lemon/cycle_canceling.h
author Peter Kovacs <kpeter@inf.elte.hu>
Fri, 16 Oct 2009 09:35:46 +0200
changeset 857 abb95d48e89e
parent 830 75c97c3786d6
parent 839 f3bc4e9b5f3a
child 864 d3ea191c3412
permissions -rw-r--r--
Add traits class + named parameters to Suurballe (#323)

The following types can be modified using named parameters:
- FlowMap
- PotentialMap
- Path
- Heap + HeapCrossRef
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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_CYCLE_CANCELING_H
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#define LEMON_CYCLE_CANCELING_H
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/// \ingroup min_cost_flow_algs
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/// \file
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/// \brief Cycle-canceling algorithms 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/maps.h>
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#include <lemon/path.h>
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#include <lemon/math.h>
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#include <lemon/static_graph.h>
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#include <lemon/adaptors.h>
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#include <lemon/circulation.h>
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#include <lemon/bellman_ford.h>
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#include <lemon/howard.h>
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namespace lemon {
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  /// \addtogroup min_cost_flow_algs
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  /// @{
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  /// \brief Implementation of cycle-canceling algorithms for
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  /// finding a \ref min_cost_flow "minimum cost flow".
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  ///
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  /// \ref CycleCanceling implements three different cycle-canceling
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  /// algorithms for finding a \ref min_cost_flow "minimum cost flow"
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  /// \ref amo93networkflows, \ref klein67primal,
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  /// \ref goldberg89cyclecanceling.
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  /// The most efficent one (both theoretically and practically)
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  /// is the \ref CANCEL_AND_TIGHTEN "Cancel and Tighten" algorithm,
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  /// thus it is the default method.
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  /// It is strongly polynomial, but in practice, it is typically much
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  /// slower than the scaling algorithms and NetworkSimplex.
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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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  ///
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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 For more information about the three available methods,
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  /// see \ref Method.
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#ifdef DOXYGEN
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  template <typename GR, typename V, typename C>
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#else
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  template <typename GR, typename V = int, typename C = V>
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#endif
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  class CycleCanceling
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  {
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  public:
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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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  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 used method.
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    ///
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    /// Enum type containing constants for selecting the used method
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    /// for the \ref run() function.
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    ///
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    /// \ref CycleCanceling provides three different cycle-canceling
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    /// methods. By default, \ref CANCEL_AND_TIGHTEN "Cancel and Tighten"
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    /// is used, which proved to be the most efficient and the most robust
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    /// 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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      /// A simple cycle-canceling method, which uses the
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      /// \ref BellmanFord "Bellman-Ford" algorithm with limited iteration
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      /// number for detecting negative cycles in the residual network.
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      SIMPLE_CYCLE_CANCELING,
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      /// The "Minimum Mean Cycle-Canceling" algorithm, which is a
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      /// well-known strongly polynomial method
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      /// \ref goldberg89cyclecanceling. It improves along a
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      /// \ref min_mean_cycle "minimum mean cycle" in each iteration.
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      /// Its running time complexity is O(n<sup>2</sup>m<sup>3</sup>log(n)).
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      MINIMUM_MEAN_CYCLE_CANCELING,
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      /// The "Cancel And Tighten" algorithm, which can be viewed as an
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      /// improved version of the previous method
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      /// \ref goldberg89cyclecanceling.
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      /// It is faster both in theory and in practice, its running time
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      /// complexity is O(n<sup>2</sup>m<sup>2</sup>log(n)).
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      CANCEL_AND_TIGHTEN
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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<double> DoubleVector;
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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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    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, Cost> CostNodeMap;
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    typedef StaticVectorMap<StaticDigraph::Arc, Cost> CostArcMap;
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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 _cost;
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    ValueVector _supply;
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    ValueVector _res_cap;
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    CostVector _pi;
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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<Cost> _cost_vec;
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    IntVector _id_vec;
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    CostArcMap _cost_map;
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    CostNodeMap _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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    /// \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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    CycleCanceling(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 CycleCanceling must be signed");
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      LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
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        "The cost type of CycleCanceling 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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    CycleCanceling& 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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    CycleCanceling& 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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    CycleCanceling& 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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    }
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    /// \brief Set the supply values of the nodes.
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    ///
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    /// This function sets the supply values of the nodes.
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    /// If neither this function nor \ref stSupply() is used before
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    /// calling \ref run(), the supply of each node will be set to zero.
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    ///
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    /// \param map A node map storing the supply values.
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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 SupplyMap>
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    CycleCanceling& supplyMap(const SupplyMap& map) {
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      for (NodeIt n(_graph); n != INVALID; ++n) {
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        _supply[_node_id[n]] = map[n];
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      }
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      return *this;
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    }
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    /// \brief Set single source and target nodes and a supply value.
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    ///
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    /// This function sets a single source node and a single target node
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    /// and the required flow value.
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    /// If neither this function nor \ref supplyMap() is used before
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    /// calling \ref run(), the supply of each node will be set to zero.
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    ///
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    /// Using this function has the same effect as using \ref supplyMap()
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    /// with such a map in which \c k is assigned to \c s, \c -k is
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    /// assigned to \c t and all other nodes have zero supply value.
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    ///
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    /// \param s The source node.
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    /// \param t The target node.
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    /// \param k The required amount of flow from node \c s to node \c t
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    /// (i.e. the supply of \c s and the demand of \c t).
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    ///
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    /// \return <tt>(*this)</tt>
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    CycleCanceling& stSupply(const Node& s, const Node& t, Value k) {
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      for (int i = 0; i != _res_node_num; ++i) {
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        _supply[i] = 0;
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      }
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      _supply[_node_id[s]] =  k;
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      _supply[_node_id[t]] = -k;
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      return *this;
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    }
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    /// @}
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    /// \name Execution control
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    /// The algorithm can be executed using \ref run().
