lemon/cost_scaling.h
author Peter Kovacs <kpeter@inf.elte.hu>
Mon, 30 Jan 2012 19:29:03 +0100
changeset 985 eb12ad2789fc
parent 937 1226290a9b7d
child 1003 16f55008c863
permissions -rw-r--r--
Fix the doc in CapacityScaling: cost can be real numbers (#261)
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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 \c V and \c C must be signed number types.
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  /// \warning All input data (capacities, supply values, and costs) 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::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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  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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      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) {
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        _upper[_arc_idf[a]] = map[a];
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      }
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      return *this;
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    }
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    /// \brief Set the costs of the arcs.
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    ///
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    /// This function sets the costs of the arcs.
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    /// If it is not used before calling \ref run(), the costs
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    /// will be set to \c 1 on all arcs.
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   402
    ///
kpeter@809
   403
    /// \param map An arc map storing the costs.
kpeter@809
   404
    /// Its \c Value type must be convertible to the \c Cost type
kpeter@809
   405
    /// of the algorithm.
kpeter@809
   406
    ///
kpeter@809
   407
    /// \return <tt>(*this)</tt>
kpeter@809
   408
    template<typename CostMap>
kpeter@809
   409
    CostScaling& costMap(const CostMap& map) {
kpeter@809
   410
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809
   411
        _scost[_arc_idf[a]] =  map[a];
kpeter@809
   412
        _scost[_arc_idb[a]] = -map[a];
kpeter@809
   413
      }
kpeter@809
   414
      return *this;
kpeter@809
   415
    }
kpeter@809
   416
kpeter@809
   417
    /// \brief Set the supply values of the nodes.
kpeter@809
   418
    ///
kpeter@809
   419
    /// This function sets the supply values of the nodes.
kpeter@809
   420
    /// If neither this function nor \ref stSupply() is used before
kpeter@809
   421
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@809
   422
    ///
kpeter@809
   423
    /// \param map A node map storing the supply values.
kpeter@809
   424
    /// Its \c Value type must be convertible to the \c Value type
kpeter@809
   425
    /// of the algorithm.
kpeter@809
   426
    ///
kpeter@809
   427
    /// \return <tt>(*this)</tt>
kpeter@809
   428
    template<typename SupplyMap>
kpeter@809
   429
    CostScaling& supplyMap(const SupplyMap& map) {
kpeter@809
   430
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@809
   431
        _supply[_node_id[n]] = map[n];
kpeter@809
   432
      }
kpeter@809
   433
      return *this;
kpeter@809
   434
    }
kpeter@809
   435
kpeter@809
   436
    /// \brief Set single source and target nodes and a supply value.
kpeter@809
   437
    ///
kpeter@809
   438
    /// This function sets a single source node and a single target node
kpeter@809
   439
    /// and the required flow value.
kpeter@809
   440
    /// If neither this function nor \ref supplyMap() is used before
kpeter@809
   441
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@809
   442
    ///
kpeter@809
   443
    /// Using this function has the same effect as using \ref supplyMap()
kpeter@919
   444
    /// with a map in which \c k is assigned to \c s, \c -k is
kpeter@809
   445
    /// assigned to \c t and all other nodes have zero supply value.
kpeter@809
   446
    ///
kpeter@809
   447
    /// \param s The source node.
kpeter@809
   448
    /// \param t The target node.
kpeter@809
   449
    /// \param k The required amount of flow from node \c s to node \c t
kpeter@809
   450
    /// (i.e. the supply of \c s and the demand of \c t).
kpeter@809
   451
    ///
kpeter@809
   452
    /// \return <tt>(*this)</tt>
kpeter@809
   453
    CostScaling& stSupply(const Node& s, const Node& t, Value k) {
kpeter@809
   454
      for (int i = 0; i != _res_node_num; ++i) {
kpeter@809
   455
        _supply[i] = 0;
kpeter@809
   456
      }
kpeter@809
   457
      _supply[_node_id[s]] =  k;
kpeter@809
   458
      _supply[_node_id[t]] = -k;
kpeter@809
   459
      return *this;
kpeter@809
   460
    }
alpar@877
   461
kpeter@809
   462
    /// @}
kpeter@809
   463
kpeter@808
   464
    /// \name Execution control
kpeter@809
   465
    /// The algorithm can be executed using \ref run().
kpeter@808
   466
kpeter@808
   467
    /// @{
kpeter@808
   468
kpeter@808
   469
    /// \brief Run the algorithm.
kpeter@808
   470
    ///
kpeter@809
   471
    /// This function runs the algorithm.
kpeter@809
   472
    /// The paramters can be specified using functions \ref lowerMap(),
kpeter@809
   473
    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@809
   474
    /// For example,
kpeter@809
   475
    /// \code
kpeter@809
   476
    ///   CostScaling<ListDigraph> cs(graph);
kpeter@809
   477
    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@809
   478
    ///     .supplyMap(sup).run();
kpeter@809
   479
    /// \endcode
kpeter@809
   480
    ///
kpeter@830
   481
    /// This function can be called more than once. All the given parameters
kpeter@830
   482
    /// are kept for the next call, unless \ref resetParams() or \ref reset()
kpeter@830
   483
    /// is used, thus only the modified parameters have to be set again.
kpeter@830
   484
    /// If the underlying digraph was also modified after the construction
kpeter@830
   485
    /// of the class (or the last \ref reset() call), then the \ref reset()
kpeter@830
   486
    /// function must be called.
kpeter@808
   487
    ///
kpeter@810
   488
    /// \param method The internal method that will be used in the
kpeter@810
   489
    /// algorithm. For more information, see \ref Method.
kpeter@938
   490
    /// \param factor The cost scaling factor. It must be at least two.
kpeter@808
   491
    ///
kpeter@809
   492
    /// \return \c INFEASIBLE if no feasible flow exists,
kpeter@809
   493
    /// \n \c OPTIMAL if the problem has optimal solution
kpeter@809
   494
    /// (i.e. it is feasible and bounded), and the algorithm has found
kpeter@809
   495
    /// optimal flow and node potentials (primal and dual solutions),
kpeter@809
   496
    /// \n \c UNBOUNDED if the digraph contains an arc of negative cost
kpeter@809
   497
    /// and infinite upper bound. It means that the objective function
kpeter@812
   498
    /// is unbounded on that arc, however, note that it could actually be
kpeter@809
   499
    /// bounded over the feasible flows, but this algroithm cannot handle
kpeter@809
   500
    /// these cases.
kpeter@809
   501
    ///
kpeter@810
   502
    /// \see ProblemType, Method
kpeter@830
   503
    /// \see resetParams(), reset()
kpeter@938
   504
    ProblemType run(Method method = PARTIAL_AUGMENT, int factor = 16) {
kpeter@938
   505
      LEMON_ASSERT(factor >= 2, "The scaling factor must be at least 2");
kpeter@810
   506
      _alpha = factor;
kpeter@809
   507
      ProblemType pt = init();
kpeter@809
   508
      if (pt != OPTIMAL) return pt;
kpeter@810
   509
      start(method);
kpeter@809
   510
      return OPTIMAL;
kpeter@809
   511
    }
kpeter@809
   512
kpeter@809
   513
    /// \brief Reset all the parameters that have been given before.
kpeter@809
   514
    ///
kpeter@809
   515
    /// This function resets all the paramaters that have been given
kpeter@809
   516
    /// before using functions \ref lowerMap(), \ref upperMap(),
kpeter@809
   517
    /// \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@809
   518
    ///
kpeter@830
   519
    /// It is useful for multiple \ref run() calls. Basically, all the given
kpeter@830
   520
    /// parameters are kept for the next \ref run() call, unless
kpeter@830
   521
    /// \ref resetParams() or \ref reset() is used.
kpeter@830
   522
    /// If the underlying digraph was also modified after the construction
kpeter@830
   523
    /// of the class or the last \ref reset() call, then the \ref reset()
kpeter@830
   524
    /// function must be used, otherwise \ref resetParams() is sufficient.
