lemon/capacity_scaling.h
author Peter Kovacs <kpeter@inf.elte.hu>
Mon, 08 Mar 2010 08:33:41 +0100
changeset 941 a93f1a27d831
parent 911 2914b6f0fde0
child 956 141f9c0db4a3
permissions -rw-r--r--
Fix gcc 3.3 compilation error (#354)

gcc 3.3 requires that a class has a default constructor if it has
template named parameters. (That constructor can be protected.)
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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_CAPACITY_SCALING_H
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#define LEMON_CAPACITY_SCALING_H
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/// \ingroup min_cost_flow_algs
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///
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/// \file
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/// \brief Capacity Scaling algorithm for finding a minimum cost flow.
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#include <vector>
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#include <limits>
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#include <lemon/core.h>
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#include <lemon/bin_heap.h>
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namespace lemon {
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  /// \brief Default traits class of CapacityScaling algorithm.
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  ///
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  /// Default traits class of CapacityScaling 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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  template <typename GR, typename V = int, typename C = V>
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  struct CapacityScalingDefaultTraits
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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 type of the heap used for internal Dijkstra computations.
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    ///
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    /// The type of the heap used for internal Dijkstra computations.
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    /// It must conform to the \ref lemon::concepts::Heap "Heap" concept,
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    /// its priority type must be \c Cost and its cross reference type
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    /// must be \ref RangeMap "RangeMap<int>".
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    typedef BinHeap<Cost, RangeMap<int> > Heap;
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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 Capacity 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 CapacityScaling implements the capacity scaling version
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  /// of the successive shortest path algorithm for finding a
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  /// \ref min_cost_flow "minimum cost flow" \ref amo93networkflows,
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  /// \ref edmondskarp72theoretical. It is an efficient dual
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  /// solution method.
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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 CapacityScalingDefaultTraits
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  /// "CapacityScalingDefaultTraits<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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#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 = CapacityScalingDefaultTraits<GR, V, C> >
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#endif
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  class CapacityScaling
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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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    /// The type of the heap used for internal Dijkstra computations
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    typedef typename TR::Heap Heap;
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    /// The \ref CapacityScalingDefaultTraits "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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  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<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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    // 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_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 _cost;
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    ValueVector _supply;
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    ValueVector _res_cap;
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    CostVector _pi;
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    ValueVector _excess;
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    IntVector _excess_nodes;
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    IntVector _deficit_nodes;
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    Value _delta;
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    int _factor;
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    IntVector _pred;
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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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  private:
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    // Special implementation of the Dijkstra algorithm for finding
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    // shortest paths in the residual network of the digraph with
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    // respect to the reduced arc costs and modifying the node
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    // potentials according to the found distance labels.
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    class ResidualDijkstra
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    {
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    private:
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      int _node_num;
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      bool _geq;
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      const IntVector &_first_out;
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      const IntVector &_target;
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      const CostVector &_cost;
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      const ValueVector &_res_cap;
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      const ValueVector &_excess;
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      CostVector &_pi;
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      IntVector &_pred;
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      IntVector _proc_nodes;
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      CostVector _dist;
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    public:
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      ResidualDijkstra(CapacityScaling& cs) :
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        _node_num(cs._node_num), _geq(cs._sum_supply < 0),
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        _first_out(cs._first_out), _target(cs._target), _cost(cs._cost),
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        _res_cap(cs._res_cap), _excess(cs._excess), _pi(cs._pi),
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        _pred(cs._pred), _dist(cs._node_num)
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      {}
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      int run(int s, Value delta = 1) {
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        RangeMap<int> heap_cross_ref(_node_num, Heap::PRE_HEAP);
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        Heap heap(heap_cross_ref);
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        heap.push(s, 0);
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        _pred[s] = -1;
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        _proc_nodes.clear();
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        // Process nodes
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        while (!heap.empty() && _excess[heap.top()] > -delta) {
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          int u = heap.top(), v;
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          Cost d = heap.prio() + _pi[u], dn;
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          _dist[u] = heap.prio();
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          _proc_nodes.push_back(u);
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          heap.pop();
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          // Traverse outgoing residual arcs
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          int last_out = _geq ? _first_out[u+1] : _first_out[u+1] - 1;
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          for (int a = _first_out[u]; a != last_out; ++a) {
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            if (_res_cap[a] < delta) continue;
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            v = _target[a];
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            switch (heap.state(v)) {
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              case Heap::PRE_HEAP:
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                heap.push(v, d + _cost[a] - _pi[v]);
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                _pred[v] = a;
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                break;
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              case Heap::IN_HEAP:
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                dn = d + _cost[a] - _pi[v];
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                if (dn < heap[v]) {
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                  heap.decrease(v, dn);
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                  _pred[v] = a;
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                }
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                break;
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              case Heap::POST_HEAP:
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                break;
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            }
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          }
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        }
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        if (heap.empty()) return -1;
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        // Update potentials of processed nodes
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        int t = heap.top();
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        Cost dt = heap.prio();
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        for (int i = 0; i < int(_proc_nodes.size()); ++i) {
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          _pi[_proc_nodes[i]] += _dist[_proc_nodes[i]] - dt;
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        }
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        return t;
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      }
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    }; //class ResidualDijkstra
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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 SetHeapTraits : public Traits {
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      typedef T Heap;
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    };
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    /// \brief \ref named-templ-param "Named parameter" for setting
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    /// \c Heap type.