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kpeter@814
   375
    /// @{
kpeter@814
   376
kpeter@814
   377
    /// \brief Run the algorithm.
kpeter@814
   378
    ///
kpeter@815
   379
    /// This function runs the algorithm.
kpeter@815
   380
    /// The paramters can be specified using functions \ref lowerMap(),
kpeter@815
   381
    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@815
   382
    /// For example,
kpeter@815
   383
    /// \code
kpeter@815
   384
    ///   CycleCanceling<ListDigraph> cc(graph);
kpeter@815
   385
    ///   cc.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@815
   386
    ///     .supplyMap(sup).run();
kpeter@815
   387
    /// \endcode
kpeter@814
   388
    ///
kpeter@830
   389
    /// This function can be called more than once. All the given parameters
kpeter@830
   390
    /// are kept for the next call, unless \ref resetParams() or \ref reset()
kpeter@830
   391
    /// is used, thus only the modified parameters have to be set again.
kpeter@830
   392
    /// If the underlying digraph was also modified after the construction
kpeter@830
   393
    /// of the class (or the last \ref reset() call), then the \ref reset()
kpeter@830
   394
    /// function must be called.
kpeter@814
   395
    ///
kpeter@815
   396
    /// \param method The cycle-canceling method that will be used.
kpeter@815
   397
    /// For more information, see \ref Method.
kpeter@815
   398
    ///
kpeter@815
   399
    /// \return \c INFEASIBLE if no feasible flow exists,
kpeter@815
   400
    /// \n \c OPTIMAL if the problem has optimal solution
kpeter@815
   401
    /// (i.e. it is feasible and bounded), and the algorithm has found
kpeter@815
   402
    /// optimal flow and node potentials (primal and dual solutions),
kpeter@815
   403
    /// \n \c UNBOUNDED if the digraph contains an arc of negative cost
kpeter@815
   404
    /// and infinite upper bound. It means that the objective function
kpeter@815
   405
    /// is unbounded on that arc, however, note that it could actually be
kpeter@815
   406
    /// bounded over the feasible flows, but this algroithm cannot handle
kpeter@815
   407
    /// these cases.
kpeter@815
   408
    ///
kpeter@815
   409
    /// \see ProblemType, Method
kpeter@830
   410
    /// \see resetParams(), reset()
kpeter@815
   411
    ProblemType run(Method method = CANCEL_AND_TIGHTEN) {
kpeter@815
   412
      ProblemType pt = init();
kpeter@815
   413
      if (pt != OPTIMAL) return pt;
kpeter@815
   414
      start(method);
kpeter@815
   415
      return OPTIMAL;
kpeter@815
   416
    }
kpeter@815
   417
kpeter@815
   418
    /// \brief Reset all the parameters that have been given before.
kpeter@815
   419
    ///
kpeter@815
   420
    /// This function resets all the paramaters that have been given
kpeter@815
   421
    /// before using functions \ref lowerMap(), \ref upperMap(),
kpeter@815
   422
    /// \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@815
   423
    ///
kpeter@830
   424
    /// It is useful for multiple \ref run() calls. Basically, all the given
kpeter@830
   425
    /// parameters are kept for the next \ref run() call, unless
kpeter@830
   426
    /// \ref resetParams() or \ref reset() is used.
kpeter@830
   427
    /// If the underlying digraph was also modified after the construction
kpeter@830
   428
    /// of the class or the last \ref reset() call, then the \ref reset()
kpeter@830
   429
    /// function must be used, otherwise \ref resetParams() is sufficient.
kpeter@815
   430
    ///
kpeter@815
   431
    /// For example,
kpeter@815
   432
    /// \code
kpeter@815
   433
    ///   CycleCanceling<ListDigraph> cs(graph);
kpeter@815
   434
    ///
kpeter@815
   435
    ///   // First run
kpeter@815
   436
    ///   cc.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@815
   437
    ///     .supplyMap(sup).run();
kpeter@815
   438
    ///
kpeter@830
   439
    ///   // Run again with modified cost map (resetParams() is not called,
kpeter@815
   440
    ///   // so only the cost map have to be set again)
kpeter@815
   441
    ///   cost[e] += 100;
kpeter@815
   442
    ///   cc.costMap(cost).run();
kpeter@815
   443
    ///
kpeter@830
   444
    ///   // Run again from scratch using resetParams()
kpeter@815
   445
    ///   // (the lower bounds will be set to zero on all arcs)
kpeter@830
   446
    ///   cc.resetParams();
kpeter@815
   447
    ///   cc.upperMap(capacity).costMap(cost)
kpeter@815
   448
    ///     .supplyMap(sup).run();
kpeter@815
   449
    /// \endcode
kpeter@815
   450
    ///
kpeter@815
   451
    /// \return <tt>(*this)</tt>
kpeter@830
   452
    ///
kpeter@830
   453
    /// \see reset(), run()
kpeter@830
   454
    CycleCanceling& resetParams() {
kpeter@815
   455
      for (int i = 0; i != _res_node_num; ++i) {
kpeter@815
   456
        _supply[i] = 0;
kpeter@815
   457
      }
kpeter@815
   458
      int limit = _first_out[_root];
kpeter@815
   459
      for (int j = 0; j != limit; ++j) {
kpeter@815
   460
        _lower[j] = 0;
kpeter@815
   461
        _upper[j] = INF;
kpeter@815
   462
        _cost[j] = _forward[j] ? 1 : -1;
kpeter@815
   463
      }
kpeter@815
   464
      for (int j = limit; j != _res_arc_num; ++j) {
kpeter@815
   465
        _lower[j] = 0;
kpeter@815
   466
        _upper[j] = INF;
kpeter@815
   467
        _cost[j] = 0;
kpeter@815
   468
        _cost[_reverse[j]] = 0;
kpeter@815
   469
      }      
kpeter@815
   470
      _have_lower = false;
kpeter@815
   471
      return *this;
kpeter@814
   472
    }
kpeter@814
   473
kpeter@830
   474
    /// \brief Reset the internal data structures and all the parameters
kpeter@830
   475
    /// that have been given before.
kpeter@830
   476
    ///
kpeter@830
   477
    /// This function resets the internal data structures and all the
kpeter@830
   478
    /// paramaters that have been given before using functions \ref lowerMap(),
kpeter@830
   479
    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@830
   480
    ///
kpeter@830
   481
    /// It is useful for multiple \ref run() calls. Basically, all the given
kpeter@830
   482
    /// parameters are kept for the next \ref run() call, unless
kpeter@830
   483
    /// \ref resetParams() or \ref reset() is used.
kpeter@830
   484
    /// If the underlying digraph was also modified after the construction
kpeter@830
   485
    /// of the class or the last \ref reset() call, then the \ref reset()
kpeter@830
   486
    /// function must be used, otherwise \ref resetParams() is sufficient.
kpeter@830
   487
    ///
kpeter@830
   488
    /// See \ref resetParams() for examples.