kpeter@809
   525
    ///
kpeter@809
   526
    /// For example,
kpeter@809
   527
    /// \code
kpeter@809
   528
    ///   CostScaling<ListDigraph> cs(graph);
kpeter@809
   529
    ///
kpeter@809
   530
    ///   // First run
kpeter@809
   531
    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@809
   532
    ///     .supplyMap(sup).run();
kpeter@809
   533
    ///
kpeter@830
   534
    ///   // Run again with modified cost map (resetParams() is not called,
kpeter@809
   535
    ///   // so only the cost map have to be set again)
kpeter@809
   536
    ///   cost[e] += 100;
kpeter@809
   537
    ///   cs.costMap(cost).run();
kpeter@809
   538
    ///
kpeter@830
   539
    ///   // Run again from scratch using resetParams()
kpeter@809
   540
    ///   // (the lower bounds will be set to zero on all arcs)
kpeter@830
   541
    ///   cs.resetParams();
kpeter@809
   542
    ///   cs.upperMap(capacity).costMap(cost)
kpeter@809
   543
    ///     .supplyMap(sup).run();
kpeter@809
   544
    /// \endcode
kpeter@809
   545
    ///
kpeter@809
   546
    /// \return <tt>(*this)</tt>
kpeter@830
   547
    ///
kpeter@830
   548
    /// \see reset(), run()
kpeter@830
   549
    CostScaling& resetParams() {
kpeter@809
   550
      for (int i = 0; i != _res_node_num; ++i) {
kpeter@809
   551
        _supply[i] = 0;
kpeter@808
   552
      }
kpeter@809
   553
      int limit = _first_out[_root];
kpeter@809
   554
      for (int j = 0; j != limit; ++j) {
kpeter@809
   555
        _lower[j] = 0;
kpeter@809
   556
        _upper[j] = INF;
kpeter@809
   557
        _scost[j] = _forward[j] ? 1 : -1;
kpeter@809
   558
      }
kpeter@809
   559
      for (int j = limit; j != _res_arc_num; ++j) {
kpeter@809
   560
        _lower[j] = 0;
kpeter@809
   561
        _upper[j] = INF;
kpeter@809
   562
        _scost[j] = 0;
kpeter@809
   563
        _scost[_reverse[j]] = 0;
alpar@877
   564
      }
kpeter@809
   565
      _have_lower = false;
kpeter@809
   566
      return *this;
kpeter@808
   567
    }
kpeter@808
   568
kpeter@934
   569
    /// \brief Reset the internal data structures and all the parameters
kpeter@934
   570
    /// that have been given before.
kpeter@830
   571
    ///
kpeter@934
   572
    /// This function resets the internal data structures and all the
kpeter@934
   573
    /// paramaters that have been given before using functions \ref lowerMap(),
kpeter@934
   574
    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@830
   575
    ///
kpeter@934
   576
    /// It is useful for multiple \ref run() calls. By default, all the given
kpeter@934
   577
    /// parameters are kept for the next \ref run() call, unless
kpeter@934
   578
    /// \ref resetParams() or \ref reset() is used.
kpeter@934
   579
    /// If the underlying digraph was also modified after the construction
kpeter@934
   580
    /// of the class or the last \ref reset() call, then the \ref reset()
kpeter@934
   581
    /// function must be used, otherwise \ref resetParams() is sufficient.
kpeter@934
   582
    ///
kpeter@934
   583
    /// See \ref resetParams() for examples.
kpeter@934
   584
    ///
kpeter@830
   585
    /// \return <tt>(*this)</tt>
kpeter@934
   586
    ///
kpeter@934
   587
    /// \see resetParams(), run()
kpeter@830
   588
    CostScaling& reset() {
kpeter@830
   589
      // Resize vectors
kpeter@830
   590
      _node_num = countNodes(_graph);
kpeter@830
   591
      _arc_num = countArcs(_graph);
kpeter@830
   592
      _res_node_num = _node_num + 1;
kpeter@830
   593
      _res_arc_num = 2 * (_arc_num + _node_num);
kpeter@830
   594
      _root = _node_num;
kpeter@830
   595
kpeter@830
   596
      _first_out.resize(_res_node_num + 1);
kpeter@830
   597
      _forward.resize(_res_arc_num);
kpeter@830
   598
      _source.resize(_res_arc_num);
kpeter@830
   599
      _target.resize(_res_arc_num);
kpeter@830
   600
      _reverse.resize(_res_arc_num);
kpeter@830
   601
kpeter@830
   602
      _lower.resize(_res_arc_num);
kpeter@830
   603
      _upper.resize(_res_arc_num);
kpeter@830
   604
      _scost.resize(_res_arc_num);
kpeter@830
   605
      _supply.resize(_res_node_num);
alpar@877
   606
kpeter@830
   607
      _res_cap.resize(_res_arc_num);
kpeter@830
   608
      _cost.resize(_res_arc_num);
kpeter@830
   609
      _pi.resize(_res_node_num);
kpeter@830
   610
      _excess.resize(_res_node_num);
kpeter@830
   611
      _next_out.resize(_res_node_num);
kpeter@830
   612
kpeter@830
   613
      // Copy the graph
kpeter@830
   614
      int i = 0, j = 0, k = 2 * _arc_num + _node_num;
kpeter@830
   615
      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@830
   616
        _node_id[n] = i;
kpeter@830
   617
      }
kpeter@830
   618
      i = 0;
kpeter@830
   619
      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@830
   620
        _first_out[i] = j;
kpeter@830
   621
        for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) {
kpeter@830
   622
          _arc_idf[a] = j;
kpeter@830
   623
          _forward[j] = true;
kpeter@830
   624
          _source[j] = i;
kpeter@830
   625
          _target[j] = _node_id[_graph.runningNode(a)];
kpeter@830
   626
        }
kpeter@830
   627
        for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) {
kpeter@830
   628
          _arc_idb[a] = j;
kpeter@830
   629
          _forward[j] = false;
kpeter@830
   630
          _source[j] = i;
kpeter@830
   631
          _target[j] = _node_id[_graph.runningNode(a)];
kpeter@830
   632
        }
kpeter@830
   633
        _forward[j] = false;
kpeter@830
   634
        _source[j] = i;
kpeter@830
   635
        _target[j] = _root;
kpeter@830
   636
        _reverse[j] = k;
kpeter@830
   637
        _forward[k] = true;
kpeter@830
   638
        _source[k] = _root;
kpeter@830
   639
        _target[k] = i;
kpeter@830
   640
        _reverse[k] = j;
kpeter@830
   641
        ++j; ++k;
kpeter@830
   642
      }
kpeter@830
   643
      _first_out[i] = j;
kpeter@830
   644
      _first_out[_res_node_num] = k;
kpeter@830
   645
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@830
   646
        int fi = _arc_idf[a];
kpeter@830
   647
        int bi = _arc_idb[a];
kpeter@830
   648
        _reverse[fi] = bi;
kpeter@830
   649
        _reverse[bi] = fi;
kpeter@830
   650
      }
alpar@877
   651
kpeter@830
   652
      // Reset parameters
kpeter@830
   653
      resetParams();
kpeter@830
   654
      return *this;
kpeter@830
   655
    }
kpeter@830
   656
kpeter@808
   657
    /// @}
kpeter@808
   658
kpeter@808
   659
    /// \name Query Functions
kpeter@809
   660
    /// The results of the algorithm can be obtained using these
kpeter@808
   661
    /// functions.\n
kpeter@809
   662
    /// The \ref run() function must be called before using them.
kpeter@808
   663
kpeter@808
   664
    /// @{
kpeter@808
   665
kpeter@809
   666
    /// \brief Return the total cost of the found flow.
kpeter@808
   667
    ///
kpeter@809
   668
    /// This function returns the total cost of the found flow.
kpeter@809
   669
    /// Its complexity is O(e).
kpeter@809
   670
    ///
kpeter@809
   671
    /// \note The return type of the function can be specified as a
kpeter@809
   672
    /// template parameter. For example,
kpeter@809
   673
    /// \code
kpeter@809
   674
    ///   cs.totalCost<double>();
kpeter@809
   675
    /// \endcode
kpeter@809
   676
    /// It is useful if the total cost cannot be stored in the \c Cost
kpeter@809
   677
    /// type of the algorithm, which is the default return type of the
kpeter@809
   678
    /// function.
kpeter@808
   679
    ///
kpeter@808
   680
    /// \pre \ref run() must be called before using this function.
kpeter@809
   681
    template <typename Number>
kpeter@809
   682
    Number totalCost() const {
kpeter@809
   683
      Number c = 0;
kpeter@809
   684
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809
   685
        int i = _arc_idb[a];
kpeter@809
   686
        c += static_cast<Number>(_res_cap[i]) *
kpeter@809
   687
             (-static_cast<Number>(_scost[i]));
kpeter@809
   688
      }
kpeter@809
   689
      return c;
kpeter@808
   690
    }
kpeter@808
   691
kpeter@809
   692
#ifndef DOXYGEN
kpeter@809
   693
    Cost totalCost() const {
kpeter@809
   694
      return totalCost<Cost>();
kpeter@808
   695
    }
kpeter@809
   696
#endif
kpeter@808
   697
kpeter@808
   698
    /// \brief Return the flow on the given arc.
