freq = int(GLOBAL_UPDATE_FACTOR *
kpeter@910
  1096
        (_res_node_num + _sup_node_num * _sup_node_num));
kpeter@910
  1097
      int next_update_limit = global_update_freq;
alpar@956
  1098
kpeter@910
  1099
      int relabel_cnt = 0;
alpar@956
  1100
kpeter@875
  1101
      // Perform cost scaling phases
kpeter@910
  1102
      std::vector<int> path;
kpeter@874
  1103
      for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
kpeter@874
  1104
                                        1 : _epsilon / _alpha )
kpeter@874
  1105
      {
kpeter@910
  1106
        // Early termination heuristic
kpeter@910
  1107
        if (_epsilon <= EARLY_TERM_EPSILON_LIMIT) {
kpeter@910
  1108
          if (earlyTermination()) break;
kpeter@874
  1109
        }
alpar@956
  1110
kpeter@910
  1111
        // Initialize current phase
kpeter@910
  1112
        initPhase();
alpar@956
  1113
kpeter@874
  1114
        // Perform partial augment and relabel operations
kpeter@875
  1115
        while (true) {
kpeter@874
  1116
          // Select an active node (FIFO selection)
kpeter@875
  1117
          while (_active_nodes.size() > 0 &&
kpeter@875
  1118
                 _excess[_active_nodes.front()] <= 0) {
kpeter@875
  1119
            _active_nodes.pop_front();
kpeter@874
  1120
          }
kpeter@875
  1121
          if (_active_nodes.size() == 0) break;
kpeter@875
  1122
          int start = _active_nodes.front();
kpeter@874
  1123
kpeter@874
  1124
          // Find an augmenting path from the start node
kpeter@910
  1125
          path.clear();
kpeter@875
  1126
          int tip = start;
kpeter@910
  1127
          while (_excess[tip] >= 0 && int(path.size()) < max_length) {
kpeter@875
  1128
            int u;
kpeter@910
  1129
            LargeCost min_red_cost, rc, pi_tip = _pi[tip];
kpeter@910
  1130
            int last_out = _first_out[tip+1];
kpeter@875
  1131
            for (int a = _next_out[tip]; a != last_out; ++a) {
kpeter@910
  1132
              u = _target[a];
kpeter@910
  1133
              if (_res_cap[a] > 0 && _cost[a] + pi_tip - _pi[u] < 0) {
kpeter@910
  1134
                path.push_back(a);
kpeter@875
  1135
                _next_out[tip] = a;
kpeter@874
  1136
                tip = u;
kpeter@874
  1137
                goto next_step;
kpeter@874
  1138
              }
kpeter@874
  1139
            }
kpeter@874
  1140
kpeter@874
  1141
            // Relabel tip node
kpeter@910
  1142
            min_red_cost = std::numeric_limits<LargeCost>::max();
kpeter@910
  1143
            if (tip != start) {
kpeter@910
  1144
              int ra = _reverse[path.back()];
kpeter@910
  1145
              min_red_cost = _cost[ra] + pi_tip - _pi[_target[ra]];
kpeter@910
  1146
            }
kpeter@875
  1147
            for (int a = _first_out[tip]; a != last_out; ++a) {
kpeter@910
  1148
              rc = _cost[a] + pi_tip - _pi[_target[a]];
kpeter@875
  1149
              if (_res_cap[a] > 0 && rc < min_red_cost) {
kpeter@875
  1150
                min_red_cost = rc;
kpeter@875
  1151
              }
kpeter@874
  1152
            }
kpeter@875
  1153
            _pi[tip] -= min_red_cost + _epsilon;
kpeter@875
  1154
            _next_out[tip] = _first_out[tip];
kpeter@910
  1155
            ++relabel_cnt;
kpeter@874
  1156
kpeter@874
  1157
            // Step back
kpeter@874
  1158
            if (tip != start) {
kpeter@910
  1159
              tip = _source[path.back()];
kpeter@910
  1160
              path.pop_back();
kpeter@874
  1161
            }
kpeter@874
  1162
kpeter@875
  1163
          next_step: ;
kpeter@874
  1164
          }
kpeter@874
  1165
kpeter@874
  1166
          // Augment along the found path (as much flow as possible)
kpeter@875
  1167
          Value delta;
kpeter@910
  1168
          int pa, u, v = start;
kpeter@910
  1169