kpeter@830
   489
    ///
kpeter@830
   490
    /// \return <tt>(*this)</tt>
kpeter@830
   491
    ///
kpeter@830
   492
    /// \see resetParams(), run()
kpeter@830
   493
    CycleCanceling& reset() {
kpeter@830
   494
      // Resize vectors
kpeter@830
   495
      _node_num = countNodes(_graph);
kpeter@830
   496
      _arc_num = countArcs(_graph);
kpeter@830
   497
      _res_node_num = _node_num + 1;
kpeter@830
   498
      _res_arc_num = 2 * (_arc_num + _node_num);
kpeter@830
   499
      _root = _node_num;
kpeter@830
   500
kpeter@830
   501
      _first_out.resize(_res_node_num + 1);
kpeter@830
   502
      _forward.resize(_res_arc_num);
kpeter@830
   503
      _source.resize(_res_arc_num);
kpeter@830
   504
      _target.resize(_res_arc_num);
kpeter@830
   505
      _reverse.resize(_res_arc_num);
kpeter@830
   506
kpeter@830
   507
      _lower.resize(_res_arc_num);
kpeter@830
   508
      _upper.resize(_res_arc_num);
kpeter@830
   509
      _cost.resize(_res_arc_num);
kpeter@830
   510
      _supply.resize(_res_node_num);
kpeter@830
   511
      
kpeter@830
   512
      _res_cap.resize(_res_arc_num);
kpeter@830
   513
      _pi.resize(_res_node_num);
kpeter@830
   514
kpeter@830
   515
      _arc_vec.reserve(_res_arc_num);
kpeter@830
   516
      _cost_vec.reserve(_res_arc_num);
kpeter@830
   517
      _id_vec.reserve(_res_arc_num);
kpeter@830
   518
kpeter@830
   519
      // Copy the graph
kpeter@830
   520
      int i = 0, j = 0, k = 2 * _arc_num + _node_num;
kpeter@830
   521
      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@830
   522
        _node_id[n] = i;
kpeter@830
   523
      }
kpeter@830
   524
      i = 0;
kpeter@830
   525
      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@830
   526
        _first_out[i] = j;
kpeter@830
   527
        for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) {
kpeter@830
   528
          _arc_idf[a] = j;
kpeter@830
   529
          _forward[j] = true;
kpeter@830
   530
          _source[j] = i;
kpeter@830
   531
          _target[j] = _node_id[_graph.runningNode(a)];
kpeter@830
   532
        }
kpeter@830
   533
        for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) {
kpeter@830
   534
          _arc_idb[a] = j;
kpeter@830
   535
          _forward[j] = false;
kpeter@830
   536
          _source[j] = i;
kpeter@830
   537
          _target[j] = _node_id[_graph.runningNode(a)];
kpeter@830
   538
        }
kpeter@830
   539
        _forward[j] = false;
kpeter@830
   540
        _source[j] = i;
kpeter@830
   541
        _target[j] = _root;
kpeter@830
   542
        _reverse[j] = k;
kpeter@830
   543
        _forward[k] = true;
kpeter@830
   544
        _source[k] = _root;
kpeter@830
   545
        _target[k] = i;
kpeter@830
   546
        _reverse[k] = j;
kpeter@830
   547
        ++j; ++k;
kpeter@830
   548
      }
kpeter@830
   549
      _first_out[i] = j;
kpeter@830
   550
      _first_out[_res_node_num] = k;
kpeter@830
   551
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@830
   552
        int fi = _arc_idf[a];
kpeter@830
   553
        int bi = _arc_idb[a];
kpeter@830
   554
        _reverse[fi] = bi;
kpeter@830
   555
        _reverse[bi] = fi;
kpeter@830
   556
      }
kpeter@830
   557
      
kpeter@830
   558
      // Reset parameters
kpeter@830
   559
      resetParams();
kpeter@830
   560
      return *this;
kpeter@830
   561
    }
kpeter@830
   562
kpeter@814
   563
    /// @}
kpeter@814
   564
kpeter@814
   565
    /// \name Query Functions
kpeter@815
   566
    /// The results of the algorithm can be obtained using these
kpeter@814
   567
    /// functions.\n
kpeter@815
   568
    /// The \ref run() function must be called before using them.
kpeter@814
   569
kpeter@814
   570
    /// @{
kpeter@814
   571
kpeter@815
   572
    /// \brief Return the total cost of the found flow.
kpeter@814
   573
    ///
kpeter@815
   574
    /// This function returns the total cost of the found flow.
kpeter@815
   575
    /// Its complexity is O(e).
kpeter@815
   576
    ///
kpeter@815
   577
    /// \note The return type of the function can be specified as a
kpeter@815
   578
    /// template parameter. For example,
kpeter@815
   579
    /// \code
kpeter@815
   580
    ///   cc.totalCost<double>();
kpeter@815
   581
    /// \endcode
kpeter@815
   582
    /// It is useful if the total cost cannot be stored in the \c Cost
kpeter@815
   583
    /// type of the algorithm, which is the default return type of the
kpeter@815
   584
    /// function.
kpeter@814
   585
    ///
kpeter@814
   586
    /// \pre \ref run() must be called before using this function.
kpeter@815
   587
    template <typename Number>
kpeter@815
   588
    Number totalCost() const {
kpeter@815
   589
      Number c = 0;
kpeter@815
   590
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@815
   591
        int i = _arc_idb[a];
kpeter@815
   592
        c += static_cast<Number>(_res_cap[i]) *
kpeter@815
   593
             (-static_cast<Number>(_cost[i]));
kpeter@815
   594
      }
kpeter@815
   595
      return c;
kpeter@814
   596
    }
kpeter@814
   597
kpeter@815
   598
#ifndef DOXYGEN
kpeter@815
   599
    Cost totalCost() const {
kpeter@815
   600
      return totalCost<Cost>();
kpeter@814
   601
    }
kpeter@815
   602
#endif
kpeter@814
   603
kpeter@814
   604
    /// \brief Return the flow on the given arc.
kpeter@814
   605
    ///
kpeter@815
   606
    /// This function returns the flow on the given arc.
kpeter@814
   607
    ///
kpeter@814
   608
    /// \pre \ref run() must be called before using this function.
kpeter@815
   609
    Value flow(const Arc& a) const {
kpeter@815
   610
      return _res_cap[_arc_idb[a]];
kpeter@814
   611
    }
kpeter@814
   612
kpeter@815
   613
    /// \brief Return the flow map (the primal solution).
kpeter@814
   614
    ///
kpeter@815
   615
    /// This function copies the flow value on each arc into the given
kpeter@815
   616
    /// map. The \c Value type of the algorithm must be convertible to
kpeter@815
   617
    /// the \c Value type of the map.