kpeter@808
   699
    ///
kpeter@809
   700
    /// This function returns the flow on the given arc.
kpeter@808
   701
    ///
kpeter@808
   702
    /// \pre \ref run() must be called before using this function.
kpeter@809
   703
    Value flow(const Arc& a) const {
kpeter@809
   704
      return _res_cap[_arc_idb[a]];
kpeter@808
   705
    }
kpeter@808
   706
kpeter@809
   707
    /// \brief Return the flow map (the primal solution).
kpeter@808
   708
    ///
kpeter@809
   709
    /// This function copies the flow value on each arc into the given
kpeter@809
   710
    /// map. The \c Value type of the algorithm must be convertible to
kpeter@809
   711
    /// the \c Value type of the map.
kpeter@808
   712
    ///
kpeter@808
   713
    /// \pre \ref run() must be called before using this function.
kpeter@809
   714
    template <typename FlowMap>
kpeter@809
   715
    void flowMap(FlowMap &map) const {
kpeter@809
   716
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809
   717
        map.set(a, _res_cap[_arc_idb[a]]);
kpeter@809
   718
      }
kpeter@808
   719
    }
kpeter@808
   720
kpeter@809
   721
    /// \brief Return the potential (dual value) of the given node.
kpeter@808
   722
    ///
kpeter@809
   723
    /// This function returns the potential (dual value) of the
kpeter@809
   724
    /// given node.
kpeter@808
   725
    ///
kpeter@808
   726
    /// \pre \ref run() must be called before using this function.
kpeter@809
   727
    Cost potential(const Node& n) const {
kpeter@809
   728
      return static_cast<Cost>(_pi[_node_id[n]]);
kpeter@809
   729
    }
kpeter@809
   730
kpeter@809
   731
    /// \brief Return the potential map (the dual solution).
kpeter@809
   732
    ///
kpeter@809
   733
    /// This function copies the potential (dual value) of each node
kpeter@809
   734
    /// into the given map.
kpeter@809
   735
    /// The \c Cost type of the algorithm must be convertible to the
kpeter@809
   736
    /// \c Value type of the map.
kpeter@809
   737
    ///
kpeter@809
   738
    /// \pre \ref run() must be called before using this function.
kpeter@809
   739
    template <typename PotentialMap>
kpeter@809
   740
    void potentialMap(PotentialMap &map) const {
kpeter@809
   741
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@809
   742
        map.set(n, static_cast<Cost>(_pi[_node_id[n]]));
kpeter@809
   743
      }
kpeter@808
   744
    }
kpeter@808
   745
kpeter@808
   746
    /// @}
kpeter@808
   747
kpeter@808
   748
  private:
kpeter@808
   749
kpeter@809
   750
    // Initialize the algorithm
kpeter@809
   751
    ProblemType init() {
kpeter@821
   752
      if (_res_node_num <= 1) return INFEASIBLE;
kpeter@809
   753
kpeter@809
   754
      // Check the sum of supply values
kpeter@809
   755
      _sum_supply = 0;
kpeter@809
   756
      for (int i = 0; i != _root; ++i) {
kpeter@809
   757
        _sum_supply += _supply[i];
kpeter@808
   758
      }
kpeter@809
   759
      if (_sum_supply > 0) return INFEASIBLE;
alpar@877
   760
kpeter@809
   761
kpeter@809
   762
      // Initialize vectors
kpeter@809
   763
      for (int i = 0; i != _res_node_num; ++i) {
kpeter@809
   764
        _pi[i] = 0;
kpeter@809
   765
        _excess[i] = _supply[i];
kpeter@809
   766
      }
alpar@877
   767
kpeter@809
   768
      // Remove infinite upper bounds and check negative arcs
kpeter@809
   769
      const Value MAX = std::numeric_limits<Value>::max();
kpeter@809
   770
      int last_out;
kpeter@809
   771
      if (_have_lower) {
kpeter@809
   772
        for (int i = 0; i != _root; ++i) {
kpeter@809
   773
          last_out = _first_out[i+1];
kpeter@809
   774
          for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@809
   775
            if (_forward[j]) {
kpeter@809
   776
              Value c = _scost[j] < 0 ? _upper[j] : _lower[j];
kpeter@809
   777
              if (c >= MAX) return UNBOUNDED;
kpeter@809
   778
              _excess[i] -= c;
kpeter@809
   779
              _excess[_target[j]] += c;
kpeter@809
   780
            }
kpeter@809
   781
          }
kpeter@809
   782
        }
kpeter@809
   783
      } else {
kpeter@809
   784
        for (int i = 0; i != _root; ++i) {
kpeter@809
   785
          last_out = _first_out[i+1];
kpeter@809
   786
          for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@809
   787
            if (_forward[j] && _scost[j] < 0) {
kpeter@809
   788
              Value c = _upper[j];
kpeter@809
   789
              if (c >= MAX) return UNBOUNDED;
kpeter@809
   790
              _excess[i] -= c;
kpeter@809
   791
              _excess[_target[j]] += c;
kpeter@809
   792
            }
kpeter@809
   793
          }
kpeter@809
   794
        }
kpeter@809
   795
      }
kpeter@809
   796
      Value ex, max_cap = 0;
kpeter@809
   797
      for (int i = 0; i != _res_node_num; ++i) {
kpeter@809
   798
        ex = _excess[i];
kpeter@809
   799
        _excess[i] = 0;
kpeter@809
   800
        if (ex < 0) max_cap -= ex;
kpeter@809
   801
      }
kpeter@809
   802
      for (int j = 0; j != _res_arc_num; ++j) {
kpeter@809
   803
        if (_upper[j] >= MAX) _upper[j] = max_cap;
kpeter@808
   804
      }
kpeter@808
   805
kpeter@809
   806
      // Initialize the large cost vector and the epsilon parameter
kpeter@809
   807
      _epsilon = 0;
kpeter@809
   808
      LargeCost lc;
kpeter@809
   809
      for (int i = 0; i != _root; ++i) {
kpeter@809
   810
        last_out = _first_out[i+1];
kpeter@809
   811
        for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@809
   812
          lc = static_cast<LargeCost>(_scost[j]) * _res_node_num * _alpha;
kpeter@809
   813
          _cost[j] = lc;
kpeter@809
   814
          if (lc > _epsilon) _epsilon = lc;
kpeter@809
   815
        }
kpeter@809
   816
      }
kpeter@809
   817
      _epsilon /= _alpha;
kpeter@808
   818
kpeter@809
   819
      // Initialize maps for Circulation and remove non-zero lower bounds
kpeter@809
   820
      ConstMap<Arc, Value> low(0);
kpeter@809
   821
      typedef typename Digraph::template ArcMap<Value> ValueArcMap;
kpeter@809
   822
      typedef typename Digraph::template NodeMap<Value> ValueNodeMap;
kpeter@809
   823
      ValueArcMap cap(_graph), flow(_graph);
kpeter@809
   824
      ValueNodeMap sup(_graph);
kpeter@809
   825
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@809
   826
        sup[n] = _supply[_node_id[n]];
kpeter@808
   827
      }
kpeter@809
   828
      if (_have_lower) {
kpeter@809
   829
        for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809
   830
          int j = _arc_idf[a];
kpeter@809
   831
          Value c = _lower[j];
kpeter@809
   832
          cap[a] = _upper[j] - c;
kpeter@809
   833
          sup[_graph.source(a)] -= c;
kpeter@809
   834
          sup[_graph.target(a)] += c;
kpeter@809
   835
        }
kpeter@809
   836
      } else {
kpeter@809
   837
        for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809
   838
          cap[a] = _upper[_arc_idf[a]];
kpeter@809
   839
        }
kpeter@809
   840
      }
kpeter@808
   841
kpeter@839
   842
      _sup_node_num = 0;
kpeter@839
   843
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@839
   844
        if (sup[n] > 0) ++_sup_node_num;
kpeter@839
   845
      }
kpeter@839
   846
kpeter@808
   847
      // Find a feasible flow using Circulation
kpeter@809
   848