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    ///
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    /// \ref named-templ-param "Named parameter" for setting \c Heap
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    /// type, which is used for internal Dijkstra computations.
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    /// It must conform to the \ref lemon::concepts::Heap "Heap" concept,
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    /// its priority type must be \c Cost and its cross reference type
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    /// must be \ref RangeMap "RangeMap<int>".
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    template <typename T>
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    struct SetHeap
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      : public CapacityScaling<GR, V, C, SetHeapTraits<T> > {
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      typedef  CapacityScaling<GR, V, C, SetHeapTraits<T> > Create;
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    };
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    /// @}
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  protected:
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    CapacityScaling() {}
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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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    CapacityScaling(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 CapacityScaling must be signed");
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      LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
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        "The cost type of CapacityScaling 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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    CapacityScaling& 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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    CapacityScaling& 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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    ///
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    /// \param map An arc map storing the costs.
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    /// Its \c Value type must be convertible to the \c Cost 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 CostMap>
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    CapacityScaling& costMap(const CostMap& map) {
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      for (ArcIt a(_graph); a != INVALID; ++a) {
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        _cost[_arc_idf[a]] =  map[a];
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        _cost[_arc_idb[a]] = -map[a];
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      }
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      return *this;
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   396
    }
kpeter@872
   397
kpeter@872
   398
    /// \brief Set the supply values of the nodes.
kpeter@872
   399
    ///
kpeter@872
   400
    /// This function sets the supply values of the nodes.
kpeter@872
   401
    /// If neither this function nor \ref stSupply() is used before
kpeter@872
   402
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@872
   403
    ///
kpeter@872
   404
    /// \param map A node map storing the supply values.
kpeter@872
   405
    /// Its \c Value type must be convertible to the \c Value type
kpeter@872
   406
    /// of the algorithm.
kpeter@872
   407
    ///
kpeter@872
   408
    /// \return <tt>(*this)</tt>
kpeter@872
   409
    template<typename SupplyMap>
kpeter@872
   410
    CapacityScaling& supplyMap(const SupplyMap& map) {
kpeter@872
   411
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@872
   412
        _supply[_node_id[n]] = map[n];
kpeter@872
   413
      }
kpeter@872
   414
      return *this;
kpeter@872
   415
    }
kpeter@872
   416
kpeter@872
   417
    /// \brief Set single source and target nodes and a supply value.
kpeter@872
   418
    ///
kpeter@872
   419
    /// This function sets a single source node and a single target node
kpeter@872
   420
    /// and the required flow value.
kpeter@872
   421
    /// If neither this function nor \ref supplyMap() is used before
kpeter@872
   422
    /// calling \ref run(), the supply of each node will be set to zero.
kpeter@872
   423
    ///
kpeter@872
   424
    /// Using this function has the same effect as using \ref supplyMap()
kpeter@872
   425
    /// with such a map in which \c k is assigned to \c s, \c -k is
kpeter@872
   426
    /// assigned to \c t and all other nodes have zero supply value.
kpeter@872
   427
    ///
kpeter@872
   428
    /// \param s The source node.
kpeter@872
   429
    /// \param t The target node.
kpeter@872
   430
    /// \param k The required amount of flow from node \c s to node \c t
kpeter@872
   431
    /// (i.e. the supply of \c s and the demand of \c t).
kpeter@872
   432
    ///
kpeter@872
   433
    /// \return <tt>(*this)</tt>
kpeter@872
   434
    CapacityScaling& stSupply(const Node& s, const Node& t, Value k) {
kpeter@872
   435
      for (int i = 0; i != _node_num; ++i) {
kpeter@872
   436
        _supply[i] = 0;
kpeter@872
   437
      }
kpeter@872
   438
      _supply[_node_id[s]] =  k;
kpeter@872
   439
      _supply[_node_id[t]] = -k;
kpeter@872
   440
      return *this;
kpeter@872
   441
    }
kpeter@872
   442
    
kpeter@872
   443
    /// @}
kpeter@872
   444
kpeter@871
   445
    /// \name Execution control
kpeter@873
   446
    /// The algorithm can be executed using \ref run().
kpeter@871
   447
kpeter@871
   448
    /// @{
kpeter@871
   449
kpeter@871
   450
    /// \brief Run the algorithm.
kpeter@871
   451
    ///
kpeter@871
   452
    /// This function runs the algorithm.