kpeter@814
   618
    ///
kpeter@814
   619
    /// \pre \ref run() must be called before using this function.
kpeter@815
   620
    template <typename FlowMap>
kpeter@815
   621
    void flowMap(FlowMap &map) const {
kpeter@815
   622
      for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@815
   623
        map.set(a, _res_cap[_arc_idb[a]]);
kpeter@815
   624
      }
kpeter@814
   625
    }
kpeter@814
   626
kpeter@815
   627
    /// \brief Return the potential (dual value) of the given node.
kpeter@814
   628
    ///
kpeter@815
   629
    /// This function returns the potential (dual value) of the
kpeter@815
   630
    /// given node.
kpeter@814
   631
    ///
kpeter@814
   632
    /// \pre \ref run() must be called before using this function.
kpeter@815
   633
    Cost potential(const Node& n) const {
kpeter@815
   634
      return static_cast<Cost>(_pi[_node_id[n]]);
kpeter@815
   635
    }
kpeter@815
   636
kpeter@815
   637
    /// \brief Return the potential map (the dual solution).
kpeter@815
   638
    ///
kpeter@815
   639
    /// This function copies the potential (dual value) of each node
kpeter@815
   640
    /// into the given map.
kpeter@815
   641
    /// The \c Cost type of the algorithm must be convertible to the
kpeter@815
   642
    /// \c Value type of the map.
kpeter@815
   643
    ///
kpeter@815
   644
    /// \pre \ref run() must be called before using this function.
kpeter@815
   645
    template <typename PotentialMap>
kpeter@815
   646
    void potentialMap(PotentialMap &map) const {
kpeter@815
   647
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@815
   648
        map.set(n, static_cast<Cost>(_pi[_node_id[n]]));
kpeter@815
   649
      }
kpeter@814
   650
    }
kpeter@814
   651
kpeter@814
   652
    /// @}
kpeter@814
   653
kpeter@814
   654
  private:
kpeter@814
   655
kpeter@815
   656
    // Initialize the algorithm
kpeter@815
   657
    ProblemType init() {
kpeter@815
   658
      if (_res_node_num <= 1) return INFEASIBLE;
kpeter@814
   659
kpeter@815
   660
      // Check the sum of supply values
kpeter@815
   661
      _sum_supply = 0;
kpeter@815
   662
      for (int i = 0; i != _root; ++i) {
kpeter@815
   663
        _sum_supply += _supply[i];
kpeter@814
   664
      }
kpeter@815
   665
      if (_sum_supply > 0) return INFEASIBLE;
kpeter@815
   666
      
kpeter@815
   667
kpeter@815
   668
      // Initialize vectors
kpeter@815
   669
      for (int i = 0; i != _res_node_num; ++i) {
kpeter@815
   670
        _pi[i] = 0;
kpeter@815
   671
      }
kpeter@815
   672
      ValueVector excess(_supply);
kpeter@815
   673
      
kpeter@815
   674
      // Remove infinite upper bounds and check negative arcs
kpeter@815
   675
      const Value MAX = std::numeric_limits<Value>::max();
kpeter@815
   676
      int last_out;
kpeter@815
   677
      if (_have_lower) {
kpeter@815
   678
        for (int i = 0; i != _root; ++i) {
kpeter@815
   679
          last_out = _first_out[i+1];
kpeter@815
   680
          for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@815
   681
            if (_forward[j]) {
kpeter@815
   682
              Value c = _cost[j] < 0 ? _upper[j] : _lower[j];
kpeter@815
   683
              if (c >= MAX) return UNBOUNDED;
kpeter@815
   684
              excess[i] -= c;
kpeter@815
   685
              excess[_target[j]] += c;
kpeter@815
   686
            }
kpeter@815
   687
          }
kpeter@815
   688
        }
kpeter@815
   689
      } else {
kpeter@815
   690
        for (int i = 0; i != _root; ++i) {
kpeter@815
   691
          last_out = _first_out[i+1];
kpeter@815
   692
          for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@815
   693
            if (_forward[j] && _cost[j] < 0) {
kpeter@815
   694
              Value c = _upper[j];
kpeter@815
   695
              if (c >= MAX) return UNBOUNDED;
kpeter@815
   696
              excess[i] -= c;
kpeter@815
   697
              excess[_target[j]] += c;
kpeter@815
   698
            }
kpeter@815
   699
          }
kpeter@815
   700
        }
kpeter@815
   701
      }
kpeter@815
   702
      Value ex, max_cap = 0;
kpeter@815
   703
      for (int i = 0; i != _res_node_num; ++i) {
kpeter@815
   704
        ex = excess[i];
kpeter@815
   705
        if (ex < 0) max_cap -= ex;
kpeter@815
   706
      }
kpeter@815
   707
      for (int j = 0; j != _res_arc_num; ++j) {
kpeter@815
   708
        if (_upper[j] >= MAX) _upper[j] = max_cap;
kpeter@814
   709
      }
kpeter@814
   710
kpeter@815
   711
      // Initialize maps for Circulation and remove non-zero lower bounds
kpeter@815
   712
      ConstMap<Arc, Value> low(0);
kpeter@815
   713
      typedef typename Digraph::template ArcMap<Value> ValueArcMap;
kpeter@815
   714
      typedef typename Digraph::template NodeMap<Value> ValueNodeMap;
kpeter@815
   715
      ValueArcMap cap(_graph), flow(_graph);
kpeter@815
   716
      ValueNodeMap sup(_graph);
kpeter@815
   717
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@815
   718
        sup[n] = _supply[_node_id[n]];
kpeter@815
   719
      }
kpeter@815
   720
      if (_have_lower) {
kpeter@815
   721
        for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@815
   722
          int j = _arc_idf[a];
kpeter@815
   723
          Value c = _lower[j];
kpeter@815
   724
          cap[a] = _upper[j] - c;
kpeter@815
   725
          sup[_graph.source(a)] -= c;
kpeter@815
   726
          sup[_graph.target(a)] += c;
kpeter@815
   727
        }
kpeter@815
   728
      } else {
kpeter@815
   729
        for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@815
   730
          cap[a] = _upper[_arc_idf[a]];
kpeter@815
   731
        }
kpeter@815
   732
      }
kpeter@814
   733
kpeter@815
   734
      // Find a feasible flow using Circulation
kpeter@815
   735
      Circulation<Digraph, ConstMap<Arc, Value>, ValueArcMap, ValueNodeMap>
kpeter@815
   736
        circ(_graph, low, cap, sup);
kpeter@815
   737
      if (!circ.flowMap(flow).run()) return INFEASIBLE;
kpeter@815
   738
kpeter@815
   739
      // Set residual capacities and handle GEQ supply type
kpeter@815
   740
      if (_sum_supply < 0) {
kpeter@815
   741
        for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@815