      Circulation<Digraph, ConstMap<Arc, Value>, ValueArcMap, ValueNodeMap>
kpeter@809
   849
        circ(_graph, low, cap, sup);
kpeter@809
   850
      if (!circ.flowMap(flow).run()) return INFEASIBLE;
kpeter@809
   851
kpeter@809
   852
      // Set residual capacities and handle GEQ supply type
kpeter@809
   853
      if (_sum_supply < 0) {
kpeter@809
   854
        for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809
   855
          Value fa = flow[a];
kpeter@809
   856
          _res_cap[_arc_idf[a]] = cap[a] - fa;
kpeter@809
   857
          _res_cap[_arc_idb[a]] = fa;
kpeter@809
   858
          sup[_graph.source(a)] -= fa;
kpeter@809
   859
          sup[_graph.target(a)] += fa;
kpeter@809
   860
        }
kpeter@809
   861
        for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@809
   862
          _excess[_node_id[n]] = sup[n];
kpeter@809
   863
        }
kpeter@809
   864
        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
kpeter@809
   865
          int u = _target[a];
kpeter@809
   866
          int ra = _reverse[a];
kpeter@809
   867
          _res_cap[a] = -_sum_supply + 1;
kpeter@809
   868
          _res_cap[ra] = -_excess[u];
kpeter@809
   869
          _cost[a] = 0;
kpeter@809
   870
          _cost[ra] = 0;
kpeter@809
   871
          _excess[u] = 0;
kpeter@809
   872
        }
kpeter@809
   873
      } else {
kpeter@809
   874
        for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809
   875
          Value fa = flow[a];
kpeter@809
   876
          _res_cap[_arc_idf[a]] = cap[a] - fa;
kpeter@809
   877
          _res_cap[_arc_idb[a]] = fa;
kpeter@809
   878
        }
kpeter@809
   879
        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
kpeter@809
   880
          int ra = _reverse[a];
kpeter@839
   881
          _res_cap[a] = 0;
kpeter@809
   882
          _res_cap[ra] = 0;
kpeter@809
   883
          _cost[a] = 0;
kpeter@809
   884
          _cost[ra] = 0;
kpeter@809
   885
        }
kpeter@809
   886
      }
alpar@877
   887
alpar@877
   888
      // Initialize data structures for buckets
kpeter@839
   889
      _max_rank = _alpha * _res_node_num;
kpeter@839
   890
      _buckets.resize(_max_rank);
kpeter@839
   891
      _bucket_next.resize(_res_node_num + 1);
kpeter@839
   892
      _bucket_prev.resize(_res_node_num + 1);
kpeter@839
   893
      _rank.resize(_res_node_num + 1);
alpar@877
   894
kpeter@934
   895
      return OPTIMAL;
kpeter@934
   896
    }
kpeter@934
   897
kpeter@934
   898
    // Execute the algorithm and transform the results
kpeter@934
   899
    void start(Method method) {
kpeter@934
   900
      const int MAX_PARTIAL_PATH_LENGTH = 4;
kpeter@934
   901
kpeter@810
   902
      switch (method) {
kpeter@810
   903
        case PUSH:
kpeter@810
   904
          startPush();
kpeter@810
   905
          break;
kpeter@810
   906
        case AUGMENT:
kpeter@931
   907
          startAugment(_res_node_num - 1);
kpeter@810
   908
          break;
kpeter@810
   909
        case PARTIAL_AUGMENT:
kpeter@934
   910
          startAugment(MAX_PARTIAL_PATH_LENGTH);
kpeter@810
   911
          break;
kpeter@809
   912
      }
kpeter@809
   913
kpeter@937
   914
      // Compute node potentials (dual solution)
kpeter@937
   915
      for (int i = 0; i != _res_node_num; ++i) {
kpeter@937
   916
        _pi[i] = static_cast<Cost>(_pi[i] / (_res_node_num * _alpha));
kpeter@937
   917
      }
kpeter@937
   918
      bool optimal = true;
kpeter@937
   919
      for (int i = 0; optimal && i != _res_node_num; ++i) {
kpeter@937
   920
        LargeCost pi_i = _pi[i];
kpeter@937
   921
        int last_out = _first_out[i+1];
kpeter@937
   922
        for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@937
   923
          if (_res_cap[j] > 0 && _scost[j] + pi_i - _pi[_target[j]] < 0) {
kpeter@937
   924
            optimal = false;
kpeter@937
   925
            break;
kpeter@937
   926
          }
kpeter@809
   927
        }
kpeter@809
   928
      }
kpeter@809
   929
kpeter@937
   930
      if (!optimal) {
kpeter@937
   931
        // Compute node potentials for the original costs with BellmanFord
kpeter@937
   932
        // (if it is necessary)
kpeter@937
   933
        typedef std::pair<int, int> IntPair;
kpeter@937
   934
        StaticDigraph sgr;
kpeter@937
   935
        std::vector<IntPair> arc_vec;
kpeter@937
   936
        std::vector<LargeCost> cost_vec;
kpeter@937
   937
        LargeCostArcMap cost_map(cost_vec);
kpeter@937
   938
kpeter@937
   939
        arc_vec.clear();
kpeter@937
   940
        cost_vec.clear();
kpeter@937
   941
        for (int j = 0; j != _res_arc_num; ++j) {
kpeter@937
   942
          if (_res_cap[j] > 0) {
kpeter@937
   943
            int u = _source[j], v = _target[j];
kpeter@937
   944
            arc_vec.push_back(IntPair(u, v));
kpeter@937
   945
            cost_vec.push_back(_scost[j] + _pi[u] - _pi[v]);
kpeter@937
   946
          }
kpeter@937
   947
        }
kpeter@937
   948
        sgr.build(_res_node_num, arc_vec.begin(), arc_vec.end());
kpeter@937
   949
kpeter@937
   950
        typename BellmanFord<StaticDigraph, LargeCostArcMap>::Create
kpeter@937
   951
          bf(sgr, cost_map);
kpeter@937
   952
        bf.init(0);
kpeter@937
   953
        bf.start();
kpeter@937
   954
kpeter@937
   955
        for (int i = 0; i != _res_node_num; ++i) {
kpeter@937
   956
          _pi[i] += bf.dist(sgr.node(i));
kpeter@937
   957
        }
kpeter@937
   958
      }
kpeter@937
   959
kpeter@937
   960
      // Shift potentials to meet the requirements of the GEQ type
kpeter@937
   961
      // optimality conditions
kpeter@937
   962
      LargeCost max_pot = _pi[_root];
kpeter@937
   963
      for (int i = 0; i != _res_node_num; ++i) {
kpeter@937
   964
        if (_pi[i] > max_pot) max_pot = _pi[i];
kpeter@937
   965
      }
kpeter@937
   966
      if (max_pot != 0) {
kpeter@937
   967
        for (int i = 0; i != _res_node_num; ++i) {
kpeter@937
   968
          _pi[i] -= max_pot;
kpeter@937
   969
        }
kpeter@937
   970
      }
kpeter@809
   971
kpeter@809
   972
      // Handle non-zero lower bounds
kpeter@809
   973
      if (_have_lower) {
kpeter@809
   974
        int limit = _first_out[_root];
kpeter@809
   975
        for (int j = 0; j != limit; ++j) {
kpeter@809
   976
          if (!_forward[j]) _res_cap[j] += _lower[j];
kpeter@809
   977
        }
kpeter@809
   978
      }
kpeter@808
   979
    }
alpar@877
   980
kpeter@839
   981
    // Initialize a cost scaling phase
kpeter@839
   982
    void initPhase() {
kpeter@839
   983
      // Saturate arcs not satisfying the optimality condition
kpeter@839
   984
      for (int u = 0; u != _res_node_num; ++u) {
kpeter@839
   985
        int last_out = _first_out[u+1];
kpeter@839
   986
        LargeCost pi_u = _pi[u];
kpeter@839
   987
        for (int a = _first_out[u]; a != last_out; ++a) {
kpeter@934
   988
          Value delta = _res_cap[a];
kpeter@934
   989
          if (delta > 0) {
kpeter@934
   990
            int v = _target[a];
kpeter@934
   991
            if (_cost[a] + pi_u - _pi[v] < 0) {
kpeter@934
   992
              _excess[u] -= delta;
kpeter@934
   993
              _excess[v] += delta;
kpeter@934
   994
              _res_cap[a] = 0;
kpeter@934
   995
              _res_cap[_reverse[a]] += delta;
kpeter@934
   996
            }
kpeter@839
   997
          }
kpeter@839
   998
        }
kpeter@839
   999
      }
alpar@877
