lemon/cost_scaling.h
author Alpar Juttner <alpar@cs.elte.hu>
Fri, 12 Feb 2010 21:53:15 +0100
changeset 826 02109e17027f
parent 821 072ec8120958
child 831 cc9e0c15d747
permissions -rw-r--r--
Merge
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/* -*- C++ -*-
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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) 2003-2008
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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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  /// 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 such
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  /// arcs that have 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 proved 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<char> BoolVector;
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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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  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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    // 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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    // 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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  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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      // Resize vectors
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      _node_num = countNodes(_graph);
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      _arc_num = countArcs(_graph);
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      _res_node_num = _node_num + 1;
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      _res_arc_num = 2 * (_arc_num + _node_num);
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      _root = _node_num;
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      _first_out.resize(_res_node_num + 1);
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      _forward.resize(_res_arc_num);
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      _source.resize(_res_arc_num);
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      _target.resize(_res_arc_num);
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      _reverse.resize(_res_arc_num);
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      _lower.resize(_res_arc_num);
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      _upper.resize(_res_arc_num);
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      _scost.resize(_res_arc_num);
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      _supply.resize(_res_node_num);
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      _res_cap.resize(_res_arc_num);
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      _cost.resize(_res_arc_num);
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      _pi.resize(_res_node_num);
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      _excess.resize(_res_node_num);
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      _next_out.resize(_res_node_num);
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      _arc_vec.reserve(_res_arc_num);
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      _cost_vec.reserve(_res_arc_num);
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      // Copy the graph
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      int i = 0, j = 0, k = 2 * _arc_num + _node_num;
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      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
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        _node_id[n] = i;
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      }
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      i = 0;
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      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
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        _first_out[i] = j;
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        for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) {
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          _arc_idf[a] = j;
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          _forward[j] = true;
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          _source[j] = i;
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          _target[j] = _node_id[_graph.runningNode(a)];
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        }
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        for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) {
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          _arc_idb[a] = j;
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          _forward[j] = false;
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          _source[j] = i;
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          _target[j] = _node_id[_graph.runningNode(a)];
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        }
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        _forward[j] = false;
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        _source[j] = i;
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        _target[j] = _root;
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        _reverse[j] = k;
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        _forward[k] = true;
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        _source[k] = _root;
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        _target[k] = i;
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        _reverse[k] = j;
kpeter@809
   395
        ++j; ++k;
kpeter@808
   396
      }
kpeter@809
   397
      _first_out[i] = j;
kpeter@809
   398
      _first_out[_res_node_num] = k;
kpeter@809
   399
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809
   400
        int fi = _arc_idf[a];
kpeter@809
   401
        int bi = _arc_idb[a];
kpeter@809
   402
        _reverse[fi] = bi;
kpeter@809
   403
        _reverse[bi] = fi;
kpeter@809
   404
      }
kpeter@809
   405
      
kpeter@809
   406
      // Reset parameters
kpeter@809
   407
      reset();
kpeter@808
   408
    }
kpeter@808
   409
kpeter@809
   410
    /// \name Parameters
kpeter@809
   411
    /// The parameters of the algorithm can be specified using these
kpeter@809
   412
    /// functions.
kpeter@809
   413
kpeter@809
   414
    /// @{
kpeter@809
   415
kpeter@809
   416
    /// \brief Set the lower bounds on the arcs.
kpeter@808
   417
    ///
kpeter@809
   418
    /// This function sets the lower bounds on the arcs.
kpeter@809
   419
    /// If it is not used before calling \ref run(), the lower bounds
kpeter@809
   420
    /// will be set to zero on all arcs.
kpeter@808
   421
    ///
kpeter@809
   422
    /// \param map An arc map storing the lower bounds.
kpeter@809
   423
    /// Its \c Value type must be convertible to the \c Value type
kpeter@809
   424
    /// of the algorithm.
kpeter@809
   425
    ///
kpeter@809
   426
    /// \return <tt>(*this)</tt>
kpeter@809
   427
    template <typename LowerMap>
kpeter@809
   428
    CostScaling& lowerMap(const LowerMap& map) {
kpeter@809
   429
      _have_lower = true;
kpeter@809
   430
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809
   431
        _lower[_arc_idf[a]] = map[a];
kpeter@809
   432
        _lower[_arc_idb[a]] = map[a];
kpeter@808
   433
      }
kpeter@808
   434
      return *this;
kpeter@808
   435
    }
kpeter@808
   436
kpeter@809
   437
    /// \brief Set the upper bounds (capacities) on the arcs.
kpeter@808
   438
    ///
kpeter@809
   439
    /// This function sets the upper bounds (capacities) on the arcs.
kpeter@809
   440
    /// If it is not used before calling \ref run(), the upper bounds
kpeter@809
   441
    /// will be set to \ref INF on all arcs (i.e. the flow value will be
kpeter@812
   442
    /// unbounded from above).
kpeter@808
   443
    ///
kpeter@809
   444
    /// \param map An arc map storing the upper bounds.
kpeter@809
   445
    /// Its \c Value type must be convertible to the \c Value type
kpeter@809
   446
    /// of the algorithm.
kpeter@809
   447
    ///
kpeter@809
   448
    /// \return <tt>(*this)</tt>
kpeter@809
   449
    template<typename UpperMap>
kpeter@809
   450
    CostScaling& upperMap(const UpperMap& map) {
kpeter@809
   451
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809
   452
        _upper[_arc_idf[a]] = map[a];
kpeter@808
   453
      }
kpeter@808
   454
      return *this;
kpeter@808
   455
    }
kpeter@808
   456
kpeter@809
   457
    /// \brief Set the costs of the arcs.
kpeter@809
   458
    ///
kpeter@809
   459
    /// This function sets the costs of the arcs.
kpeter@809
   460
    /// If it is not used before calling \ref run(), the costs
kpeter@809
   461
    /// will be set to \c 1 on all arcs.