kpeter@872
   453
    /// The paramters can be specified using functions \ref lowerMap(),
kpeter@872
   454
    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@872
   455
    /// For example,
kpeter@872
   456
    /// \code
kpeter@872
   457
    ///   CapacityScaling<ListDigraph> cs(graph);
kpeter@872
   458
    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@872
   459
    ///     .supplyMap(sup).run();
kpeter@872
   460
    /// \endcode
kpeter@872
   461
    ///
kpeter@898
   462
    /// This function can be called more than once. All the given parameters
kpeter@898
   463
    /// are kept for the next call, unless \ref resetParams() or \ref reset()
kpeter@898
   464
    /// is used, thus only the modified parameters have to be set again.
kpeter@898
   465
    /// If the underlying digraph was also modified after the construction
kpeter@898
   466
    /// of the class (or the last \ref reset() call), then the \ref reset()
kpeter@898
   467
    /// function must be called.
kpeter@871
   468
    ///
kpeter@876
   469
    /// \param factor The capacity scaling factor. It must be larger than
kpeter@876
   470
    /// one to use scaling. If it is less or equal to one, then scaling
kpeter@876
   471
    /// will be disabled.
kpeter@871
   472
    ///
kpeter@872
   473
    /// \return \c INFEASIBLE if no feasible flow exists,
kpeter@872
   474
    /// \n \c OPTIMAL if the problem has optimal solution
kpeter@872
   475
    /// (i.e. it is feasible and bounded), and the algorithm has found
kpeter@872
   476
    /// optimal flow and node potentials (primal and dual solutions),
kpeter@872
   477
    /// \n \c UNBOUNDED if the digraph contains an arc of negative cost
kpeter@872
   478
    /// and infinite upper bound. It means that the objective function
kpeter@878
   479
    /// is unbounded on that arc, however, note that it could actually be
kpeter@872
   480
    /// bounded over the feasible flows, but this algroithm cannot handle
kpeter@872
   481
    /// these cases.
kpeter@872
   482
    ///
kpeter@872
   483
    /// \see ProblemType
kpeter@898
   484
    /// \see resetParams(), reset()
kpeter@876
   485
    ProblemType run(int factor = 4) {
kpeter@876
   486
      _factor = factor;
kpeter@876
   487
      ProblemType pt = init();
kpeter@872
   488
      if (pt != OPTIMAL) return pt;
kpeter@872
   489
      return start();
kpeter@872
   490
    }
kpeter@872
   491
kpeter@872
   492
    /// \brief Reset all the parameters that have been given before.
kpeter@872
   493
    ///
kpeter@872
   494
    /// This function resets all the paramaters that have been given
kpeter@872
   495
    /// before using functions \ref lowerMap(), \ref upperMap(),
kpeter@872
   496
    /// \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@872
   497
    ///
kpeter@898
   498
    /// It is useful for multiple \ref run() calls. Basically, all the given
kpeter@898
   499
    /// parameters are kept for the next \ref run() call, unless
kpeter@898
   500
    /// \ref resetParams() or \ref reset() is used.
kpeter@898
   501
    /// If the underlying digraph was also modified after the construction
kpeter@898
   502
    /// of the class or the last \ref reset() call, then the \ref reset()
kpeter@898
   503
    /// function must be used, otherwise \ref resetParams() is sufficient.
kpeter@872
   504
    ///
kpeter@872
   505
    /// For example,
kpeter@872
   506
    /// \code
kpeter@872
   507
    ///   CapacityScaling<ListDigraph> cs(graph);
kpeter@872
   508
    ///
kpeter@872
   509
    ///   // First run
kpeter@872
   510
    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@872
   511
    ///     .supplyMap(sup).run();
kpeter@872
   512
    ///
kpeter@898
   513
    ///   // Run again with modified cost map (resetParams() is not called,
kpeter@872
   514
    ///   // so only the cost map have to be set again)
kpeter@872
   515
    ///   cost[e] += 100;
kpeter@872
   516
    ///   cs.costMap(cost).run();
kpeter@872
   517
    ///
kpeter@898
   518
    ///   // Run again from scratch using resetParams()
kpeter@872
   519
    ///   // (the lower bounds will be set to zero on all arcs)
kpeter@898
   520
    ///   cs.resetParams();
kpeter@872
   521
    ///   cs.upperMap(capacity).costMap(cost)
kpeter@872
   522
    ///     .supplyMap(sup).run();
kpeter@872
   523
    /// \endcode
kpeter@872
   524
    ///
kpeter@872
   525
    /// \return <tt>(*this)</tt>
kpeter@898
   526
    ///
kpeter@898
   527
    /// \see reset(), run()
kpeter@898
   528
    CapacityScaling& resetParams() {
kpeter@872
   529
      for (int i = 0; i != _node_num; ++i) {
kpeter@872
   530
        _supply[i] = 0;
kpeter@872
   531
      }
kpeter@872
   532
      for (int j = 0; j != _res_arc_num; ++j) {
kpeter@872
   533
        _lower[j] = 0;
kpeter@872
   534
        _upper[j] = INF;
kpeter@872
   535
        _cost[j] = _forward[j] ? 1 : -1;
kpeter@872
   536
      }
kpeter@872
   537
      _have_lower = false;
kpeter@872
   538
      return *this;
kpeter@871
   539
    }
kpeter@871
   540
kpeter@898
   541
    /// \brief Reset the internal data structures and all the parameters
kpeter@898
   542
    /// that have been given before.