  1000
kpeter@839
  1001
      // Find active nodes (i.e. nodes with positive excess)
kpeter@839
  1002
      for (int u = 0; u != _res_node_num; ++u) {
kpeter@839
  1003
        if (_excess[u] > 0) _active_nodes.push_back(u);
kpeter@839
  1004
      }
kpeter@839
  1005
kpeter@839
  1006
      // Initialize the next arcs
kpeter@839
  1007
      for (int u = 0; u != _res_node_num; ++u) {
kpeter@839
  1008
        _next_out[u] = _first_out[u];
kpeter@839
  1009
      }
kpeter@839
  1010
    }
alpar@877
  1011
kpeter@936
  1012
    // Price (potential) refinement heuristic
kpeter@936
  1013
    bool priceRefinement() {
kpeter@839
  1014
kpeter@936
  1015
      // Stack for stroing the topological order
kpeter@936
  1016
      IntVector stack(_res_node_num);
kpeter@936
  1017
      int stack_top;
kpeter@936
  1018
kpeter@936
  1019
      // Perform phases
kpeter@936
  1020
      while (topologicalSort(stack, stack_top)) {
kpeter@936
  1021
kpeter@936
  1022
        // Compute node ranks in the acyclic admissible network and
kpeter@936
  1023
        // store the nodes in buckets
kpeter@936
  1024
        for (int i = 0; i != _res_node_num; ++i) {
kpeter@936
  1025
          _rank[i] = 0;
kpeter@839
  1026
        }
kpeter@936
  1027
        const int bucket_end = _root + 1;
kpeter@936
  1028
        for (int r = 0; r != _max_rank; ++r) {
kpeter@936
  1029
          _buckets[r] = bucket_end;
kpeter@936
  1030
        }
kpeter@936
  1031
        int top_rank = 0;
kpeter@936
  1032
        for ( ; stack_top >= 0; --stack_top) {
kpeter@936
  1033
          int u = stack[stack_top], v;
kpeter@936
  1034
          int rank_u = _rank[u];
kpeter@936
  1035
kpeter@936
  1036
          LargeCost rc, pi_u = _pi[u];
kpeter@936
  1037
          int last_out = _first_out[u+1];
kpeter@936
  1038
          for (int a = _first_out[u]; a != last_out; ++a) {
kpeter@936
  1039
            if (_res_cap[a] > 0) {
kpeter@936
  1040
              v = _target[a];
kpeter@936
  1041
              rc = _cost[a] + pi_u - _pi[v];
kpeter@936
  1042
              if (rc < 0) {
kpeter@936
  1043
                LargeCost nrc = static_cast<LargeCost>((-rc - 0.5) / _epsilon);
kpeter@936
  1044
                if (nrc < LargeCost(_max_rank)) {
kpeter@936
  1045
                  int new_rank_v = rank_u + static_cast<int>(nrc);
kpeter@936
  1046
                  if (new_rank_v > _rank[v]) {
kpeter@936
  1047
                    _rank[v] = new_rank_v;
kpeter@936
  1048
                  }
kpeter@936
  1049
                }
kpeter@936
  1050
              }
kpeter@936
  1051
            }
kpeter@936
  1052
          }
kpeter@936
  1053
kpeter@936
  1054
          if (rank_u > 0) {
kpeter@936
  1055
            top_rank = std::max(top_rank, rank_u);
kpeter@936
  1056
            int bfirst = _buckets[rank_u];
kpeter@936
  1057
            _bucket_next[u] = bfirst;
kpeter@936
  1058
            _bucket_prev[bfirst] = u;
kpeter@936
  1059
            _buckets[rank_u] = u;
kpeter@936
  1060
          }
kpeter@936
  1061
        }
kpeter@936
  1062
kpeter@936
  1063
        // Check if the current flow is epsilon-optimal
kpeter@936
  1064
        if (top_rank == 0) {
kpeter@936
  1065
          return true;
kpeter@936
  1066
        }
kpeter@936
  1067
kpeter@936
  1068
        // Process buckets in top-down order
kpeter@936
  1069
        for (int rank = top_rank; rank > 0; --rank) {
kpeter@936
  1070
          while (_buckets[rank] != bucket_end) {
kpeter@936
  1071
            // Remove the first node from the current bucket
kpeter@936
  1072
            int u = _buckets[rank];
kpeter@936
  1073
            _buckets[rank] = _bucket_next[u];
kpeter@936
  1074
kpeter@936
  1075
            // Search the outgoing arcs of u
kpeter@936
  1076
            LargeCost rc, pi_u = _pi[u];
kpeter@936
  1077
            int last_out = _first_out[u+1];
kpeter@936
  1078
            int v, old_rank_v, new_rank_v;
kpeter@936
  1079
            for (int a = _first_out[u]; a != last_out; ++a) {
kpeter@936
  1080
              if (_res_cap[a] > 0) {
kpeter@936
  1081
                v = _target[a];
kpeter@936
  1082
                old_rank_v = _rank[v];
kpeter@936
  1083
kpeter@936
  1084
                if (old_rank_v < rank) {
kpeter@936
  1085
kpeter@936
  1086
                  // Compute the new rank of node v
kpeter@936
  1087
                  rc = _cost[a] + pi_u - _pi[v];
kpeter@936
  1088
                  if (rc < 0) {
kpeter@936
  1089
                    new_rank_v = rank;
kpeter@936
  1090
                  } else {
kpeter@936
  1091
                    LargeCost nrc = rc / _epsilon;
kpeter@936
  1092
                    new_rank_v = 0;
kpeter@936
  1093
                    if (nrc < LargeCost(_max_rank)) {
kpeter@936
  1094
                      new_rank_v = rank - 1 - static_cast<int>(nrc);
kpeter@936
  1095
                    }
kpeter@936
  1096
                  }
kpeter@936
  1097
kpeter@936
  1098
                  // Change the rank of node v
kpeter@936
  1099
                  if (new_rank_v > old_rank_v) {
kpeter@936
  1100
                    _rank[v] = new_rank_v;
kpeter@936
  1101
kpeter@936
  1102
                    // Remove v from its old bucket
kpeter@936
  1103
                    if (old_rank_v > 0) {
kpeter@936
  1104
                      if (_buckets[old_rank_v] == v) {
kpeter@936
  1105
                        _buckets[old_rank_v] = _bucket_next[v];
kpeter@936
  1106
                      } else {
kpeter@936
  1107
                        int pv = _bucket_prev[v], nv = _bucket_next[v];
kpeter@936
  1108
                        _bucket_next[pv] = nv;
kpeter@936
  1109
                        _bucket_prev[nv] = pv;
kpeter@936
  1110
                      }
kpeter@936
  1111
                    }
kpeter@936
  1112
kpeter@936
  1113
                    // Insert v into its new bucket
kpeter@936
  1114
                    int nv = _buckets[new_rank_v];
kpeter@936
  1115
                    _bucket_next[v] = nv;
kpeter@936
  1116
                    _bucket_prev[nv] = v;
kpeter@936
  1117
                    _buckets[new_rank_v] = v;
kpeter@936
  1118
                  }
kpeter@936
  1119
                }
kpeter@936
  1120
              }
kpeter@936
  1121
            }
kpeter@936
  1122
kpeter@936
  1123
            // Refine potential of node u
kpeter@936
  1124
            _pi[u] -= rank * _epsilon;
kpeter@936
  1125
          }
kpeter@936
  1126
        }
kpeter@936
  1127
kpeter@839
  1128
      }
kpeter@839
  1129
kpeter@936
  1130
      return false;
kpeter@936
  1131
    }
kpeter@936
  1132
kpeter@936
  1133
    // Find and cancel cycles in the admissible network and
kpeter@936
  1134
    // determine topological order using DFS
kpeter@936
  1135
    bool topologicalSort(IntVector &stack, int &stack_top) {
kpeter@936
  1136
      const int MAX_CYCLE_CANCEL = 1;
kpeter@936
  1137
kpeter@936
  1138
      BoolVector reached(_res_node_num, false);
kpeter@936
  1139
      BoolVector processed(_res_node_num, false);
kpeter@936
  1140
      IntVector pred(_res_node_num);
kpeter@936
  1141
      for (int i = 0; i != _res_node_num; ++i) {
kpeter@936
  1142
        _next_out[i] = _first_out[i];
kpeter@839
  1143
      }
kpeter@936
  1144
      stack_top = -1;
kpeter@936
  1145
kpeter@936
  1146
      int cycle_cnt = 0;
kpeter@936
  1147
      for (int start = 0; start != _res_node_num; ++start) {
kpeter@936
  1148