kpeter@809
   462
    ///
kpeter@809
   463
    /// \param map An arc map storing the costs.
kpeter@809
   464
    /// Its \c Value type must be convertible to the \c Cost type
kpeter@809
   465
    /// of the algorithm.
kpeter@809
   466
    ///
kpeter@809
   467
    /// \return <tt>(*this)</tt>
kpeter@809
   468
    template<typename CostMap>
kpeter@809
   469
    CostScaling& costMap(const CostMap& map) {
kpeter@809
   470
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809
   471
        _scost[_arc_idf[a]] =  map[a];
kpeter@809
   472
        _scost[_arc_idb[a]] = -map[a];
kpeter@809
   473
      }
kpeter@809
   474
      return *this;
kpeter@809
   475
    }
kpeter@809
   476
kpeter@809
   477
    /// \brief Set the supply values of the nodes.
kpeter@809
   478
    ///
kpeter@809
   479
    /// This function sets the supply values of the nodes.
kpeter@809
   480
    /// If neither this function nor \ref stSupply() is used before
kpeter@809
   481
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@809
   482
    ///
kpeter@809
   483
    /// \param map A node map storing the supply values.
kpeter@809
   484
    /// Its \c Value type must be convertible to the \c Value type
kpeter@809
   485
    /// of the algorithm.
kpeter@809
   486
    ///
kpeter@809
   487
    /// \return <tt>(*this)</tt>
kpeter@809
   488
    template<typename SupplyMap>
kpeter@809
   489
    CostScaling& supplyMap(const SupplyMap& map) {
kpeter@809
   490
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@809
   491
        _supply[_node_id[n]] = map[n];
kpeter@809
   492
      }
kpeter@809
   493
      return *this;
kpeter@809
   494
    }
kpeter@809
   495
kpeter@809
   496
    /// \brief Set single source and target nodes and a supply value.
kpeter@809
   497
    ///
kpeter@809
   498
    /// This function sets a single source node and a single target node
kpeter@809
   499
    /// and the required flow value.
kpeter@809
   500
    /// If neither this function nor \ref supplyMap() is used before
kpeter@809
   501
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@809
   502
    ///
kpeter@809
   503
    /// Using this function has the same effect as using \ref supplyMap()
kpeter@809
   504
    /// with such a map in which \c k is assigned to \c s, \c -k is
kpeter@809
   505
    /// assigned to \c t and all other nodes have zero supply value.
kpeter@809
   506
    ///
kpeter@809
   507
    /// \param s The source node.
kpeter@809
   508
    /// \param t The target node.
kpeter@809
   509
    /// \param k The required amount of flow from node \c s to node \c t
kpeter@809
   510
    /// (i.e. the supply of \c s and the demand of \c t).
kpeter@809
   511
    ///
kpeter@809
   512
    /// \return <tt>(*this)</tt>
kpeter@809
   513
    CostScaling& stSupply(const Node& s, const Node& t, Value k) {
kpeter@809
   514
      for (int i = 0; i != _res_node_num; ++i) {
kpeter@809
   515
        _supply[i] = 0;
kpeter@809
   516
      }
kpeter@809
   517
      _supply[_node_id[s]] =  k;
kpeter@809
   518
      _supply[_node_id[t]] = -k;
kpeter@809
   519
      return *this;
kpeter@809
   520
    }
kpeter@809
   521
    
kpeter@809
   522
    /// @}
kpeter@809
   523
kpeter@808
   524
    /// \name Execution control
kpeter@809
   525
    /// The algorithm can be executed using \ref run().
kpeter@808
   526
kpeter@808
   527
    /// @{
kpeter@808
   528
kpeter@808
   529
    /// \brief Run the algorithm.
kpeter@808
   530
    ///
kpeter@809
   531
    /// This function runs the algorithm.
kpeter@809
   532
    /// The paramters can be specified using functions \ref lowerMap(),
kpeter@809
   533
    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@809
   534
    /// For example,
kpeter@809
   535
    /// \code
kpeter@809
   536
    ///   CostScaling<ListDigraph> cs(graph);
kpeter@809
   537
    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@809
   538
    ///     .supplyMap(sup).run();
kpeter@809
   539
    /// \endcode
kpeter@809
   540
    ///
kpeter@809
   541
    /// This function can be called more than once. All the parameters
kpeter@809
   542
    /// that have been given are kept for the next call, unless
kpeter@809
   543
    /// \ref reset() is called, thus only the modified parameters
kpeter@809
   544
    /// have to be set again. See \ref reset() for examples.
kpeter@810
   545
    /// However, the underlying digraph must not be modified after this
kpeter@810
   546
    /// class have been constructed, since it copies and extends the graph.
kpeter@808
   547
    ///
kpeter@810
   548
    /// \param method The internal method that will be used in the
kpeter@810
   549
    /// algorithm. For more information, see \ref Method.
kpeter@810
   550
    /// \param factor The cost scaling factor. It must be larger than one.
kpeter@808
   551
    ///
kpeter@809
   552
    /// \return \c INFEASIBLE if no feasible flow exists,
kpeter@809
   553
    /// \n \c OPTIMAL if the problem has optimal solution
kpeter@809
   554
    /// (i.e. it is feasible and bounded), and the algorithm has found
kpeter@809
   555
    /// optimal flow and node potentials (primal and dual solutions),
kpeter@809
   556
    /// \n \c UNBOUNDED if the digraph contains an arc of negative cost
kpeter@809
   557
    /// and infinite upper bound. It means that the objective function
kpeter@812
   558
    /// is unbounded on that arc, however, note that it could actually be
kpeter@809
   559
    /// bounded over the feasible flows, but this algroithm cannot handle
kpeter@809
   560
    /// these cases.