   742
          Value fa = flow[a];
kpeter@815
   743
          _res_cap[_arc_idf[a]] = cap[a] - fa;
kpeter@815
   744
          _res_cap[_arc_idb[a]] = fa;
kpeter@815
   745
          sup[_graph.source(a)] -= fa;
kpeter@815
   746
          sup[_graph.target(a)] += fa;
kpeter@815
   747
        }
kpeter@815
   748
        for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@815
   749
          excess[_node_id[n]] = sup[n];
kpeter@815
   750
        }
kpeter@815
   751
        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
kpeter@815
   752
          int u = _target[a];
kpeter@815
   753
          int ra = _reverse[a];
kpeter@815
   754
          _res_cap[a] = -_sum_supply + 1;
kpeter@815
   755
          _res_cap[ra] = -excess[u];
kpeter@815
   756
          _cost[a] = 0;
kpeter@815
   757
          _cost[ra] = 0;
kpeter@815
   758
        }
kpeter@815
   759
      } else {
kpeter@815
   760
        for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@815
   761
          Value fa = flow[a];
kpeter@815
   762
          _res_cap[_arc_idf[a]] = cap[a] - fa;
kpeter@815
   763
          _res_cap[_arc_idb[a]] = fa;
kpeter@815
   764
        }
kpeter@815
   765
        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
kpeter@815
   766
          int ra = _reverse[a];
kpeter@815
   767
          _res_cap[a] = 1;
kpeter@815
   768
          _res_cap[ra] = 0;
kpeter@815
   769
          _cost[a] = 0;
kpeter@815
   770
          _cost[ra] = 0;
kpeter@815
   771
        }
kpeter@815
   772
      }
kpeter@815
   773
      
kpeter@815
   774
      return OPTIMAL;
kpeter@815
   775
    }
kpeter@815
   776
    
kpeter@815
   777
    // Build a StaticDigraph structure containing the current
kpeter@815
   778
    // residual network
kpeter@815
   779
    void buildResidualNetwork() {
kpeter@815
   780
      _arc_vec.clear();
kpeter@815
   781
      _cost_vec.clear();
kpeter@815
   782
      _id_vec.clear();
kpeter@815
   783
      for (int j = 0; j != _res_arc_num; ++j) {
kpeter@815
   784
        if (_res_cap[j] > 0) {
kpeter@815
   785
          _arc_vec.push_back(IntPair(_source[j], _target[j]));
kpeter@815
   786
          _cost_vec.push_back(_cost[j]);
kpeter@815
   787
          _id_vec.push_back(j);
kpeter@815
   788
        }
kpeter@815
   789
      }
kpeter@815
   790
      _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end());
kpeter@814
   791
    }
kpeter@814
   792
kpeter@815
   793
    // Execute the algorithm and transform the results
kpeter@815
   794
    void start(Method method) {
kpeter@815
   795
      // Execute the algorithm
kpeter@815
   796
      switch (method) {
kpeter@815
   797
        case SIMPLE_CYCLE_CANCELING:
kpeter@815
   798
          startSimpleCycleCanceling();
kpeter@815
   799
          break;
kpeter@815
   800
        case MINIMUM_MEAN_CYCLE_CANCELING:
kpeter@815
   801
          startMinMeanCycleCanceling();
kpeter@815
   802
          break;
kpeter@815
   803
        case CANCEL_AND_TIGHTEN:
kpeter@815
   804
          startCancelAndTighten();
kpeter@815
   805
          break;
kpeter@815
   806
      }
kpeter@814
   807
kpeter@815
   808
      // Compute node potentials
kpeter@815
   809
      if (method != SIMPLE_CYCLE_CANCELING) {
kpeter@815
   810
        buildResidualNetwork();
kpeter@815
   811
        typename BellmanFord<StaticDigraph, CostArcMap>
kpeter@815
   812
          ::template SetDistMap<CostNodeMap>::Create bf(_sgr, _cost_map);
kpeter@815
   813
        bf.distMap(_pi_map);
kpeter@815
   814
        bf.init(0);
kpeter@815
   815
        bf.start();
kpeter@814
   816
      }
kpeter@815
   817
kpeter@815
   818
      // Handle non-zero lower bounds
kpeter@815
   819
      if (_have_lower) {
kpeter@815
   820
        int limit = _first_out[_root];
kpeter@815
   821
        for (int j = 0; j != limit; ++j) {
kpeter@815
   822
          if (!_forward[j]) _res_cap[j] += _lower[j];
kpeter@815
   823
        }
kpeter@815
   824
      }
kpeter@814
   825
    }
kpeter@814
   826
kpeter@815
   827
    // Execute the "Simple Cycle Canceling" method
kpeter@815
   828
    void startSimpleCycleCanceling() {
kpeter@815
   829
      // Constants for computing the iteration limits
kpeter@815
   830
      const int BF_FIRST_LIMIT  = 2;
kpeter@815
   831
      const double BF_LIMIT_FACTOR = 1.5;
kpeter@815
   832
      
kpeter@820
   833
      typedef StaticVectorMap<StaticDigraph::Arc, Value> FilterMap;
kpeter@815
   834
      typedef FilterArcs<StaticDigraph, FilterMap> ResDigraph;
kpeter@820
   835
      typedef StaticVectorMap<StaticDigraph::Node, StaticDigraph::Arc> PredMap;
kpeter@815
   836
      typedef typename BellmanFord<ResDigraph, CostArcMap>
kpeter@815
   837
        ::template SetDistMap<CostNodeMap>
kpeter@815
   838
        ::template SetPredMap<PredMap>::Create BF;
kpeter@815
   839
      
kpeter@815
   840
      // Build the residual network
kpeter@815
   841
      _arc_vec.clear();
kpeter@815
   842
      _cost_vec.clear();
kpeter@815
   843
      for (int j = 0; j != _res_arc_num; ++j) {
kpeter@815
   844
        _arc_vec.push_back(IntPair(_source[j], _target[j]));
kpeter@815
   845
        _cost_vec.push_back(_cost[j]);
kpeter@815
   846
      }
kpeter@815
   847
      _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end());
kpeter@815
   848
kpeter@815
   849
      FilterMap filter_map(_res_cap);
kpeter@815
   850
      ResDigraph rgr(_sgr, filter_map);
kpeter@815
   851
      std::vector<int> cycle;
kpeter@815
   852
      std::vector<StaticDigraph::Arc> pred(_res_arc_num);
kpeter@815
   853
      PredMap pred_map(pred);
kpeter@815
   854
      BF bf(rgr, _cost_map);
kpeter@815
   855
      bf.distMap(_pi_map).predMap(pred_map);
kpeter@814
   856
kpeter@814
   857
      int length_bound = BF_FIRST_LIMIT;
kpeter@814
   858
      bool optimal = false;
kpeter@814
   859
      while (!optimal) {
kpeter@814
   860
        bf.init(0);
kpeter@814
   861
        int iter_num = 0;
kpeter@814
   862
        bool cycle_found = false;
kpeter@814
   863
        while (!cycle_found) {
kpeter@815
   864
          // Perform some iterations of the Bellman-Ford algorithm
kpeter@815
   865
          int curr_iter_num = iter_num + length_bound <= _node_num ?