        if (reached[start]) continue;
kpeter@936
  1149
kpeter@936
  1150
        // Start DFS search from this start node
kpeter@936
  1151
        pred[start] = -1;
kpeter@936
  1152
        int tip = start, v;
kpeter@936
  1153
        while (true) {
kpeter@936
  1154
          // Check the outgoing arcs of the current tip node
kpeter@936
  1155
          reached[tip] = true;
kpeter@936
  1156
          LargeCost pi_tip = _pi[tip];
kpeter@936
  1157
          int a, last_out = _first_out[tip+1];
kpeter@936
  1158
          for (a = _next_out[tip]; a != last_out; ++a) {
kpeter@936
  1159
            if (_res_cap[a] > 0) {
kpeter@936
  1160
              v = _target[a];
kpeter@936
  1161
              if (_cost[a] + pi_tip - _pi[v] < 0) {
kpeter@936
  1162
                if (!reached[v]) {
kpeter@936
  1163
                  // A new node is reached
kpeter@936
  1164
                  reached[v] = true;
kpeter@936
  1165
                  pred[v] = tip;
kpeter@936
  1166
                  _next_out[tip] = a;
kpeter@936
  1167
                  tip = v;
kpeter@936
  1168
                  a = _next_out[tip];
kpeter@936
  1169
                  last_out = _first_out[tip+1];
kpeter@936
  1170
                  break;
kpeter@936
  1171
                }
kpeter@936
  1172
                else if (!processed[v]) {
kpeter@936
  1173
                  // A cycle is found
kpeter@936
  1174
                  ++cycle_cnt;
kpeter@936
  1175
                  _next_out[tip] = a;
kpeter@936
  1176
kpeter@936
  1177
                  // Find the minimum residual capacity along the cycle
kpeter@936
  1178
                  Value d, delta = _res_cap[a];
kpeter@936
  1179
                  int u, delta_node = tip;
kpeter@936
  1180
                  for (u = tip; u != v; ) {
kpeter@936
  1181
                    u = pred[u];
kpeter@936
  1182
                    d = _res_cap[_next_out[u]];
kpeter@936
  1183
                    if (d <= delta) {
kpeter@936
  1184
                      delta = d;
kpeter@936
  1185
                      delta_node = u;
kpeter@936
  1186
                    }
kpeter@936
  1187
                  }
kpeter@936
  1188
kpeter@936
  1189
                  // Augment along the cycle
kpeter@936
  1190
                  _res_cap[a] -= delta;
kpeter@936
  1191
                  _res_cap[_reverse[a]] += delta;
kpeter@936
  1192
                  for (u = tip; u != v; ) {
kpeter@936
  1193
                    u = pred[u];
kpeter@936
  1194
                    int ca = _next_out[u];
kpeter@936
  1195
                    _res_cap[ca] -= delta;
kpeter@936
  1196
                    _res_cap[_reverse[ca]] += delta;
kpeter@936
  1197
                  }
kpeter@936
  1198
kpeter@936
  1199
                  // Check the maximum number of cycle canceling
kpeter@936
  1200
                  if (cycle_cnt >= MAX_CYCLE_CANCEL) {
kpeter@936
  1201
                    return false;
kpeter@936
  1202
                  }
kpeter@936
  1203
kpeter@936
  1204
                  // Roll back search to delta_node
kpeter@936
  1205
                  if (delta_node != tip) {
kpeter@936
  1206
                    for (u = tip; u != delta_node; u = pred[u]) {
kpeter@936
  1207
                      reached[u] = false;
kpeter@936
  1208
                    }
kpeter@936
  1209
                    tip = delta_node;
kpeter@936
  1210
                    a = _next_out[tip] + 1;
kpeter@936
  1211
                    last_out = _first_out[tip+1];
kpeter@936
  1212
                    break;
kpeter@936
  1213
                  }
kpeter@936
  1214
                }
kpeter@936
  1215
              }
kpeter@936
  1216
            }
kpeter@936
  1217
          }
kpeter@936
  1218
kpeter@936
  1219
          // Step back to the previous node
kpeter@936
  1220
          if (a == last_out) {
kpeter@936
  1221
            processed[tip] = true;
kpeter@936
  1222
            stack[++stack_top] = tip;
kpeter@936
  1223
            tip = pred[tip];
kpeter@936
  1224
            if (tip < 0) {
kpeter@936
  1225
              // Finish DFS from the current start node
kpeter@936
  1226
              break;
kpeter@936
  1227
            }
kpeter@936
  1228
            ++_next_out[tip];
kpeter@936
  1229
          }
kpeter@936
  1230
        }
kpeter@936
  1231
kpeter@936
  1232
      }
kpeter@936
  1233
kpeter@936
  1234
      return (cycle_cnt == 0);
kpeter@839
  1235
    }
kpeter@839
  1236
kpeter@839
  1237
    // Global potential update heuristic
kpeter@839
  1238
    void globalUpdate() {
kpeter@934
  1239
      const int bucket_end = _root + 1;
alpar@877
  1240
kpeter@839
  1241
      // Initialize buckets
kpeter@839
  1242
      for (int r = 0; r != _max_rank; ++r) {
kpeter@839
  1243
        _buckets[r] = bucket_end;
kpeter@839
  1244
      }
kpeter@839
  1245
      Value total_excess = 0;
kpeter@934
  1246
      int b0 = bucket_end;
kpeter@839
  1247
      for (int i = 0; i != _res_node_num; ++i) {
kpeter@839
  1248
        if (_excess[i] < 0) {
kpeter@839
  1249
          _rank[i] = 0;
kpeter@934
  1250
          _bucket_next[i] = b0;
kpeter@934
  1251
          _bucket_prev[b0] = i;
kpeter@934
  1252
          b0 = i;
kpeter@839
  1253
        } else {
kpeter@839
  1254
          total_excess += _excess[i];
kpeter@839
  1255
          _rank[i] = _max_rank;
kpeter@839
  1256
        }
kpeter@839
  1257
      }
kpeter@839
  1258
      if (total_excess == 0) return;
kpeter@934
  1259
      _buckets[0] = b0;
kpeter@839
  1260
kpeter@839
  1261
      // Search the buckets
kpeter@839
  1262
      int r = 0;
kpeter@839
  1263
      for ( ; r != _max_rank; ++r) {
kpeter@839
  1264
        while (_buckets[r] != bucket_end) {
kpeter@839
  1265
          // Remove the first node from the current bucket
kpeter@839
  1266
          int u = _buckets[r];
kpeter@839
  1267
          _buckets[r] = _bucket_next[u];
alpar@877
  1268
kpeter@839
  1269
          // Search the incomming arcs of u
kpeter@839
  1270
          LargeCost pi_u = _pi[u];
kpeter@839
  1271
          int last_out = _first_out[u+1];
kpeter@839
  1272
          for (int a = _first_out[u]; a != last_out; ++a) {
kpeter@839
  1273
            int ra = _reverse[a];
kpeter@839
  1274
            if (_res_cap[ra] > 0) {
kpeter@839
  1275
              int v = _source[ra];
kpeter@839
  1276
              int old_rank_v = _rank[v];
kpeter@839
  1277
              if (r < old_rank_v) {
kpeter@839
  1278
                // Compute the new rank of v
kpeter@839
  1279
                LargeCost nrc = (_cost[ra] + _pi[v] - pi_u) / _epsilon;
kpeter@839
  1280
                int new_rank_v = old_rank_v;
kpeter@934
  1281
                if (nrc < LargeCost(_max_rank)) {
kpeter@934
  1282
                  new_rank_v = r + 1 + static_cast<int>(nrc);
kpeter@934
  1283
                }
alpar@877
  1284
kpeter@839
  1285
                // Change the rank of v
kpeter@839
  1286
                if (new_rank_v < old_rank_v) {
kpeter@839
  1287
                  _rank[v] = new_rank_v;
kpeter@839
  1288
                  _next_out[v] = _first_out[v];
alpar@877
  1289
kpeter@839
  1290
                  // Remove v from its old bucket
kpeter@839
  1291
                  if (old_rank_v < _max_rank) {
kpeter@839
  1292
                    if (_buckets[old_rank_v] == v) {
kpeter@839
  1293
                      _buckets[old_rank_v] = _bucket_next[v];
kpeter@839
  1294
                    } else {