kpeter@898
   543
    ///
kpeter@898
   544
    /// This function resets the internal data structures and all the
kpeter@898
   545
    /// paramaters that have been given before using functions \ref lowerMap(),
kpeter@898
   546
    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@898
   547
    ///
kpeter@898
   548
    /// It is useful for multiple \ref run() calls. Basically, all the given
kpeter@898
   549
    /// parameters are kept for the next \ref run() call, unless
kpeter@898
   550
    /// \ref resetParams() or \ref reset() is used.
kpeter@898
   551
    /// If the underlying digraph was also modified after the construction
kpeter@898
   552
    /// of the class or the last \ref reset() call, then the \ref reset()
kpeter@898
   553
    /// function must be used, otherwise \ref resetParams() is sufficient.
kpeter@898
   554
    ///
kpeter@898
   555
    /// See \ref resetParams() for examples.
kpeter@898
   556
    ///
kpeter@898
   557
    /// \return <tt>(*this)</tt>
kpeter@898
   558
    ///
kpeter@898
   559
    /// \see resetParams(), run()
kpeter@898
   560
    CapacityScaling& reset() {
kpeter@898
   561
      // Resize vectors
kpeter@898
   562
      _node_num = countNodes(_graph);
kpeter@898
   563
      _arc_num = countArcs(_graph);
kpeter@898
   564
      _res_arc_num = 2 * (_arc_num + _node_num);
kpeter@898
   565
      _root = _node_num;
kpeter@898
   566
      ++_node_num;
kpeter@898
   567
kpeter@898
   568
      _first_out.resize(_node_num + 1);
kpeter@898
   569
      _forward.resize(_res_arc_num);
kpeter@898
   570
      _source.resize(_res_arc_num);
kpeter@898
   571
      _target.resize(_res_arc_num);
kpeter@898
   572
      _reverse.resize(_res_arc_num);
kpeter@898
   573
kpeter@898
   574
      _lower.resize(_res_arc_num);
kpeter@898
   575
      _upper.resize(_res_arc_num);
kpeter@898
   576
      _cost.resize(_res_arc_num);
kpeter@898
   577
      _supply.resize(_node_num);
kpeter@898
   578
      
kpeter@898
   579
      _res_cap.resize(_res_arc_num);
kpeter@898
   580
      _pi.resize(_node_num);
kpeter@898
   581
      _excess.resize(_node_num);
kpeter@898
   582
      _pred.resize(_node_num);
kpeter@898
   583
kpeter@898
   584
      // Copy the graph
kpeter@898
   585
      int i = 0, j = 0, k = 2 * _arc_num + _node_num - 1;
kpeter@898
   586
      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@898
   587
        _node_id[n] = i;
kpeter@898
   588
      }
kpeter@898
   589
      i = 0;
kpeter@898
   590
      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@898
   591
        _first_out[i] = j;
kpeter@898
   592
        for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) {
kpeter@898
   593
          _arc_idf[a] = j;
kpeter@898
   594
          _forward[j] = true;
kpeter@898
   595
          _source[j] = i;
kpeter@898
   596
          _target[j] = _node_id[_graph.runningNode(a)];
kpeter@898
   597
        }
kpeter@898
   598
        for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) {
kpeter@898
   599
          _arc_idb[a] = j;
kpeter@898
   600
          _forward[j] = false;
kpeter@898
   601
          _source[j] = i;
kpeter@898
   602
          _target[j] = _node_id[_graph.runningNode(a)];
kpeter@898
   603
        }
kpeter@898
   604
        _forward[j] = false;
kpeter@898
   605
        _source[j] = i;
kpeter@898
   606
        _target[j] = _root;
kpeter@898
   607
        _reverse[j] = k;
kpeter@898
   608
        _forward[k] = true;
kpeter@898
   609
        _source[k] = _root;
kpeter@898
   610
        _target[k] = i;
kpeter@898
   611
        _reverse[k] = j;
kpeter@898
   612
        ++j; ++k;
kpeter@898
   613
      }
kpeter@898
   614
      _first_out[i] = j;
kpeter@898
   615
      _first_out[_node_num] = k;
kpeter@898
   616
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@898
   617
        int fi = _arc_idf[a];
kpeter@898
   618
        int bi = _arc_idb[a];
kpeter@898
   619
        _reverse[fi] = bi;
kpeter@898
   620
        _reverse[bi] = fi;
kpeter@898
   621
      }
kpeter@898
   622
      
kpeter@898
   623
      // Reset parameters
kpeter@898
   624
      resetParams();
kpeter@898
   625
      return *this;
kpeter@898
   626
    }
kpeter@898
   627
kpeter@871
   628
    /// @}
kpeter@871
   629
kpeter@871
   630
    /// \name Query Functions
kpeter@871
   631
    /// The results of the algorithm can be obtained using these
kpeter@871
   632
    /// functions.\n
kpeter@872
   633
    /// The \ref run() function must be called before using them.