          for (int i = 0; i != int(path.size()); ++i) {
kpeter@910
  1170
            pa = path[i];
kpeter@875
  1171
            u = v;
kpeter@910
  1172
            v = _target[pa];
kpeter@875
  1173
            delta = std::min(_res_cap[pa], _excess[u]);
kpeter@875
  1174
            _res_cap[pa] -= delta;
kpeter@875
  1175
            _res_cap[_reverse[pa]] += delta;
kpeter@875
  1176
            _excess[u] -= delta;
kpeter@875
  1177
            _excess[v] += delta;
kpeter@875
  1178
            if (_excess[v] > 0 && _excess[v] <= delta)
kpeter@875
  1179
              _active_nodes.push_back(v);
kpeter@874
  1180
          }
kpeter@910
  1181
kpeter@910
  1182
          // Global update heuristic
kpeter@910
  1183
          if (relabel_cnt >= next_update_limit) {
kpeter@910
  1184
            globalUpdate();
kpeter@910
  1185
            next_update_limit += global_update_freq;
kpeter@910
  1186
          }
kpeter@874
  1187
        }
kpeter@874
  1188
      }
kpeter@874
  1189
    }
kpeter@874
  1190
kpeter@875
  1191
    /// Execute the algorithm performing push and relabel operations
kpeter@876
  1192
    void startPush() {
kpeter@874
  1193
      // Paramters for heuristics
kpeter@910
  1194
      const int EARLY_TERM_EPSILON_LIMIT = 1000;
kpeter@910
  1195
      const double GLOBAL_UPDATE_FACTOR = 2.0;
kpeter@874
  1196
kpeter@910
  1197
      const int global_update_freq = int(GLOBAL_UPDATE_FACTOR *
kpeter@910
  1198
        (_res_node_num + _sup_node_num * _sup_node_num));
kpeter@910
  1199
      int next_update_limit = global_update_freq;
kpeter@910
  1200
kpeter@910
  1201
      int relabel_cnt = 0;
alpar@956
  1202
kpeter@875
  1203
      // Perform cost scaling phases
kpeter@875
  1204
      BoolVector hyper(_res_node_num, false);
kpeter@910
  1205
      LargeCostVector hyper_cost(_res_node_num);
kpeter@874
  1206
      for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
kpeter@874
  1207
                                        1 : _epsilon / _alpha )
kpeter@874
  1208
      {
kpeter@910
  1209
        // Early termination heuristic
kpeter@910
  1210
        if (_epsilon <= EARLY_TERM_EPSILON_LIMIT) {
kpeter@910
  1211
          if (earlyTermination()) break;
kpeter@874
  1212
        }
alpar@956
  1213
kpeter@910
  1214
        // Initialize current phase
kpeter@910
  1215
        initPhase();
kpeter@874
  1216
kpeter@874
  1217
        // Perform push and relabel operations
kpeter@875
  1218
        while (_active_nodes.size() > 0) {
kpeter@910
  1219
          LargeCost min_red_cost, rc, pi_n;
kpeter@875
  1220
          Value delta;
kpeter@875
  1221
          int n, t, a, last_out = _res_arc_num;
kpeter@875
  1222
kpeter@910
  1223
        next_node:
kpeter@874
  1224
          // Select an active node (FIFO selection)
kpeter@875
  1225
          n = _active_nodes.front();
kpeter@910
  1226
          last_out = _first_out[n+1];
kpeter@910
  1227
          pi_n = _pi[n];
alpar@956
  1228
kpeter@874
  1229
          // Perform push operations if there are admissible arcs
kpeter@875
  1230
          if (_excess[n] > 0) {
kpeter@875
  1231
            for (a = _next_out[n]; a != last_out; ++a) {
kpeter@875
  1232
              if (_res_cap[a] > 0 &&
kpeter@910
  1233
                  _cost[a] + pi_n - _pi[_target[a]] < 0) {
kpeter@875
  1234
                delta = std::min(_res_cap[a], _excess[n]);
kpeter@875
  1235
                t = _target[a];
kpeter@874
  1236
kpeter@874
  1237
                // Push-look-ahead heuristic
kpeter@875
  1238
                Value ahead = -_excess[t];
kpeter@910
  1239
                int last_out_t = _first_out[t+1];
kpeter@910
  1240
                LargeCost pi_t = _pi[t];
kpeter@875
  1241
                for (int ta = _next_out[t]; ta != last_out_t; ++ta) {
alpar@956
  1242
                  if (_res_cap[ta] > 0 &&
kpeter@910