kpeter@815
   866
            length_bound : _node_num - iter_num;
kpeter@814
   867
          iter_num += curr_iter_num;
kpeter@814
   868
          int real_iter_num = curr_iter_num;
kpeter@814
   869
          for (int i = 0; i < curr_iter_num; ++i) {
kpeter@814
   870
            if (bf.processNextWeakRound()) {
kpeter@814
   871
              real_iter_num = i;
kpeter@814
   872
              break;
kpeter@814
   873
            }
kpeter@814
   874
          }
kpeter@814
   875
          if (real_iter_num < curr_iter_num) {
kpeter@814
   876
            // Optimal flow is found
kpeter@814
   877
            optimal = true;
kpeter@814
   878
            break;
kpeter@814
   879
          } else {
kpeter@815
   880
            // Search for node disjoint negative cycles
kpeter@815
   881
            std::vector<int> state(_res_node_num, 0);
kpeter@814
   882
            int id = 0;
kpeter@815
   883
            for (int u = 0; u != _res_node_num; ++u) {
kpeter@815
   884
              if (state[u] != 0) continue;
kpeter@815
   885
              ++id;
kpeter@815
   886
              int v = u;
kpeter@815
   887
              for (; v != -1 && state[v] == 0; v = pred[v] == INVALID ?
kpeter@815
   888
                   -1 : rgr.id(rgr.source(pred[v]))) {
kpeter@815
   889
                state[v] = id;
kpeter@814
   890
              }
kpeter@815
   891
              if (v != -1 && state[v] == id) {
kpeter@815
   892
                // A negative cycle is found
kpeter@814
   893
                cycle_found = true;
kpeter@814
   894
                cycle.clear();
kpeter@815
   895
                StaticDigraph::Arc a = pred[v];
kpeter@815
   896
                Value d, delta = _res_cap[rgr.id(a)];
kpeter@815
   897
                cycle.push_back(rgr.id(a));
kpeter@815
   898
                while (rgr.id(rgr.source(a)) != v) {
kpeter@815
   899
                  a = pred_map[rgr.source(a)];
kpeter@815
   900
                  d = _res_cap[rgr.id(a)];
kpeter@815
   901
                  if (d < delta) delta = d;
kpeter@815
   902
                  cycle.push_back(rgr.id(a));
kpeter@814
   903
                }
kpeter@814
   904
kpeter@815
   905
                // Augment along the cycle
kpeter@815
   906
                for (int i = 0; i < int(cycle.size()); ++i) {
kpeter@815
   907
                  int j = cycle[i];
kpeter@815
   908
                  _res_cap[j] -= delta;
kpeter@815
   909
                  _res_cap[_reverse[j]] += delta;
kpeter@815
   910
                }
kpeter@814
   911
              }
kpeter@814
   912
            }
kpeter@814
   913
          }
kpeter@814
   914
kpeter@815
   915
          // Increase iteration limit if no cycle is found
kpeter@815
   916
          if (!cycle_found) {
kpeter@815
   917
            length_bound = static_cast<int>(length_bound * BF_LIMIT_FACTOR);
kpeter@815
   918
          }
kpeter@814
   919
        }
kpeter@814
   920
      }
kpeter@814
   921
    }
kpeter@814
   922
kpeter@815
   923
    // Execute the "Minimum Mean Cycle Canceling" method
kpeter@815
   924
    void startMinMeanCycleCanceling() {
kpeter@815
   925
      typedef SimplePath<StaticDigraph> SPath;
kpeter@815
   926
      typedef typename SPath::ArcIt SPathArcIt;
kpeter@815
   927
      typedef typename Howard<StaticDigraph, CostArcMap>
kpeter@815
   928
        ::template SetPath<SPath>::Create MMC;
kpeter@815
   929
      
kpeter@815
   930
      SPath cycle;
kpeter@815
   931
      MMC mmc(_sgr, _cost_map);
kpeter@815
   932
      mmc.cycle(cycle);
kpeter@815
   933
      buildResidualNetwork();
kpeter@815
   934
      while (mmc.findMinMean() && mmc.cycleLength() < 0) {
kpeter@815
   935
        // Find the cycle
kpeter@815
   936
        mmc.findCycle();
kpeter@814
   937
kpeter@815
   938
        // Compute delta value
kpeter@815
   939
        Value delta = INF;
kpeter@815
   940
        for (SPathArcIt a(cycle); a != INVALID; ++a) {
kpeter@815
   941
          Value d = _res_cap[_id_vec[_sgr.id(a)]];
kpeter@815
   942
          if (d < delta) delta = d;
kpeter@815
   943
        }
kpeter@814
   944
kpeter@815
   945
        // Augment along the cycle
kpeter@815
   946
        for (SPathArcIt a(cycle); a != INVALID; ++a) {
kpeter@815
   947
          int j = _id_vec[_sgr.id(a)];
kpeter@815
   948
          _res_cap[j] -= delta;
kpeter@815
   949
          _res_cap[_reverse[j]] += delta;
kpeter@815
   950
        }
kpeter@815
   951
kpeter@815
   952
        // Rebuild the residual network        
kpeter@815
   953
        buildResidualNetwork();
kpeter@815
   954
      }
kpeter@815
   955
    }
kpeter@815
   956
kpeter@815
   957
    // Execute the "Cancel And Tighten" method
kpeter@815
   958
    void startCancelAndTighten() {
kpeter@815
   959
      // Constants for the min mean cycle computations
kpeter@815
   960
      const double LIMIT_FACTOR = 1.0;
kpeter@815
   961
      const int MIN_LIMIT = 5;
kpeter@815
   962
kpeter@815
   963
      // Contruct auxiliary data vectors
kpeter@815
   964
      DoubleVector pi(_res_node_num, 0.0);
kpeter@815
   965
      IntVector level(_res_node_num);
kpeter@839
   966
      BoolVector reached(_res_node_num);
kpeter@839
   967
      BoolVector processed(_res_node_num);
kpeter@815
   968
      IntVector pred_node(_res_node_num);