kpeter@871
   634
kpeter@871
   635
    /// @{
kpeter@871
   636
kpeter@872
   637
    /// \brief Return the total cost of the found flow.
kpeter@871
   638
    ///
kpeter@872
   639
    /// This function returns the total cost of the found flow.
kpeter@872
   640
    /// Its complexity is O(e).
kpeter@872
   641
    ///
kpeter@872
   642
    /// \note The return type of the function can be specified as a
kpeter@872
   643
    /// template parameter. For example,
kpeter@872
   644
    /// \code
kpeter@872
   645
    ///   cs.totalCost<double>();
kpeter@872
   646
    /// \endcode
kpeter@872
   647
    /// It is useful if the total cost cannot be stored in the \c Cost
kpeter@872
   648
    /// type of the algorithm, which is the default return type of the
kpeter@872
   649
    /// function.
kpeter@871
   650
    ///
kpeter@871
   651
    /// \pre \ref run() must be called before using this function.
kpeter@872
   652
    template <typename Number>
kpeter@872
   653
    Number totalCost() const {
kpeter@872
   654
      Number c = 0;
kpeter@872
   655
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@872
   656
        int i = _arc_idb[a];
kpeter@872
   657
        c += static_cast<Number>(_res_cap[i]) *
kpeter@872
   658
             (-static_cast<Number>(_cost[i]));
kpeter@872
   659
      }
kpeter@872
   660
      return c;
kpeter@871
   661
    }
kpeter@871
   662
kpeter@872
   663
#ifndef DOXYGEN
kpeter@872
   664
    Cost totalCost() const {
kpeter@872
   665
      return totalCost<Cost>();
kpeter@871
   666
    }
kpeter@872
   667
#endif
kpeter@871
   668
kpeter@871
   669
    /// \brief Return the flow on the given arc.
kpeter@871
   670
    ///
kpeter@872
   671
    /// This function returns the flow on the given arc.
kpeter@871
   672
    ///
kpeter@871
   673
    /// \pre \ref run() must be called before using this function.
kpeter@872
   674
    Value flow(const Arc& a) const {
kpeter@872
   675
      return _res_cap[_arc_idb[a]];
kpeter@871
   676
    }
kpeter@871
   677
kpeter@872
   678
    /// \brief Return the flow map (the primal solution).
kpeter@871
   679
    ///
kpeter@872
   680
    /// This function copies the flow value on each arc into the given
kpeter@872
   681
    /// map. The \c Value type of the algorithm must be convertible to
kpeter@872
   682
    /// the \c Value type of the map.
kpeter@871
   683
    ///
kpeter@871
   684
    /// \pre \ref run() must be called before using this function.
kpeter@872
   685
    template <typename FlowMap>
kpeter@872
   686
    void flowMap(FlowMap &map) const {
kpeter@872
   687
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@872
   688
        map.set(a, _res_cap[_arc_idb[a]]);
kpeter@872
   689
      }
kpeter@871
   690
    }
kpeter@871
   691
kpeter@872
   692
    /// \brief Return the potential (dual value) of the given node.
kpeter@871
   693
    ///
kpeter@872
   694
    /// This function returns the potential (dual value) of the
kpeter@872
   695
    /// given node.
kpeter@871
   696
    ///
kpeter@871
   697
    /// \pre \ref run() must be called before using this function.
kpeter@872
   698
    Cost potential(const Node& n) const {
kpeter@872
   699
      return _pi[_node_id[n]];
kpeter@872
   700
    }
kpeter@872
   701
kpeter@872
   702
    /// \brief Return the potential map (the dual solution).
kpeter@872
   703
    ///
kpeter@872
   704
    /// This function copies the potential (dual value) of each node
kpeter@872
   705
    /// into the given map.
kpeter@872
   706
    /// The \c Cost type of the algorithm must be convertible to the
kpeter@872
   707
    /// \c Value type of the map.
kpeter@872
   708
    ///
kpeter@872
   709
    /// \pre \ref run() must be called before using this function.