  1243
                      _cost[ta] + pi_t - _pi[_target[ta]] < 0)
kpeter@875
  1244
                    ahead += _res_cap[ta];
kpeter@875
  1245
                  if (ahead >= delta) break;
kpeter@874
  1246
                }
kpeter@874
  1247
                if (ahead < 0) ahead = 0;
kpeter@874
  1248
kpeter@874
  1249
                // Push flow along the arc
kpeter@910
  1250
                if (ahead < delta && !hyper[t]) {
kpeter@875
  1251
                  _res_cap[a] -= ahead;
kpeter@875
  1252
                  _res_cap[_reverse[a]] += ahead;
kpeter@874
  1253
                  _excess[n] -= ahead;
kpeter@874
  1254
                  _excess[t] += ahead;
kpeter@875
  1255
                  _active_nodes.push_front(t);
kpeter@874
  1256
                  hyper[t] = true;
kpeter@910
  1257
                  hyper_cost[t] = _cost[a] + pi_n - pi_t;
kpeter@875
  1258
                  _next_out[n] = a;
kpeter@875
  1259
                  goto next_node;
kpeter@874
  1260
                } else {
kpeter@875
  1261
                  _res_cap[a] -= delta;
kpeter@875
  1262
                  _res_cap[_reverse[a]] += delta;
kpeter@874
  1263
                  _excess[n] -= delta;
kpeter@874
  1264
                  _excess[t] += delta;
kpeter@874
  1265
                  if (_excess[t] > 0 && _excess[t] <= delta)
kpeter@875
  1266
                    _active_nodes.push_back(t);
kpeter@874
  1267
                }
kpeter@874
  1268
kpeter@875
  1269
                if (_excess[n] == 0) {
kpeter@875
  1270
                  _next_out[n] = a;
kpeter@875
  1271
                  goto remove_nodes;
kpeter@875
  1272
                }
kpeter@874
  1273
              }
kpeter@874
  1274
            }
kpeter@875
  1275
            _next_out[n] = a;
kpeter@874
  1276
          }
kpeter@874
  1277
kpeter@874
  1278
          // Relabel the node if it is still active (or hyper)
kpeter@875
  1279
          if (_excess[n] > 0 || hyper[n]) {
kpeter@910
  1280
             min_red_cost = hyper[n] ? -hyper_cost[n] :
kpeter@910
  1281
               std::numeric_limits<LargeCost>::max();
kpeter@875
  1282
            for (int a = _first_out[n]; a != last_out; ++a) {
kpeter@910
  1283
              rc = _cost[a] + pi_n - _pi[_target[a]];
kpeter@875
  1284
              if (_res_cap[a] > 0 && rc < min_red_cost) {
kpeter@875
  1285
                min_red_cost = rc;
kpeter@875
  1286
              }
kpeter@874
  1287
            }
kpeter@875
  1288
            _pi[n] -= min_red_cost + _epsilon;
kpeter@910
  1289
            _next_out[n] = _first_out[n];
kpeter@874
  1290
            hyper[n] = false;
kpeter@910
  1291
            ++relabel_cnt;
kpeter@874
  1292
          }
alpar@956
  1293
kpeter@874
  1294
          // Remove nodes that are not active nor hyper
kpeter@875
  1295
        remove_nodes:
kpeter@875
  1296
          while ( _active_nodes.size() > 0 &&
kpeter@875
  1297
                  _excess[_active_nodes.front()] <= 0 &&
kpeter@875
  1298
                  !hyper[_active_nodes.front()] ) {
kpeter@875
  1299
            _active_nodes.pop_front();
kpeter@874
  1300
          }
alpar@956
  1301
kpeter@910
  1302
          // Global update heuristic
kpeter@910
  1303
          if (relabel_cnt >= next_update_limit) {
kpeter@910
  1304
            globalUpdate();
kpeter@910
  1305
            for (int u = 0; u != _res_node_num; ++u)
kpeter@910
  1306
              hyper[u] = false;
kpeter@910
  1307
            next_update_limit += global_update_freq;
kpeter@910
  1308
          }
kpeter@874
  1309
        }
kpeter@874
  1310
      }
kpeter@874
  1311
    }
kpeter@874
  1312
kpeter@874
  1313
  }; //class CostScaling
kpeter@874
  1314
kpeter@874
  1315
  ///@}
kpeter@874
  1316
kpeter@874
  1317
} //namespace lemon
kpeter@874
  1318
kpeter@874
  1319
#endif //LEMON_COST_SCALING_H