kpeter@815
   969
      IntVector pred_arc(_res_node_num);
kpeter@815
   970
      std::vector<int> stack(_res_node_num);
kpeter@815
   971
      std::vector<int> proc_vector(_res_node_num);
kpeter@815
   972
kpeter@815
   973
      // Initialize epsilon
kpeter@815
   974
      double epsilon = 0;
kpeter@815
   975
      for (int a = 0; a != _res_arc_num; ++a) {
kpeter@815
   976
        if (_res_cap[a] > 0 && -_cost[a] > epsilon)
kpeter@815
   977
          epsilon = -_cost[a];
kpeter@815
   978
      }
kpeter@815
   979
kpeter@815
   980
      // Start phases
kpeter@815
   981
      Tolerance<double> tol;
kpeter@815
   982
      tol.epsilon(1e-6);
kpeter@815
   983
      int limit = int(LIMIT_FACTOR * std::sqrt(double(_res_node_num)));
kpeter@815
   984
      if (limit < MIN_LIMIT) limit = MIN_LIMIT;
kpeter@815
   985
      int iter = limit;
kpeter@815
   986
      while (epsilon * _res_node_num >= 1) {
kpeter@815
   987
        // Find and cancel cycles in the admissible network using DFS
kpeter@815
   988
        for (int u = 0; u != _res_node_num; ++u) {
kpeter@815
   989
          reached[u] = false;
kpeter@815
   990
          processed[u] = false;
kpeter@815
   991
        }
kpeter@815
   992
        int stack_head = -1;
kpeter@815
   993
        int proc_head = -1;
kpeter@815
   994
        for (int start = 0; start != _res_node_num; ++start) {
kpeter@815
   995
          if (reached[start]) continue;
kpeter@815
   996
kpeter@815
   997
          // New start node
kpeter@815
   998
          reached[start] = true;
kpeter@815
   999
          pred_arc[start] = -1;
kpeter@815
  1000
          pred_node[start] = -1;
kpeter@815
  1001
kpeter@815
  1002
          // Find the first admissible outgoing arc
kpeter@815
  1003
          double p = pi[start];
kpeter@815
  1004
          int a = _first_out[start];
kpeter@815
  1005
          int last_out = _first_out[start+1];
kpeter@815
  1006
          for (; a != last_out && (_res_cap[a] == 0 ||
kpeter@815
  1007
               !tol.negative(_cost[a] + p - pi[_target[a]])); ++a) ;
kpeter@815
  1008
          if (a == last_out) {
kpeter@815
  1009
            processed[start] = true;
kpeter@815
  1010
            proc_vector[++proc_head] = start;
kpeter@815
  1011
            continue;
kpeter@815
  1012
          }
kpeter@815
  1013
          stack[++stack_head] = a;
kpeter@815
  1014
kpeter@815
  1015
          while (stack_head >= 0) {
kpeter@815
  1016
            int sa = stack[stack_head];
kpeter@815
  1017
            int u = _source[sa];
kpeter@815
  1018
            int v = _target[sa];
kpeter@815
  1019
kpeter@815
  1020
            if (!reached[v]) {
kpeter@815
  1021
              // A new node is reached
kpeter@815
  1022
              reached[v] = true;
kpeter@815
  1023
              pred_node[v] = u;
kpeter@815
  1024
              pred_arc[v] = sa;
kpeter@815
  1025
              p = pi[v];
kpeter@815
  1026
              a = _first_out[v];
kpeter@815
  1027
              last_out = _first_out[v+1];
kpeter@815
  1028
              for (; a != last_out && (_res_cap[a] == 0 ||
kpeter@815
  1029
                   !tol.negative(_cost[a] + p - pi[_target[a]])); ++a) ;
kpeter@815
  1030
              stack[++stack_head] = a == last_out ? -1 : a;
kpeter@815
  1031
            } else {
kpeter@815
  1032
              if (!processed[v]) {
kpeter@815
  1033
                // A cycle is found
kpeter@815
  1034
                int n, w = u;
kpeter@815
  1035
                Value d, delta = _res_cap[sa];
kpeter@815
  1036
                for (n = u; n != v; n = pred_node[n]) {
kpeter@815
  1037
                  d = _res_cap[pred_arc[n]];
kpeter@815
  1038
                  if (d <= delta) {
kpeter@815
  1039
                    delta = d;
kpeter@815
  1040
                    w = pred_node[n];
kpeter@815
  1041
                  }
kpeter@815
  1042
                }
kpeter@815
  1043
kpeter@815
  1044
                // Augment along the cycle
kpeter@815
  1045
                _res_cap[sa] -= delta;
kpeter@815
  1046
                _res_cap[_reverse[sa]] += delta;
kpeter@815
  1047
                for (n = u; n != v; n = pred_node[n]) {
kpeter@815
  1048
                  int pa = pred_arc[n];
kpeter@815
  1049
                  _res_cap[pa] -= delta;
kpeter@815
  1050
                  _res_cap[_reverse[pa]] += delta;
kpeter@815
  1051
                }
kpeter@815
  1052
                for (n = u; stack_head > 0 && n != w; n = pred_node[n]) {
kpeter@815
  1053
                  --stack_head;
kpeter@815
  1054
                  reached[n] = false;
kpeter@815
  1055
                }
kpeter@815
  1056
                u = w;
kpeter@815
  1057
              }
kpeter@815
  1058
              v = u;
kpeter@815
  1059
kpeter@815
  1060
              // Find the next admissible outgoing arc
kpeter@815
  1061
              p = pi[v];
kpeter@815
  1062
              a = stack[stack_head] + 1;
kpeter@815
  1063
              last_out = _first_out[v+1];
kpeter@815
  1064
              for (; a != last_out && (_res_cap[a] == 0 ||
kpeter@815
  1065
                   !tol.negative(_cost[a] + p - pi[_target[a]])); ++a) ;
kpeter@815
  1066
              stack[stack_head] = a == last_out ? -1 : a;
kpeter@815
  1067
            }
kpeter@815