kpeter@934
  1295
                      int pv = _bucket_prev[v], nv = _bucket_next[v];
kpeter@934
  1296
                      _bucket_next[pv] = nv;
kpeter@934
  1297
                      _bucket_prev[nv] = pv;
kpeter@839
  1298
                    }
kpeter@839
  1299
                  }
alpar@877
  1300
kpeter@934
  1301
                  // Insert v into its new bucket
kpeter@934
  1302
                  int nv = _buckets[new_rank_v];
kpeter@934
  1303
                  _bucket_next[v] = nv;
kpeter@934
  1304
                  _bucket_prev[nv] = v;
kpeter@839
  1305
                  _buckets[new_rank_v] = v;
kpeter@839
  1306
                }
kpeter@839
  1307
              }
kpeter@839
  1308
            }
kpeter@839
  1309
          }
kpeter@839
  1310
kpeter@839
  1311
          // Finish search if there are no more active nodes
kpeter@839
  1312
          if (_excess[u] > 0) {
kpeter@839
  1313
            total_excess -= _excess[u];
kpeter@839
  1314
            if (total_excess <= 0) break;
kpeter@839
  1315
          }
kpeter@839
  1316
        }
kpeter@839
  1317
        if (total_excess <= 0) break;
kpeter@839
  1318
      }
alpar@877
  1319
kpeter@839
  1320
      // Relabel nodes
kpeter@839
  1321
      for (int u = 0; u != _res_node_num; ++u) {
kpeter@839
  1322
        int k = std::min(_rank[u], r);
kpeter@839
  1323
        if (k > 0) {
kpeter@839
  1324
          _pi[u] -= _epsilon * k;
kpeter@839
  1325
          _next_out[u] = _first_out[u];
kpeter@839
  1326
        }
kpeter@839
  1327
      }
kpeter@839
  1328
    }
kpeter@808
  1329
kpeter@810
  1330
    /// Execute the algorithm performing augment and relabel operations
kpeter@931
  1331
    void startAugment(int max_length) {
kpeter@808
  1332
      // Paramters for heuristics
kpeter@936
  1333
      const int PRICE_REFINEMENT_LIMIT = 2;
kpeter@935
  1334
      const double GLOBAL_UPDATE_FACTOR = 1.0;
kpeter@935
  1335
      const int global_update_skip = static_cast<int>(GLOBAL_UPDATE_FACTOR *
kpeter@839
  1336
        (_res_node_num + _sup_node_num * _sup_node_num));
kpeter@935
  1337
      int next_global_update_limit = global_update_skip;
alpar@877
  1338
kpeter@809
  1339
      // Perform cost scaling phases
kpeter@935
  1340
      IntVector path;
kpeter@935
  1341
      BoolVector path_arc(_res_arc_num, false);
kpeter@935
  1342
      int relabel_cnt = 0;
kpeter@936
  1343
      int eps_phase_cnt = 0;
kpeter@808
  1344
      for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
kpeter@808
  1345
                                        1 : _epsilon / _alpha )
kpeter@808
  1346
      {
kpeter@936
  1347
        ++eps_phase_cnt;
kpeter@936
  1348
kpeter@936
  1349
        // Price refinement heuristic
kpeter@936
  1350
        if (eps_phase_cnt >= PRICE_REFINEMENT_LIMIT) {
kpeter@936
  1351
          if (priceRefinement()) continue;
kpeter@808
  1352
        }
alpar@877
  1353
kpeter@839
  1354
        // Initialize current phase
kpeter@839
  1355
        initPhase();
alpar@877
  1356
kpeter@808
  1357
        // Perform partial augment and relabel operations
kpeter@809
  1358
        while (true) {
kpeter@808
  1359
          // Select an active node (FIFO selection)
kpeter@809
  1360
          while (_active_nodes.size() > 0 &&
kpeter@809
  1361
                 _excess[_active_nodes.front()] <= 0) {
kpeter@809
  1362
            _active_nodes.pop_front();
kpeter@808
  1363
          }
kpeter@809
  1364
          if (_active_nodes.size() == 0) break;
kpeter@809
  1365
          int start = _active_nodes.front();
kpeter@808
  1366
kpeter@808
  1367
          // Find an augmenting path from the start node
kpeter@809
  1368
          int tip = start;
kpeter@935
  1369
          while (int(path.size()) < max_length && _excess[tip] >= 0) {
kpeter@809
  1370
            int u;
kpeter@935
  1371
            LargeCost rc, min_red_cost = std::numeric_limits<LargeCost>::max();
kpeter@935
  1372
            LargeCost pi_tip = _pi[tip];
kpeter@839
  1373
            int last_out = _first_out[tip+1];
kpeter@809
  1374
            for (int a = _next_out[tip]; a != last_out; ++a) {
kpeter@935
  1375
              if (_res_cap[a] > 0) {
kpeter@935
  1376
                u = _target[a];
kpeter@935
  1377
                rc = _cost[a] + pi_tip - _pi[u];
kpeter@935
  1378
                if (rc < 0) {
kpeter@935
  1379
                  path.push_back(a);
kpeter@935
  1380
                  _next_out[tip] = a;
kpeter@935
  1381
                  if (path_arc[a]) {
kpeter@935
  1382
                    goto augment;   // a cycle is found, stop path search
kpeter@935
  1383
                  }
kpeter@935
  1384
                  tip = u;
kpeter@935
  1385
                  path_arc[a] = true;
kpeter@935
  1386
                  goto next_step;
kpeter@935
  1387
                }
kpeter@935
  1388
                else if (rc < min_red_cost) {
kpeter@935
  1389
                  min_red_cost = rc;
kpeter@935
  1390
                }
kpeter@808
  1391
              }
kpeter@808
  1392
            }
kpeter@808
  1393
kpeter@808
  1394
            // Relabel tip node
kpeter@839
  1395
            if (tip != start) {
kpeter@839
  1396
              int ra = _reverse[path.back()];
kpeter@935
  1397
              min_red_cost =
kpeter@935
  1398
                std::min(min_red_cost, _cost[ra] + pi_tip - _pi[_target[ra]]);
kpeter@839
  1399
            }
kpeter@935
  1400
            last_out = _next_out[tip];
kpeter@809
  1401
            for (int a = _first_out[tip]; a != last_out; ++a) {
kpeter@935
  1402
              if (_res_cap[a] > 0) {
kpeter@935
  1403
                rc = _cost[a] + pi_tip - _pi[_target[a]];
kpeter@935
  1404
                if (rc < min_red_cost) {
kpeter@935
  1405
                  min_red_cost = rc;
kpeter@935
  1406
                }
kpeter@809
  1407
              }
kpeter@808
  1408
            }
kpeter@809
  1409
            _pi[tip] -= min_red_cost + _epsilon;
kpeter@809
  1410
            _next_out[tip] = _first_out[tip];
kpeter@839
  1411
            ++relabel_cnt;
kpeter@808
  1412
kpeter@808
  1413
            // Step back
kpeter@808
  1414
            if (tip != start) {
kpeter@935
  1415
              int pa = path.back();
kpeter@935
  1416
              path_arc[pa] = false;
kpeter@935
  1417
              tip = _source[pa];
kpeter@839
  1418
              path.pop_back();
kpeter@808
  1419
            }
kpeter@808
  1420
kpeter@809
  1421
          next_step: ;
kpeter@808
  1422
          }
kpeter@808
  1423
kpeter@808
  1424
          // Augment along the found path (as much flow as possible)
kpeter@935
  1425
        augment:
kpeter@809
  1426
          Value delta;
kpeter@839
  1427
          int pa, u, v = start;
kpeter@839
  1428
          for (int i = 0; i != int(path.size()); ++i) {
kpeter@839
  1429
            pa = path[i];
kpeter@809
  1430
            u = v;
kpeter@839
  1431
            v = _target[pa];
kpeter@935
  1432
            path_arc[pa] = false;
kpeter@809
  1433
            delta = std::min(_res_cap[pa], _excess[u]);
kpeter@809
  1434
            _res_cap[pa] -= delta;
kpeter@809
  1435
            _res_cap[_reverse[pa]] += delta;
kpeter@809
  1436
            _excess[u] -= delta;
kpeter@809
  1437
            _excess[v] += delta;
kpeter@935
  1438
            if (_excess[v] > 0 && _excess[v] <= delta) {
kpeter@809
  1439
              _active_nodes.push_back(v);