kpeter@809
   561
    ///
kpeter@810
   562
    /// \see ProblemType, Method
kpeter@810
   563
    ProblemType run(Method method = PARTIAL_AUGMENT, int factor = 8) {
kpeter@810
   564
      _alpha = factor;
kpeter@809
   565
      ProblemType pt = init();
kpeter@809
   566
      if (pt != OPTIMAL) return pt;
kpeter@810
   567
      start(method);
kpeter@809
   568
      return OPTIMAL;
kpeter@809
   569
    }
kpeter@809
   570
kpeter@809
   571
    /// \brief Reset all the parameters that have been given before.
kpeter@809
   572
    ///
kpeter@809
   573
    /// This function resets all the paramaters that have been given
kpeter@809
   574
    /// before using functions \ref lowerMap(), \ref upperMap(),
kpeter@809
   575
    /// \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@809
   576
    ///
kpeter@809
   577
    /// It is useful for multiple run() calls. If this function is not
kpeter@809
   578
    /// used, all the parameters given before are kept for the next
kpeter@809
   579
    /// \ref run() call.
kpeter@812
   580
    /// However, the underlying digraph must not be modified after this
kpeter@809
   581
    /// class have been constructed, since it copies and extends the graph.
kpeter@809
   582
    ///
kpeter@809
   583
    /// For example,
kpeter@809
   584
    /// \code
kpeter@809
   585
    ///   CostScaling<ListDigraph> cs(graph);
kpeter@809
   586
    ///
kpeter@809
   587
    ///   // First run
kpeter@809
   588
    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@809
   589
    ///     .supplyMap(sup).run();
kpeter@809
   590
    ///
kpeter@809
   591
    ///   // Run again with modified cost map (reset() is not called,
kpeter@809
   592
    ///   // so only the cost map have to be set again)
kpeter@809
   593
    ///   cost[e] += 100;
kpeter@809
   594
    ///   cs.costMap(cost).run();
kpeter@809
   595
    ///
kpeter@809
   596
    ///   // Run again from scratch using reset()
kpeter@809
   597
    ///   // (the lower bounds will be set to zero on all arcs)
kpeter@809
   598
    ///   cs.reset();
kpeter@809
   599
    ///   cs.upperMap(capacity).costMap(cost)
kpeter@809
   600
    ///     .supplyMap(sup).run();
kpeter@809
   601
    /// \endcode
kpeter@809
   602
    ///
kpeter@809
   603
    /// \return <tt>(*this)</tt>
kpeter@809
   604
    CostScaling& reset() {
kpeter@809
   605
      for (int i = 0; i != _res_node_num; ++i) {
kpeter@809
   606
        _supply[i] = 0;
kpeter@808
   607
      }
kpeter@809
   608
      int limit = _first_out[_root];
kpeter@809
   609
      for (int j = 0; j != limit; ++j) {
kpeter@809
   610
        _lower[j] = 0;
kpeter@809
   611
        _upper[j] = INF;
kpeter@809
   612
        _scost[j] = _forward[j] ? 1 : -1;
kpeter@809
   613
      }
kpeter@809
   614
      for (int j = limit; j != _res_arc_num; ++j) {
kpeter@809
   615
        _lower[j] = 0;
kpeter@809
   616
        _upper[j] = INF;
kpeter@809
   617
        _scost[j] = 0;
kpeter@809
   618
        _scost[_reverse[j]] = 0;
kpeter@809
   619
      }      
kpeter@809
   620
      _have_lower = false;
kpeter@809
   621
      return *this;
kpeter@808
   622
    }
kpeter@808
   623
kpeter@808
   624
    /// @}
kpeter@808
   625
kpeter@808
   626
    /// \name Query Functions
kpeter@809
   627
    /// The results of the algorithm can be obtained using these
kpeter@808
   628
    /// functions.\n
kpeter@809
   629
    /// The \ref run() function must be called before using them.
kpeter@808
   630
kpeter@808
   631
    /// @{
kpeter@808
   632
kpeter@809
   633
    /// \brief Return the total cost of the found flow.
kpeter@808
   634
    ///
kpeter@809
   635
    /// This function returns the total cost of the found flow.
kpeter@809
   636
    /// Its complexity is O(e).
kpeter@809
   637
    ///
kpeter@809
   638
    /// \note The return type of the function can be specified as a
kpeter@809
   639
    /// template parameter. For example,
kpeter@809
   640
    /// \code
kpeter@809
   641
    ///   cs.totalCost<double>();
kpeter@809
   642
    /// \endcode
kpeter@809
   643
    /// It is useful if the total cost cannot be stored in the \c Cost
kpeter@809
   644
    /// type of the algorithm, which is the default return type of the
kpeter@809
   645
    /// function.
kpeter@808
   646
    ///
kpeter@808
   647
    /// \pre \ref run() must be called before using this function.
kpeter@809
   648
    template <typename Number>
kpeter@809
   649
    Number totalCost() const {
kpeter@809
   650
      Number c = 0;
kpeter@809
   651
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809
   652
        int i = _arc_idb[a];
kpeter@809
   653
        c += static_cast<Number>(_res_cap[i]) *
kpeter@809
   654
             (-static_cast<Number>(_scost[i]));
kpeter@809
   655
      }
kpeter@809
   656
      return c;
kpeter@808
   657
    }
kpeter@808
   658
kpeter@809
   659
#ifndef DOXYGEN
kpeter@809
   660
    Cost totalCost() const {
kpeter@809
   661
      return totalCost<Cost>();
kpeter@808
   662
    }
kpeter@809
   663
#endif
kpeter@808
   664
kpeter@808
   665
    /// \brief Return the flow on the given arc.
kpeter@808
   666
    ///
kpeter@809
   667
    /// This function returns the flow on the given arc.
kpeter@808
   668
    ///
kpeter@808
   669
    /// \pre \ref run() must be called before using this function.