  1068
kpeter@815
  1069
            while (stack_head >= 0 && stack[stack_head] == -1) {
kpeter@815
  1070
              processed[v] = true;
kpeter@815
  1071
              proc_vector[++proc_head] = v;
kpeter@815
  1072
              if (--stack_head >= 0) {
kpeter@815
  1073
                // Find the next admissible outgoing arc
kpeter@815
  1074
                v = _source[stack[stack_head]];
kpeter@815
  1075
                p = pi[v];
kpeter@815
  1076
                a = stack[stack_head] + 1;
kpeter@815
  1077
                last_out = _first_out[v+1];
kpeter@815
  1078
                for (; a != last_out && (_res_cap[a] == 0 ||
kpeter@815
  1079
                     !tol.negative(_cost[a] + p - pi[_target[a]])); ++a) ;
kpeter@815
  1080
                stack[stack_head] = a == last_out ? -1 : a;
kpeter@815
  1081
              }
kpeter@815
  1082
            }
kpeter@815
  1083
          }
kpeter@815
  1084
        }
kpeter@815
  1085
kpeter@815
  1086
        // Tighten potentials and epsilon
kpeter@815
  1087
        if (--iter > 0) {
kpeter@815
  1088
          for (int u = 0; u != _res_node_num; ++u) {
kpeter@815
  1089
            level[u] = 0;
kpeter@815
  1090
          }
kpeter@815
  1091
          for (int i = proc_head; i > 0; --i) {
kpeter@815
  1092
            int u = proc_vector[i];
kpeter@815
  1093
            double p = pi[u];
kpeter@815
  1094
            int l = level[u] + 1;
kpeter@815
  1095
            int last_out = _first_out[u+1];
kpeter@815
  1096
            for (int a = _first_out[u]; a != last_out; ++a) {
kpeter@815
  1097
              int v = _target[a];
kpeter@815
  1098
              if (_res_cap[a] > 0 && tol.negative(_cost[a] + p - pi[v]) &&
kpeter@815
  1099
                  l > level[v]) level[v] = l;
kpeter@815
  1100
            }
kpeter@814
  1101
          }
kpeter@814
  1102
kpeter@815
  1103
          // Modify potentials
kpeter@815
  1104
          double q = std::numeric_limits<double>::max();
kpeter@815
  1105
          for (int u = 0; u != _res_node_num; ++u) {
kpeter@815
  1106
            int lu = level[u];
kpeter@815
  1107
            double p, pu = pi[u];
kpeter@815
  1108
            int last_out = _first_out[u+1];
kpeter@815
  1109
            for (int a = _first_out[u]; a != last_out; ++a) {
kpeter@815
  1110
              if (_res_cap[a] == 0) continue;
kpeter@815
  1111
              int v = _target[a];
kpeter@815
  1112
              int ld = lu - level[v];
kpeter@815
  1113
              if (ld > 0) {
kpeter@815
  1114
                p = (_cost[a] + pu - pi[v] + epsilon) / (ld + 1);
kpeter@815
  1115
                if (p < q) q = p;
kpeter@815
  1116
              }
kpeter@815
  1117
            }
kpeter@815
  1118
          }
kpeter@815
  1119
          for (int u = 0; u != _res_node_num; ++u) {
kpeter@815
  1120
            pi[u] -= q * level[u];
kpeter@815
  1121
          }
kpeter@814
  1122
kpeter@815
  1123
          // Modify epsilon
kpeter@815
  1124
          epsilon = 0;
kpeter@815
  1125
          for (int u = 0; u != _res_node_num; ++u) {
kpeter@815
  1126
            double curr, pu = pi[u];
kpeter@815
  1127
            int last_out = _first_out[u+1];
kpeter@815
  1128
            for (int a = _first_out[u]; a != last_out; ++a) {
kpeter@815
  1129
              if (_res_cap[a] == 0) continue;
kpeter@815
  1130
              curr = _cost[a] + pu - pi[_target[a]];
kpeter@815
  1131
              if (-curr > epsilon) epsilon = -curr;
kpeter@815
  1132
            }
kpeter@815
  1133
          }
kpeter@815
  1134
        } else {
kpeter@815
  1135
          typedef Howard<StaticDigraph, CostArcMap> MMC;
kpeter@815
  1136
          typedef typename BellmanFord<StaticDigraph, CostArcMap>
kpeter@815
  1137
            ::template SetDistMap<CostNodeMap>::Create BF;
kpeter@815
  1138
kpeter@815
  1139
          // Set epsilon to the minimum cycle mean
kpeter@815
  1140
          buildResidualNetwork();
kpeter@815
  1141
          MMC mmc(_sgr, _cost_map);
kpeter@815
  1142
          mmc.findMinMean();
kpeter@815
  1143
          epsilon = -mmc.cycleMean();
kpeter@815
  1144
          Cost cycle_cost = mmc.cycleLength();
kpeter@815
  1145
          int cycle_size = mmc.cycleArcNum();
kpeter@815
  1146
          
kpeter@815
  1147
          // Compute feasible potentials for the current epsilon
kpeter@815
  1148
          for (int i = 0; i != int(_cost_vec.size()); ++i) {
kpeter@815
  1149
            _cost_vec[i] = cycle_size * _cost_vec[i] - cycle_cost;
kpeter@815
  1150
          }
kpeter@815
  1151
          BF bf(_sgr, _cost_map);
kpeter@815
  1152
          bf.distMap(_pi_map);
kpeter@815
  1153
          bf.init(0);
kpeter@815
  1154
          bf.start();
kpeter@815
  1155
          for (int u = 0; u != _res_node_num; ++u) {
kpeter@815
  1156
            pi[u] = static_cast<double>(_pi[u]) / cycle_size;
kpeter@815
  1157
          }
kpeter@815
  1158
        
kpeter@815
  1159
          iter = limit;
kpeter@814
  1160
        }
kpeter@814
  1161
      }
kpeter@814
  1162
    }
kpeter@814
  1163
kpeter@814
  1164
  }; //class CycleCanceling
kpeter@814
  1165
kpeter@814
  1166
  ///@}
kpeter@814
  1167
kpeter@814
  1168
} //namespace lemon
kpeter@814
  1169
kpeter@814
  1170
#endif //LEMON_CYCLE_CANCELING_H