kpeter@872
   710
    template <typename PotentialMap>
kpeter@872
   711
    void potentialMap(PotentialMap &map) const {
kpeter@872
   712
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@872
   713
        map.set(n, _pi[_node_id[n]]);
kpeter@872
   714
      }
kpeter@871
   715
    }
kpeter@871
   716
kpeter@871
   717
    /// @}
kpeter@871
   718
kpeter@871
   719
  private:
kpeter@871
   720
kpeter@872
   721
    // Initialize the algorithm
kpeter@876
   722
    ProblemType init() {
kpeter@887
   723
      if (_node_num <= 1) return INFEASIBLE;
kpeter@871
   724
kpeter@872
   725
      // Check the sum of supply values
kpeter@872
   726
      _sum_supply = 0;
kpeter@872
   727
      for (int i = 0; i != _root; ++i) {
kpeter@872
   728
        _sum_supply += _supply[i];
kpeter@871
   729
      }
kpeter@872
   730
      if (_sum_supply > 0) return INFEASIBLE;
kpeter@872
   731
      
kpeter@877
   732
      // Initialize vectors
kpeter@872
   733
      for (int i = 0; i != _root; ++i) {
kpeter@872
   734
        _pi[i] = 0;
kpeter@872
   735
        _excess[i] = _supply[i];
kpeter@871
   736
      }
kpeter@871
   737
kpeter@872
   738
      // Remove non-zero lower bounds
kpeter@877
   739
      const Value MAX = std::numeric_limits<Value>::max();
kpeter@877
   740
      int last_out;
kpeter@872
   741
      if (_have_lower) {
kpeter@872
   742
        for (int i = 0; i != _root; ++i) {
kpeter@877
   743
          last_out = _first_out[i+1];
kpeter@877
   744
          for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@872
   745
            if (_forward[j]) {
kpeter@872
   746
              Value c = _lower[j];
kpeter@872
   747
              if (c >= 0) {
kpeter@877
   748
                _res_cap[j] = _upper[j] < MAX ? _upper[j] - c : INF;
kpeter@872
   749
              } else {
kpeter@877
   750
                _res_cap[j] = _upper[j] < MAX + c ? _upper[j] - c : INF;
kpeter@872
   751
              }
kpeter@872
   752
              _excess[i] -= c;
kpeter@872
   753
              _excess[_target[j]] += c;
kpeter@872
   754
            } else {
kpeter@872
   755
              _res_cap[j] = 0;
kpeter@872
   756
            }
kpeter@872
   757
          }
kpeter@872
   758
        }
kpeter@872
   759
      } else {
kpeter@872
   760
        for (int j = 0; j != _res_arc_num; ++j) {
kpeter@872
   761
          _res_cap[j] = _forward[j] ? _upper[j] : 0;
kpeter@872
   762
        }
kpeter@872
   763
      }
kpeter@871
   764
kpeter@872
   765
      // Handle negative costs
kpeter@877
   766
      for (int i = 0; i != _root; ++i) {
kpeter@877
   767
        last_out = _first_out[i+1] - 1;
kpeter@877
   768
        for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@877
   769
          Value rc = _res_cap[j];
kpeter@877
   770
          if (_cost[j] < 0 && rc > 0) {
kpeter@877
   771
            if (rc >= MAX) return UNBOUNDED;
kpeter@877
   772
            _excess[i] -= rc;
kpeter@877
   773
            _excess[_target[j]] += rc;
kpeter@877
   774
            _res_cap[j] = 0;
kpeter@877
   775
            _res_cap[_reverse[j]] += rc;
kpeter@872
   776
          }
kpeter@872
   777
        }
kpeter@872
   778
      }
kpeter@872
   779
      
kpeter@872
   780
      // Handle GEQ supply type
kpeter@872
   781
      if (_sum_supply < 0) {
kpeter@872
   782
        _pi[_root] = 0;
kpeter@872
   783
        _excess[_root] = -_sum_supply;
kpeter@872
   784
        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
kpeter@877
   785
          int ra = _reverse[a];
kpeter@877
   786
          _res_cap[a] = -_sum_supply + 1;
kpeter@877
   787
          _res_cap[ra] = 0;
kpeter@872
   788
          _cost[a] = 0;
kpeter@877
   789
          _cost[ra] = 0;
kpeter@872
   790
        }
kpeter@872
   791
      } else {
kpeter@872
   792
        _pi[_root] = 0;
kpeter@872
   793
        _excess[_root] = 0;
kpeter@872
   794
        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
kpeter@877
   795
          int ra = _reverse[a];
kpeter@872
   796
          _res_cap[a] = 1;
kpeter@877
   797
          _res_cap[ra] = 0;
kpeter@872
   798
          _cost[a] = 0;
kpeter@877
   799
          _cost[ra] = 0;
kpeter@872
   800
        }
kpeter@872
   801
      }
kpeter@872
   802
kpeter@872
   803
      // Initialize delta value
kpeter@876
   804
      if (_factor > 1) {