kpeter@809
   670
    Value flow(const Arc& a) const {
kpeter@809
   671
      return _res_cap[_arc_idb[a]];
kpeter@808
   672
    }
kpeter@808
   673
kpeter@809
   674
    /// \brief Return the flow map (the primal solution).
kpeter@808
   675
    ///
kpeter@809
   676
    /// This function copies the flow value on each arc into the given
kpeter@809
   677
    /// map. The \c Value type of the algorithm must be convertible to
kpeter@809
   678
    /// the \c Value type of the map.
kpeter@808
   679
    ///
kpeter@808
   680
    /// \pre \ref run() must be called before using this function.
kpeter@809
   681
    template <typename FlowMap>
kpeter@809
   682
    void flowMap(FlowMap &map) const {
kpeter@809
   683
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809
   684
        map.set(a, _res_cap[_arc_idb[a]]);
kpeter@809
   685
      }
kpeter@808
   686
    }
kpeter@808
   687
kpeter@809
   688
    /// \brief Return the potential (dual value) of the given node.
kpeter@808
   689
    ///
kpeter@809
   690
    /// This function returns the potential (dual value) of the
kpeter@809
   691
    /// given node.
kpeter@808
   692
    ///
kpeter@808
   693
    /// \pre \ref run() must be called before using this function.
kpeter@809
   694
    Cost potential(const Node& n) const {
kpeter@809
   695
      return static_cast<Cost>(_pi[_node_id[n]]);
kpeter@809
   696
    }
kpeter@809
   697
kpeter@809
   698
    /// \brief Return the potential map (the dual solution).
kpeter@809
   699
    ///
kpeter@809
   700
    /// This function copies the potential (dual value) of each node
kpeter@809
   701
    /// into the given map.
kpeter@809
   702
    /// The \c Cost type of the algorithm must be convertible to the
kpeter@809
   703
    /// \c Value type of the map.
kpeter@809
   704
    ///
kpeter@809
   705
    /// \pre \ref run() must be called before using this function.
kpeter@809
   706
    template <typename PotentialMap>
kpeter@809
   707
    void potentialMap(PotentialMap &map) const {
kpeter@809
   708
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@809
   709
        map.set(n, static_cast<Cost>(_pi[_node_id[n]]));
kpeter@809
   710
      }
kpeter@808
   711
    }
kpeter@808
   712
kpeter@808
   713
    /// @}
kpeter@808
   714
kpeter@808
   715
  private:
kpeter@808
   716
kpeter@809
   717
    // Initialize the algorithm
kpeter@809
   718
    ProblemType init() {
kpeter@821
   719
      if (_res_node_num <= 1) return INFEASIBLE;
kpeter@809
   720
kpeter@809
   721
      // Check the sum of supply values
kpeter@809
   722
      _sum_supply = 0;
kpeter@809
   723
      for (int i = 0; i != _root; ++i) {
kpeter@809
   724
        _sum_supply += _supply[i];
kpeter@808
   725
      }
kpeter@809
   726
      if (_sum_supply > 0) return INFEASIBLE;
kpeter@809
   727
      
kpeter@809
   728
kpeter@809
   729
      // Initialize vectors
kpeter@809
   730
      for (int i = 0; i != _res_node_num; ++i) {
kpeter@809
   731
        _pi[i] = 0;
kpeter@809
   732
        _excess[i] = _supply[i];
kpeter@809
   733
      }
kpeter@809
   734
      
kpeter@809
   735
      // Remove infinite upper bounds and check negative arcs
kpeter@809
   736
      const Value MAX = std::numeric_limits<Value>::max();
kpeter@809
   737
      int last_out;
kpeter@809
   738
      if (_have_lower) {
kpeter@809
   739
        for (int i = 0; i != _root; ++i) {
kpeter@809
   740
          last_out = _first_out[i+1];
kpeter@809
   741
          for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@809
   742
            if (_forward[j]) {
kpeter@809
   743
              Value c = _scost[j] < 0 ? _upper[j] : _lower[j];
kpeter@809
   744
              if (c >= MAX) return UNBOUNDED;
kpeter@809
   745
              _excess[i] -= c;
kpeter@809
   746
              _excess[_target[j]] += c;
kpeter@809
   747
            }
kpeter@809
   748
          }
kpeter@809
   749
        }
kpeter@809
   750
      } else {
kpeter@809
   751
        for (int i = 0; i != _root; ++i) {
kpeter@809
   752
          last_out = _first_out[i+1];
kpeter@809
   753
          for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@809
   754
            if (_forward[j] && _scost[j] < 0) {
kpeter@809
   755
              Value c = _upper[j];
kpeter@809
   756
              if (c >= MAX) return UNBOUNDED;
kpeter@809
   757
              _excess[i] -= c;
kpeter@809
   758
              _excess[_target[j]] += c;
kpeter@809
   759
            }
kpeter@809
   760
          }
kpeter@809
   761
        }
kpeter@809
   762
      }
kpeter@809
   763
      Value ex, max_cap = 0;
kpeter@809
   764
      for (int i = 0; i != _res_node_num; ++i) {
kpeter@809
   765
        ex = _excess[i];
kpeter@809
   766
        _excess[i] = 0;
kpeter@809
   767
        if (ex < 0) max_cap -= ex;
kpeter@809
   768
      }
kpeter@809
   769
      for (int j = 0; j != _res_arc_num; ++j) {
kpeter@809
   770
        if (_upper[j] >= MAX) _upper[j] = max_cap;
kpeter@808
   771
      }
kpeter@808
   772
kpeter@809
   773
      // Initialize the large cost vector and the epsilon parameter
kpeter@809
   774
      _epsilon = 0;