kpeter@935
  1440
            }
kpeter@808
  1441
          }
kpeter@935
  1442
          path.clear();
kpeter@839
  1443
kpeter@839
  1444
          // Global update heuristic
kpeter@935
  1445
          if (relabel_cnt >= next_global_update_limit) {
kpeter@839
  1446
            globalUpdate();
kpeter@935
  1447
            next_global_update_limit += global_update_skip;
kpeter@839
  1448
          }
kpeter@808
  1449
        }
kpeter@935
  1450
kpeter@808
  1451
      }
kpeter@935
  1452
kpeter@808
  1453
    }
kpeter@808
  1454
kpeter@809
  1455
    /// Execute the algorithm performing push and relabel operations
kpeter@810
  1456
    void startPush() {
kpeter@808
  1457
      // Paramters for heuristics
kpeter@936
  1458
      const int PRICE_REFINEMENT_LIMIT = 2;
kpeter@839
  1459
      const double GLOBAL_UPDATE_FACTOR = 2.0;
kpeter@808
  1460
kpeter@935
  1461
      const int global_update_skip = static_cast<int>(GLOBAL_UPDATE_FACTOR *
kpeter@839
  1462
        (_res_node_num + _sup_node_num * _sup_node_num));
kpeter@935
  1463
      int next_global_update_limit = global_update_skip;
alpar@877
  1464
kpeter@809
  1465
      // Perform cost scaling phases
kpeter@809
  1466
      BoolVector hyper(_res_node_num, false);
kpeter@839
  1467
      LargeCostVector hyper_cost(_res_node_num);
kpeter@935
  1468
      int relabel_cnt = 0;
kpeter@936
  1469
      int eps_phase_cnt = 0;
kpeter@808
  1470
      for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
kpeter@808
  1471
                                        1 : _epsilon / _alpha )
kpeter@808
  1472
      {
kpeter@936
  1473
        ++eps_phase_cnt;
kpeter@936
  1474
kpeter@936
  1475
        // Price refinement heuristic
kpeter@936
  1476
        if (eps_phase_cnt >= PRICE_REFINEMENT_LIMIT) {
kpeter@936
  1477
          if (priceRefinement()) continue;
kpeter@808
  1478
        }
alpar@877
  1479
kpeter@839
  1480
        // Initialize current phase
kpeter@839
  1481
        initPhase();
kpeter@808
  1482
kpeter@808
  1483
        // Perform push and relabel operations
kpeter@809
  1484
        while (_active_nodes.size() > 0) {
kpeter@839
  1485
          LargeCost min_red_cost, rc, pi_n;
kpeter@809
  1486
          Value delta;
kpeter@809
  1487
          int n, t, a, last_out = _res_arc_num;
kpeter@809
  1488
kpeter@839
  1489
        next_node:
kpeter@808
  1490
          // Select an active node (FIFO selection)
kpeter@809
  1491
          n = _active_nodes.front();
kpeter@839
  1492
          last_out = _first_out[n+1];
kpeter@839
  1493
          pi_n = _pi[n];
alpar@877
  1494
kpeter@808
  1495
          // Perform push operations if there are admissible arcs
kpeter@809
  1496
          if (_excess[n] > 0) {
kpeter@809
  1497
            for (a = _next_out[n]; a != last_out; ++a) {
kpeter@809
  1498
              if (_res_cap[a] > 0 &&
kpeter@839
  1499
                  _cost[a] + pi_n - _pi[_target[a]] < 0) {
kpeter@809
  1500
                delta = std::min(_res_cap[a], _excess[n]);
kpeter@809
  1501
                t = _target[a];
kpeter@808
  1502
kpeter@808
  1503
                // Push-look-ahead heuristic
kpeter@809
  1504
                Value ahead = -_excess[t];
kpeter@839
  1505
                int last_out_t = _first_out[t+1];
kpeter@839
  1506
                LargeCost pi_t = _pi[t];
kpeter@809
  1507
                for (int ta = _next_out[t]; ta != last_out_t; ++ta) {
alpar@877
  1508
                  if (_res_cap[ta] > 0 &&
kpeter@839
  1509
                      _cost[ta] + pi_t - _pi[_target[ta]] < 0)
kpeter@809
  1510
                    ahead += _res_cap[ta];
kpeter@809
  1511
                  if (ahead >= delta) break;
kpeter@808
  1512
                }
kpeter@808
  1513
                if (ahead < 0) ahead = 0;
kpeter@808
  1514
kpeter@808
  1515
                // Push flow along the arc
kpeter@839
  1516
                if (ahead < delta && !hyper[t]) {
kpeter@809
  1517
                  _res_cap[a] -= ahead;
kpeter@809
  1518
                  _res_cap[_reverse[a]] += ahead;
kpeter@808
  1519
                  _excess[n] -= ahead;
kpeter@808
  1520
                  _excess[t] += ahead;
kpeter@809
  1521
                  _active_nodes.push_front(t);
kpeter@808
  1522
                  hyper[t] = true;
kpeter@839
  1523
                  hyper_cost[t] = _cost[a] + pi_n - pi_t;
kpeter@809
  1524
                  _next_out[n] = a;
kpeter@809
  1525
                  goto next_node;
kpeter@808
  1526
                } else {
kpeter@809
  1527
                  _res_cap[a] -= delta;
kpeter@809
  1528
                  _res_cap[_reverse[a]] += delta;
kpeter@808
  1529
                  _excess[n] -= delta;
kpeter@808
  1530
                  _excess[t] += delta;
kpeter@808
  1531
                  if (_excess[t] > 0 && _excess[t] <= delta)
kpeter@809
  1532
                    _active_nodes.push_back(t);
kpeter@808
  1533
                }
kpeter@808
  1534
kpeter@809
  1535
                if (_excess[n] == 0) {
kpeter@809
  1536
                  _next_out[n] = a;
kpeter@809
  1537
                  goto remove_nodes;
kpeter@809
  1538
                }
kpeter@808
  1539
              }
kpeter@808
  1540
            }
kpeter@809
  1541
            _next_out[n] = a;
kpeter@808
  1542
          }
kpeter@808
  1543
kpeter@808
  1544
          // Relabel the node if it is still active (or hyper)
kpeter@809
  1545
          if (_excess[n] > 0 || hyper[n]) {
kpeter@839
  1546
             min_red_cost = hyper[n] ? -hyper_cost[n] :
kpeter@839
  1547
               std::numeric_limits<LargeCost>::max();
kpeter@809
  1548
            for (int a = _first_out[n]; a != last_out; ++a) {
kpeter@935
  1549
              if (_res_cap[a] > 0) {
kpeter@935
  1550
                rc = _cost[a] + pi_n - _pi[_target[a]];
kpeter@935
  1551
                if (rc < min_red_cost) {
kpeter@935
  1552
                  min_red_cost = rc;
kpeter@935
  1553
                }
kpeter@809
  1554
              }
kpeter@808
  1555
            }
kpeter@809
  1556
            _pi[n] -= min_red_cost + _epsilon;
kpeter@839
  1557
            _next_out[n] = _first_out[n];
kpeter@808
  1558
            hyper[n] = false;
kpeter@839
  1559
            ++relabel_cnt;
kpeter@808
  1560
          }
alpar@877
  1561
kpeter@808
  1562
          // Remove nodes that are not active nor hyper
kpeter@809
  1563
        remove_nodes:
kpeter@809
  1564
          while ( _active_nodes.size() > 0 &&
kpeter@809
  1565
                  _excess[_active_nodes.front()] <= 0 &&
kpeter@809
  1566
                  !hyper[_active_nodes.front()] ) {
kpeter@809
  1567
            _active_nodes.pop_front();
kpeter@808
  1568
          }
alpar@877
  1569
kpeter@839
  1570
          // Global update heuristic
kpeter@935
  1571
          if (relabel_cnt >= next_global_update_limit) {
kpeter@839
  1572
            globalUpdate();
kpeter@839
  1573
            for (int u = 0; u != _res_node_num; ++u)
kpeter@839
  1574
              hyper[u] = false;
kpeter@935
  1575
            next_global_update_limit += global_update_skip;
kpeter@839
  1576
          }
kpeter@808
  1577
        }
kpeter@808
  1578
      }
kpeter@808
  1579
    }
kpeter@808
  1580
kpeter@808
  1581
  }; //class CostScaling
kpeter@808
  1582
kpeter@808
  1583
  ///@}
kpeter@808
  1584
kpeter@808
  1585
} //namespace lemon
kpeter@808
  1586
kpeter@808
  1587
#endif //LEMON_COST_SCALING_H