kpeter@871
   805
        // With scaling
kpeter@910
   806
        Value max_sup = 0, max_dem = 0, max_cap = 0;
kpeter@910
   807
        for (int i = 0; i != _root; ++i) {
kpeter@877
   808
          Value ex = _excess[i];
kpeter@877
   809
          if ( ex > max_sup) max_sup =  ex;
kpeter@877
   810
          if (-ex > max_dem) max_dem = -ex;
kpeter@910
   811
          int last_out = _first_out[i+1] - 1;
kpeter@910
   812
          for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@910
   813
            if (_res_cap[j] > max_cap) max_cap = _res_cap[j];
kpeter@910
   814
          }
kpeter@871
   815
        }
kpeter@871
   816
        max_sup = std::min(std::min(max_sup, max_dem), max_cap);
kpeter@876
   817
        for (_delta = 1; 2 * _delta <= max_sup; _delta *= 2) ;
kpeter@871
   818
      } else {
kpeter@871
   819
        // Without scaling
kpeter@871
   820
        _delta = 1;
kpeter@871
   821
      }
kpeter@871
   822
kpeter@872
   823
      return OPTIMAL;
kpeter@871
   824
    }
kpeter@871
   825
kpeter@872
   826
    ProblemType start() {
kpeter@872
   827
      // Execute the algorithm
kpeter@872
   828
      ProblemType pt;
kpeter@871
   829
      if (_delta > 1)
kpeter@872
   830
        pt = startWithScaling();
kpeter@871
   831
      else
kpeter@872
   832
        pt = startWithoutScaling();
kpeter@872
   833
kpeter@872
   834
      // Handle non-zero lower bounds
kpeter@872
   835
      if (_have_lower) {
kpeter@877
   836
        int limit = _first_out[_root];
kpeter@877
   837
        for (int j = 0; j != limit; ++j) {
kpeter@872
   838
          if (!_forward[j]) _res_cap[j] += _lower[j];
kpeter@872
   839
        }
kpeter@872
   840
      }
kpeter@872
   841
kpeter@872
   842
      // Shift potentials if necessary
kpeter@872
   843
      Cost pr = _pi[_root];
kpeter@872
   844
      if (_sum_supply < 0 || pr > 0) {
kpeter@872
   845
        for (int i = 0; i != _node_num; ++i) {
kpeter@872
   846
          _pi[i] -= pr;
kpeter@872
   847
        }        
kpeter@872
   848
      }
kpeter@872
   849
      
kpeter@872
   850
      return pt;
kpeter@871
   851
    }
kpeter@871
   852
kpeter@872
   853
    // Execute the capacity scaling algorithm
kpeter@872
   854
    ProblemType startWithScaling() {
kpeter@873
   855
      // Perform capacity scaling phases
kpeter@872
   856
      int s, t;
kpeter@872
   857
      ResidualDijkstra _dijkstra(*this);
kpeter@871
   858
      while (true) {
kpeter@872
   859
        // Saturate all arcs not satisfying the optimality condition
kpeter@877
   860
        int last_out;
kpeter@872
   861
        for (int u = 0; u != _node_num; ++u) {
kpeter@877
   862
          last_out = _sum_supply < 0 ?
kpeter@877
   863
            _first_out[u+1] : _first_out[u+1] - 1;
kpeter@877
   864
          for (int a = _first_out[u]; a != last_out; ++a) {
kpeter@872
   865
            int v = _target[a];
kpeter@872
   866
            Cost c = _cost[a] + _pi[u] - _pi[v];
kpeter@872
   867
            Value rc = _res_cap[a];
kpeter@872
   868
            if (c < 0 && rc >= _delta) {
kpeter@872
   869
              _excess[u] -= rc;
kpeter@872
   870
              _excess[v] += rc;
kpeter@872
   871
              _res_cap[a] = 0;
kpeter@872
   872
              _res_cap[_reverse[a]] += rc;
kpeter@872
   873
            }
kpeter@871
   874
          }
kpeter@871
   875
        }
kpeter@871
   876
kpeter@872
   877
        // Find excess nodes and deficit nodes
kpeter@871
   878
        _excess_nodes.clear();
kpeter@871
   879
        _deficit_nodes.clear();
kpeter@872
   880
        for (int u = 0; u != _node_num; ++u) {
kpeter@877
   881
          Value ex = _excess[u];
kpeter@877
   882
          if (ex >=  _delta) _excess_nodes.push_back(u);
kpeter@877
   883
          if (ex <= -_delta) _deficit_nodes.push_back(u);
kpeter@871
   884
        }
kpeter@871
   885
        int next_node = 0, next_def_node = 0;
kpeter@871
   886
kpeter@872
   887
        // Find augmenting shortest paths
kpeter@871
   888
        while (next_node < int(_excess_nodes.size())) {
kpeter@872
   889
          // Check deficit nodes
kpeter@871
   890
          if (_delta > 1) {
kpeter@871
   891
            bool delta_deficit = false;
kpeter@871
   892
            for ( ; next_def_node < int(_deficit_nodes.size());
kpeter@871