kpeter@809
   775
      LargeCost lc;
kpeter@809
   776
      for (int i = 0; i != _root; ++i) {
kpeter@809
   777
        last_out = _first_out[i+1];
kpeter@809
   778
        for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@809
   779
          lc = static_cast<LargeCost>(_scost[j]) * _res_node_num * _alpha;
kpeter@809
   780
          _cost[j] = lc;
kpeter@809
   781
          if (lc > _epsilon) _epsilon = lc;
kpeter@809
   782
        }
kpeter@809
   783
      }
kpeter@809
   784
      _epsilon /= _alpha;
kpeter@808
   785
kpeter@809
   786
      // Initialize maps for Circulation and remove non-zero lower bounds
kpeter@809
   787
      ConstMap<Arc, Value> low(0);
kpeter@809
   788
      typedef typename Digraph::template ArcMap<Value> ValueArcMap;
kpeter@809
   789
      typedef typename Digraph::template NodeMap<Value> ValueNodeMap;
kpeter@809
   790
      ValueArcMap cap(_graph), flow(_graph);
kpeter@809
   791
      ValueNodeMap sup(_graph);
kpeter@809
   792
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@809
   793
        sup[n] = _supply[_node_id[n]];
kpeter@808
   794
      }
kpeter@809
   795
      if (_have_lower) {
kpeter@809
   796
        for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809
   797
          int j = _arc_idf[a];
kpeter@809
   798
          Value c = _lower[j];
kpeter@809
   799
          cap[a] = _upper[j] - c;
kpeter@809
   800
          sup[_graph.source(a)] -= c;
kpeter@809
   801
          sup[_graph.target(a)] += c;
kpeter@809
   802
        }
kpeter@809
   803
      } else {
kpeter@809
   804
        for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809
   805
          cap[a] = _upper[_arc_idf[a]];
kpeter@809
   806
        }
kpeter@809
   807
      }
kpeter@808
   808
kpeter@808
   809
      // Find a feasible flow using Circulation
kpeter@809
   810
      Circulation<Digraph, ConstMap<Arc, Value>, ValueArcMap, ValueNodeMap>
kpeter@809
   811
        circ(_graph, low, cap, sup);
kpeter@809
   812
      if (!circ.flowMap(flow).run()) return INFEASIBLE;
kpeter@809
   813
kpeter@809
   814
      // Set residual capacities and handle GEQ supply type
kpeter@809
   815
      if (_sum_supply < 0) {
kpeter@809
   816
        for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809
   817
          Value fa = flow[a];
kpeter@809
   818
          _res_cap[_arc_idf[a]] = cap[a] - fa;
kpeter@809
   819
          _res_cap[_arc_idb[a]] = fa;
kpeter@809
   820
          sup[_graph.source(a)] -= fa;
kpeter@809
   821
          sup[_graph.target(a)] += fa;
kpeter@809
   822
        }
kpeter@809
   823
        for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@809
   824
          _excess[_node_id[n]] = sup[n];
kpeter@809
   825
        }
kpeter@809
   826
        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
kpeter@809
   827
          int u = _target[a];
kpeter@809
   828
          int ra = _reverse[a];
kpeter@809
   829
          _res_cap[a] = -_sum_supply + 1;
kpeter@809
   830
          _res_cap[ra] = -_excess[u];
kpeter@809
   831
          _cost[a] = 0;
kpeter@809
   832
          _cost[ra] = 0;
kpeter@809
   833
          _excess[u] = 0;
kpeter@809
   834
        }
kpeter@809
   835
      } else {
kpeter@809
   836
        for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809
   837
          Value fa = flow[a];
kpeter@809
   838
          _res_cap[_arc_idf[a]] = cap[a] - fa;
kpeter@809
   839
          _res_cap[_arc_idb[a]] = fa;
kpeter@809
   840
        }
kpeter@809
   841
        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
kpeter@809
   842
          int ra = _reverse[a];
kpeter@809
   843
          _res_cap[a] = 1;
kpeter@809
   844
          _res_cap[ra] = 0;
kpeter@809
   845
          _cost[a] = 0;
kpeter@809
   846
          _cost[ra] = 0;
kpeter@809
   847
        }
kpeter@809
   848
      }
kpeter@809
   849
      
kpeter@809
   850
      return OPTIMAL;
kpeter@809
   851
    }
kpeter@809
   852
kpeter@809
   853
    // Execute the algorithm and transform the results
kpeter@810
   854
    void start(Method method) {
kpeter@810
   855
      // Maximum path length for partial augment
kpeter@810
   856
      const int MAX_PATH_LENGTH = 4;
kpeter@810
   857
      
kpeter@809
   858
      // Execute the algorithm
kpeter@810
   859
      switch (method) {
kpeter@810
   860
        case PUSH:
kpeter@810
   861
          startPush();
kpeter@810
   862
          break;
kpeter@810
   863
        case AUGMENT:
kpeter@810
   864
          startAugment();
kpeter@810
   865
          break;
kpeter@810
   866
        case PARTIAL_AUGMENT:
kpeter@810
   867
          startAugment(MAX_PATH_LENGTH);
kpeter@810
   868
          break;
kpeter@809
   869
      }
kpeter@809
   870
kpeter@809
   871
      // Compute node potentials for the original costs
kpeter@809
   872
      _arc_vec.clear();
kpeter@809
   873
      _cost_vec.clear();
kpeter@809
   874
      for (int j = 0; j != _res_arc_num; ++j) {
kpeter@809
   875
        if (_res_cap[j] > 0) {
kpeter@809
   876
          _arc_vec.push_back(IntPair(_source[j], _target[j]));
kpeter@809
   877
          _cost_vec.push_back(_scost[j]);
kpeter@809
   878
        }
kpeter@809
   879
      }
kpeter@809
   880
      _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end());
kpeter@809
   881
kpeter@809
   882
      typename BellmanFord<StaticDigraph, LargeCostArcMap>
kpeter@809
   883
        ::template SetDistMap<LargeCostNodeMap>::Create bf(_sgr, _cost_map);
kpeter@809
   884
      bf.distMap(_pi_map);
kpeter@809
   885
      bf.init(0);
kpeter@809
   886
      bf.start();
kpeter@809
   887
kpeter@809
   888
      // Handle non-zero lower bounds
kpeter@809
   889
      if (_have_lower) {
kpeter@809
   890
        int limit = _first_out[_root];
kpeter@809
   891
        for (int j = 0; j != limit; ++j) {
kpeter@809
   892
          if (!_forward[j]) _res_cap[j] += _lower[j];
kpeter@809
   893
        }
kpeter@809
   894
      }
kpeter@808
   895
    }
kpeter@808
   896
kpeter@810
   897
    /// Execute the algorithm performing augment and relabel operations
kpeter@810
   898
    void startAugment(int max_length = std::numeric_limits<int>::max()) {
kpeter@808
   899
      // Paramters for heuristics
kpeter@809
   900
      const int BF_HEURISTIC_EPSILON_BOUND = 1000;
kpeter@809
   901
      const int BF_HEURISTIC_BOUND_FACTOR  = 3;
kpeter@808
   902
kpeter@809
   903
      // Perform cost scaling phases
kpeter@809
   904
      IntVector pred_arc(_res_node_num);
kpeter@809
   905
      std::vector<int> path_nodes;
kpeter@808
   906
      for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
kpeter@808
   907
                                        1 : _epsilon / _alpha )
kpeter@808
   908
      {
kpeter@808
   909
        // "Early Termination" heuristic: use Bellman-Ford algorithm
kpeter@808
   910
        // to check if the current flow is optimal
kpeter@808
   911
        if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) {
kpeter@809
   912
          _arc_vec.clear();
kpeter@809
   913
          _cost_vec.clear();
kpeter@809
   914
          for (int j = 0; j != _res_arc_num; ++j) {
kpeter@809
   915
            if (_res_cap[j] > 0) {
kpeter@809
   916
              _arc_vec.push_back(IntPair(_source[j], _target[j]));
kpeter@809
   917
              _cost_vec.push_back(_cost[j] + 1);
kpeter@809
   918
            }
kpeter@809
   919
          }
kpeter@809
   920
          _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end());
kpeter@809
   921
kpeter@809
   922
          BellmanFord<StaticDigraph, LargeCostArcMap> bf(_sgr, _cost_map);
kpeter@808
   923
          bf.init(0);
kpeter@808
   924
          bool done = false;
kpeter@809
   925
          int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(_res_node_num));
kpeter@808
   926
          for (int i = 0; i < K && !done; ++i)
kpeter@808
   927
            done = bf.processNextWeakRound();
kpeter@808
   928
          if (done) break;
kpeter@808
   929
        }
kpeter@809
   930
kpeter@808
   931
        // Saturate arcs not satisfying the optimality condition
kpeter@809
   932
        for (int a = 0; a != _res_arc_num; ++a) {
kpeter@809
   933
          if (_res_cap[a] > 0 &&
kpeter@809
   934
              _cost[a] + _pi[_source[a]] - _pi[_target[a]] < 0) {
kpeter@809
   935
            Value delta = _res_cap[a];
kpeter@809
   936
            _excess[_source[a]] -= delta;
kpeter@809
   937
            _excess[_target[a]] += delta;
kpeter@809
   938
            _res_cap[a] = 0;
kpeter@809
   939
            _res_cap[_reverse[a]] += delta;
kpeter@808
   940
          }
kpeter@808
   941
        }
kpeter@809
   942
        
kpeter@808
   943
        // Find active nodes (i.e. nodes with positive excess)
kpeter@809
   944
        for (int u = 0; u != _res_node_num; ++u) {
kpeter@809
   945
          if (_excess[u] > 0) _active_nodes.push_back(u);
kpeter@808
   946
        }
kpeter@808
   947
kpeter@809
   948
        // Initialize the next arcs
kpeter@809
   949
        for (int u = 0; u != _res_node_num; ++u) {
kpeter@809
   950
          _next_out[u] = _first_out[u];
kpeter@808
   951
        }
kpeter@808
   952
kpeter@808
   953
        // Perform partial augment and relabel operations
kpeter@809
   954
        while (true) {
kpeter@808
   955
          // Select an active node (FIFO selection)
kpeter@809
   956
          while (_active_nodes.size() > 0 &&
kpeter@809
   957
                 _excess[_active_nodes.front()] <= 0) {
kpeter@809
   958
            _active_nodes.pop_front();
kpeter@808
   959
          }
kpeter@809
   960
          if (_active_nodes.size() == 0) break;
kpeter@809
   961
          int start = _active_nodes.front();
kpeter@808
   962
          path_nodes.clear();
kpeter@808
   963
          path_nodes.push_back(start);
kpeter@808
   964
kpeter@808
   965
          // Find an augmenting path from the start node
kpeter@809
   966
          int tip = start;
kpeter@809
   967
          while (_excess[tip] >= 0 &&
kpeter@810
   968
                 int(path_nodes.size()) <= max_length) {
kpeter@809
   969
            int u;
kpeter@809
   970
            LargeCost min_red_cost, rc;
kpeter@809
   971
            int last_out = _sum_supply < 0 ?