   893
                    ++next_def_node ) {
kpeter@871
   894
              if (_excess[_deficit_nodes[next_def_node]] <= -_delta) {
kpeter@871
   895
                delta_deficit = true;
kpeter@871
   896
                break;
kpeter@871
   897
              }
kpeter@871
   898
            }
kpeter@871
   899
            if (!delta_deficit) break;
kpeter@871
   900
          }
kpeter@871
   901
kpeter@872
   902
          // Run Dijkstra in the residual network
kpeter@871
   903
          s = _excess_nodes[next_node];
kpeter@872
   904
          if ((t = _dijkstra.run(s, _delta)) == -1) {
kpeter@871
   905
            if (_delta > 1) {
kpeter@871
   906
              ++next_node;
kpeter@871
   907
              continue;
kpeter@871
   908
            }
kpeter@872
   909
            return INFEASIBLE;
kpeter@871
   910
          }
kpeter@871
   911
kpeter@872
   912
          // Augment along a shortest path from s to t
kpeter@872
   913
          Value d = std::min(_excess[s], -_excess[t]);
kpeter@872
   914
          int u = t;
kpeter@872
   915
          int a;
kpeter@871
   916
          if (d > _delta) {
kpeter@872
   917
            while ((a = _pred[u]) != -1) {
kpeter@872
   918
              if (_res_cap[a] < d) d = _res_cap[a];
kpeter@872
   919
              u = _source[a];
kpeter@871
   920
            }
kpeter@871
   921
          }
kpeter@871
   922
          u = t;
kpeter@872
   923
          while ((a = _pred[u]) != -1) {
kpeter@872
   924
            _res_cap[a] -= d;
kpeter@872
   925
            _res_cap[_reverse[a]] += d;
kpeter@872
   926
            u = _source[a];
kpeter@871
   927
          }
kpeter@871
   928
          _excess[s] -= d;
kpeter@871
   929
          _excess[t] += d;
kpeter@871
   930
kpeter@871
   931
          if (_excess[s] < _delta) ++next_node;
kpeter@871
   932
        }
kpeter@871
   933
kpeter@871
   934
        if (_delta == 1) break;
kpeter@876
   935
        _delta = _delta <= _factor ? 1 : _delta / _factor;
kpeter@871
   936
      }
kpeter@871
   937
kpeter@872
   938
      return OPTIMAL;
kpeter@871
   939
    }
kpeter@871
   940
kpeter@872
   941
    // Execute the successive shortest path algorithm
kpeter@872
   942
    ProblemType startWithoutScaling() {
kpeter@872
   943
      // Find excess nodes
kpeter@872
   944
      _excess_nodes.clear();
kpeter@872
   945
      for (int i = 0; i != _node_num; ++i) {
kpeter@872
   946
        if (_excess[i] > 0) _excess_nodes.push_back(i);
kpeter@872
   947
      }
kpeter@872
   948
      if (_excess_nodes.size() == 0) return OPTIMAL;
kpeter@871
   949
      int next_node = 0;
kpeter@871
   950
kpeter@872
   951
      // Find shortest paths
kpeter@872
   952
      int s, t;
kpeter@872
   953
      ResidualDijkstra _dijkstra(*this);
kpeter@871
   954
      while ( _excess[_excess_nodes[next_node]] > 0 ||
kpeter@871
   955
              ++next_node < int(_excess_nodes.size()) )
kpeter@871
   956
      {
kpeter@872
   957
        // Run Dijkstra in the residual network
kpeter@871
   958
        s = _excess_nodes[next_node];
kpeter@872
   959
        if ((t = _dijkstra.run(s)) == -1) return INFEASIBLE;
kpeter@871
   960
kpeter@872
   961
        // Augment along a shortest path from s to t
kpeter@872
   962
        Value d = std::min(_excess[s], -_excess[t]);
kpeter@872
   963
        int u = t;
kpeter@872
   964
        int a;
kpeter@871
   965
        if (d > 1) {
kpeter@872
   966
          while ((a = _pred[u]) != -1) {
kpeter@872
   967
            if (_res_cap[a] < d) d = _res_cap[a];
kpeter@872
   968
            u = _source[a];
kpeter@871
   969
          }
kpeter@871
   970
        }
kpeter@871
   971
        u = t;
kpeter@872
   972
        while ((a = _pred[u]) != -1) {
kpeter@872
   973
          _res_cap[a] -= d;
kpeter@872
   974
          _res_cap[_reverse[a]] += d;
kpeter@872
   975
          u = _source[a];
kpeter@871
   976
        }
kpeter@871
   977
        _excess[s] -= d;
kpeter@871
   978
        _excess[t] += d;
kpeter@871
   979
      }
kpeter@871
   980
kpeter@872
   981
      return OPTIMAL;
kpeter@871
   982
    }
kpeter@871
   983
kpeter@871
   984
  }; //class CapacityScaling
kpeter@871
   985
kpeter@871
   986
  ///@}
kpeter@871
   987
kpeter@871
   988
} //namespace lemon
kpeter@871
   989
kpeter@871
   990
#endif //LEMON_CAPACITY_SCALING_H