kpeter@809
   972
              _first_out[tip+1] : _first_out[tip+1] - 1;
kpeter@809
   973
            for (int a = _next_out[tip]; a != last_out; ++a) {
kpeter@809
   974
              if (_res_cap[a] > 0 &&
kpeter@809
   975
                  _cost[a] + _pi[_source[a]] - _pi[_target[a]] < 0) {
kpeter@809
   976
                u = _target[a];
kpeter@809
   977
                pred_arc[u] = a;
kpeter@809
   978
                _next_out[tip] = a;
kpeter@808
   979
                tip = u;
kpeter@808
   980
                path_nodes.push_back(tip);
kpeter@808
   981
                goto next_step;
kpeter@808
   982
              }
kpeter@808
   983
            }
kpeter@808
   984
kpeter@808
   985
            // Relabel tip node
kpeter@809
   986
            min_red_cost = std::numeric_limits<LargeCost>::max() / 2;
kpeter@809
   987
            for (int a = _first_out[tip]; a != last_out; ++a) {
kpeter@809
   988
              rc = _cost[a] + _pi[_source[a]] - _pi[_target[a]];
kpeter@809
   989
              if (_res_cap[a] > 0 && rc < min_red_cost) {
kpeter@809
   990
                min_red_cost = rc;
kpeter@809
   991
              }
kpeter@808
   992
            }
kpeter@809
   993
            _pi[tip] -= min_red_cost + _epsilon;
kpeter@808
   994
kpeter@809
   995
            // Reset the next arc of tip
kpeter@809
   996
            _next_out[tip] = _first_out[tip];
kpeter@808
   997
kpeter@808
   998
            // Step back
kpeter@808
   999
            if (tip != start) {
kpeter@808
  1000
              path_nodes.pop_back();
kpeter@809
  1001
              tip = path_nodes.back();
kpeter@808
  1002
            }
kpeter@808
  1003
kpeter@809
  1004
          next_step: ;
kpeter@808
  1005
          }
kpeter@808
  1006
kpeter@808
  1007
          // Augment along the found path (as much flow as possible)
kpeter@809
  1008
          Value delta;
kpeter@809
  1009
          int u, v = path_nodes.front(), pa;
kpeter@808
  1010
          for (int i = 1; i < int(path_nodes.size()); ++i) {
kpeter@809
  1011
            u = v;
kpeter@809
  1012
            v = path_nodes[i];
kpeter@809
  1013
            pa = pred_arc[v];
kpeter@809
  1014
            delta = std::min(_res_cap[pa], _excess[u]);
kpeter@809
  1015
            _res_cap[pa] -= delta;
kpeter@809
  1016
            _res_cap[_reverse[pa]] += delta;
kpeter@809
  1017
            _excess[u] -= delta;
kpeter@809
  1018
            _excess[v] += delta;
kpeter@809
  1019
            if (_excess[v] > 0 && _excess[v] <= delta)
kpeter@809
  1020
              _active_nodes.push_back(v);
kpeter@808
  1021
          }
kpeter@808
  1022
        }
kpeter@808
  1023
      }
kpeter@808
  1024
    }
kpeter@808
  1025
kpeter@809
  1026
    /// Execute the algorithm performing push and relabel operations
kpeter@810
  1027
    void startPush() {
kpeter@808
  1028
      // Paramters for heuristics
kpeter@809
  1029
      const int BF_HEURISTIC_EPSILON_BOUND = 1000;
kpeter@809
  1030
      const int BF_HEURISTIC_BOUND_FACTOR  = 3;
kpeter@808
  1031
kpeter@809
  1032
      // Perform cost scaling phases
kpeter@809
  1033
      BoolVector hyper(_res_node_num, false);
kpeter@808
  1034
      for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
kpeter@808
  1035
                                        1 : _epsilon / _alpha )
kpeter@808
  1036
      {
kpeter@808
  1037
        // "Early Termination" heuristic: use Bellman-Ford algorithm
kpeter@808
  1038
        // to check if the current flow is optimal
kpeter@808
  1039
        if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) {
kpeter@809
  1040
          _arc_vec.clear();
kpeter@809
  1041
          _cost_vec.clear();
kpeter@809
  1042
          for (int j = 0; j != _res_arc_num; ++j) {
kpeter@809
  1043
            if (_res_cap[j] > 0) {
kpeter@809
  1044
              _arc_vec.push_back(IntPair(_source[j], _target[j]));
kpeter@809
  1045
              _cost_vec.push_back(_cost[j] + 1);
kpeter@809
  1046
            }
kpeter@809
  1047
          }
kpeter@809
  1048
          _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end());
kpeter@809
  1049
kpeter@809
  1050
          BellmanFord<StaticDigraph, LargeCostArcMap> bf(_sgr, _cost_map);
kpeter@808
  1051
          bf.init(0);
kpeter@808
  1052
          bool done = false;
kpeter@809
  1053
          int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(_res_node_num));
kpeter@808
  1054
          for (int i = 0; i < K && !done; ++i)
kpeter@808
  1055
            done = bf.processNextWeakRound();
kpeter@808
  1056
          if (done) break;
kpeter@808
  1057
        }
kpeter@808
  1058
kpeter@808
  1059
        // Saturate arcs not satisfying the optimality condition
kpeter@809
  1060
        for (int a = 0; a != _res_arc_num; ++a) {
kpeter@809
  1061
          if (_res_cap[a] > 0 &&
kpeter@809
  1062
              _cost[a] + _pi[_source[a]] - _pi[_target[a]] < 0) {
kpeter@809
  1063
            Value delta = _res_cap[a];
kpeter@809
  1064
            _excess[_source[a]] -= delta;
kpeter@809
  1065
            _excess[_target[a]] += delta;
kpeter@809
  1066
            _res_cap[a] = 0;
kpeter@809
  1067
            _res_cap[_reverse[a]] += delta;
kpeter@808
  1068
          }
kpeter@808
  1069
        }
kpeter@808
  1070
kpeter@808
  1071
        // Find active nodes (i.e. nodes with positive excess)
kpeter@809
  1072
        for (int u = 0; u != _res_node_num; ++u) {
kpeter@809
  1073
          if (_excess[u] > 0) _active_nodes.push_back(u);
kpeter@808
  1074
        }
kpeter@808
  1075
kpeter@809
  1076
        // Initialize the next arcs
kpeter@809
  1077
        for (int u = 0; u != _res_node_num; ++u) {
kpeter@809
  1078
          _next_out[u] = _first_out[u];
kpeter@808
  1079
        }
kpeter@808
  1080
kpeter@808
  1081
        // Perform push and relabel operations
kpeter@809
  1082
        while (_active_nodes.size() > 0) {
kpeter@809
  1083
          LargeCost min_red_cost, rc;
kpeter@809
  1084
          Value delta;
kpeter@809
  1085
          int n, t, a, last_out = _res_arc_num;
kpeter@809
  1086
kpeter@808
  1087
          // Select an active node (FIFO selection)
kpeter@809
  1088
        next_node:
kpeter@809
  1089
          n = _active_nodes.front();
kpeter@809
  1090
          last_out = _sum_supply < 0 ?
kpeter@809
  1091
            _first_out[n+1] : _first_out[n+1] - 1;
kpeter@808
  1092
kpeter@808
  1093
          // Perform push operations if there are admissible arcs
kpeter@809
  1094
          if (_excess[n] > 0) {
kpeter@809
  1095
            for (a = _next_out[n]; a != last_out; ++a) {
kpeter@809
  1096
              if (_res_cap[a] > 0 &&
kpeter@809
  1097
                  _cost[a] + _pi[_source[a]] - _pi[_target[a]] < 0) {
kpeter@809
  1098
                delta = std::min(_res_cap[a], _excess[n]);
kpeter@809
  1099
                t = _target[a];
kpeter@808
  1100
kpeter@808
  1101
                // Push-look-ahead heuristic
kpeter@809
  1102
                Value ahead = -_excess[t];
kpeter@809
  1103
                int last_out_t = _sum_supply < 0 ?
kpeter@809
  1104
                  _first_out[t+1] : _first_out[t+1] - 1;
kpeter@809
  1105
                for (int ta = _next_out[t]; ta != last_out_t; ++ta) {
kpeter@809
  1106
                  if (_res_cap[ta] > 0 && 
kpeter@809
  1107
                      _cost[ta] + _pi[_source[ta]] - _pi[_target[ta]] < 0)
kpeter@809
  1108
                    ahead += _res_cap[ta];
kpeter@809
  1109
                  if (ahead >= delta) break;
kpeter@808
  1110
                }
kpeter@808
  1111
                if (ahead < 0) ahead = 0;
kpeter@808
  1112
kpeter@808
  1113
                // Push flow along the arc
kpeter@808
  1114
                if (ahead < delta) {
kpeter@809
  1115
                  _res_cap[a] -= ahead;
kpeter@809
  1116
                  _res_cap[_reverse[a]] += ahead;
kpeter@808
  1117
                  _excess[n] -= ahead;
kpeter@808
  1118
                  _excess[t] += ahead;
kpeter@809
  1119
                  _active_nodes.push_front(t);
kpeter@808
  1120
                  hyper[t] = true;
kpeter@809
  1121
                  _next_out[n] = a;
kpeter@809
  1122
                  goto next_node;
kpeter@808
  1123
                } else {
kpeter@809
  1124
                  _res_cap[a] -= delta;
kpeter@809
  1125
                  _res_cap[_reverse[a]] += delta;
kpeter@808
  1126
                  _excess[n] -= delta;
kpeter@808
  1127
                  _excess[t] += delta;
kpeter@808
  1128
                  if (_excess[t] > 0 && _excess[t] <= delta)
kpeter@809
  1129
                    _active_nodes.push_back(t);
kpeter@808
  1130
                }
kpeter@808
  1131
kpeter@809
  1132
                if (_excess[n] == 0) {
kpeter@809
  1133
                  _next_out[n] = a;
kpeter@809
  1134
                  goto remove_nodes;
kpeter@809
  1135
                }
kpeter@808
  1136
              }
kpeter@808
  1137
            }
kpeter@809
  1138
            _next_out[n] = a;
kpeter@808
  1139
          }
kpeter@808
  1140
kpeter@808
  1141
          // Relabel the node if it is still active (or hyper)
kpeter@809
  1142
          if (_excess[n] > 0 || hyper[n]) {
kpeter@809
  1143
            min_red_cost = std::numeric_limits<LargeCost>::max() / 2;
kpeter@809
  1144
            for (int a = _first_out[n]; a != last_out; ++a) {
kpeter@809
  1145
              rc = _cost[a] + _pi[_source[a]] - _pi[_target[a]];
kpeter@809
  1146
              if (_res_cap[a] > 0 && rc < min_red_cost) {
kpeter@809
  1147
                min_red_cost = rc;
kpeter@809
  1148
              }
kpeter@808
  1149
            }
kpeter@809
  1150
            _pi[n] -= min_red_cost + _epsilon;
kpeter@808
  1151
            hyper[n] = false;
kpeter@808
  1152
kpeter@809
  1153
            // Reset the next arc
kpeter@809
  1154
            _next_out[n] = _first_out[n];
kpeter@808
  1155
          }
kpeter@809
  1156
        
kpeter@808
  1157
          // Remove nodes that are not active nor hyper
kpeter@809
  1158
        remove_nodes:
kpeter@809
  1159
          while ( _active_nodes.size() > 0 &&
kpeter@809
  1160
                  _excess[_active_nodes.front()] <= 0 &&
kpeter@809
  1161
                  !hyper[_active_nodes.front()] ) {
kpeter@809
  1162
            _active_nodes.pop_front();
kpeter@808
  1163
          }
kpeter@808
  1164
        }
kpeter@808
  1165
      }
kpeter@808
  1166
    }
kpeter@808
  1167
kpeter@808
  1168
  }; //class CostScaling
kpeter@808
  1169
kpeter@808
  1170
  ///@}
kpeter@808
  1171
kpeter@808
  1172
} //namespace lemon
kpeter@808
  1173
kpeter@808
  1174
#endif //LEMON_COST_SCALING_H