lemon/howard_mmc.h
author Alpar Juttner <alpar@cs.elte.hu>
Sat, 25 May 2013 06:59:31 +0200
changeset 1064 fc3854d936f7
parent 1002 f63ba40a60f4
child 1049 7bf489cf624e
permissions -rw-r--r--
Enable/disable options for LP/MIP backends (#465)
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/* -*- mode: C++; indent-tabs-mode: nil; -*-
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 *
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 * This file is a part of LEMON, a generic C++ optimization library.
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 *
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 * Copyright (C) 2003-2010
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 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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 *
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 * Permission to use, modify and distribute this software is granted
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 * provided that this copyright notice appears in all copies. For
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 * precise terms see the accompanying LICENSE file.
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 *
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 * This software is provided "AS IS" with no warranty of any kind,
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 * express or implied, and with no claim as to its suitability for any
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 * purpose.
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 *
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 */
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#ifndef LEMON_HOWARD_MMC_H
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#define LEMON_HOWARD_MMC_H
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/// \ingroup min_mean_cycle
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///
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/// \file
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/// \brief Howard's algorithm for finding a minimum mean cycle.
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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/path.h>
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#include <lemon/tolerance.h>
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#include <lemon/connectivity.h>
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namespace lemon {
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  /// \brief Default traits class of HowardMmc class.
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  ///
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  /// Default traits class of HowardMmc class.
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  /// \tparam GR The type of the digraph.
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  /// \tparam CM The type of the cost map.
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  /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
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#ifdef DOXYGEN
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  template <typename GR, typename CM>
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#else
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  template <typename GR, typename CM,
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    bool integer = std::numeric_limits<typename CM::Value>::is_integer>
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#endif
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  struct HowardMmcDefaultTraits
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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 cost map
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    typedef CM CostMap;
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    /// The type of the arc costs
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    typedef typename CostMap::Value Cost;
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    /// \brief The large cost type used for internal computations
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    ///
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    /// The large cost type used for internal computations.
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    /// It is \c long \c long if the \c Cost type is integer,
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    /// otherwise it is \c double.
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    /// \c Cost must be convertible to \c LargeCost.
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    typedef double LargeCost;
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    /// The tolerance type used for internal computations
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    typedef lemon::Tolerance<LargeCost> Tolerance;
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    /// \brief The path type of the found cycles
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    ///
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    /// The path type of the found cycles.
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    /// It must conform to the \ref lemon::concepts::Path "Path" concept
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    /// and it must have an \c addBack() function.
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    typedef lemon::Path<Digraph> Path;
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  };
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  // Default traits class for integer cost types
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  template <typename GR, typename CM>
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  struct HowardMmcDefaultTraits<GR, CM, true>
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  {
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    typedef GR Digraph;
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    typedef CM CostMap;
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    typedef typename CostMap::Value Cost;
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#ifdef LEMON_HAVE_LONG_LONG
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    typedef long long LargeCost;
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#else
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    typedef long LargeCost;
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#endif
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    typedef lemon::Tolerance<LargeCost> Tolerance;
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    typedef lemon::Path<Digraph> Path;
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  };
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  /// \addtogroup min_mean_cycle
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  /// @{
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  /// \brief Implementation of Howard's algorithm for finding a minimum
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  /// mean cycle.
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  ///
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  /// This class implements Howard's policy iteration algorithm for finding
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  /// a directed cycle of minimum mean cost in a digraph
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  /// \ref dasdan98minmeancycle, \ref dasdan04experimental.
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  /// This class provides the most efficient algorithm for the
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  /// minimum mean cycle problem, though the best known theoretical
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  /// bound on its running time is exponential.
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  ///
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  /// \tparam GR The type of the digraph the algorithm runs on.
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  /// \tparam CM The type of the cost map. The default
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  /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
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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 HowardMmcDefaultTraits
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  /// "HowardMmcDefaultTraits<GR, CM>".
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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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#ifdef DOXYGEN
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  template <typename GR, typename CM, typename TR>
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#else
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  template < typename GR,
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             typename CM = typename GR::template ArcMap<int>,
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             typename TR = HowardMmcDefaultTraits<GR, CM> >
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#endif
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  class HowardMmc
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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 cost map
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    typedef typename TR::CostMap CostMap;
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    /// The type of the arc costs
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    typedef typename TR::Cost Cost;
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    /// \brief The large cost type
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    ///
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    /// The large cost type used for internal computations.
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    /// By default, it is \c long \c long if the \c Cost type is integer,
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    /// otherwise it is \c double.
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    typedef typename TR::LargeCost LargeCost;
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    /// The tolerance type
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    typedef typename TR::Tolerance Tolerance;
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    /// \brief The path type of the found cycles
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    ///
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    /// The path type of the found cycles.
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    /// Using the \ref HowardMmcDefaultTraits "default traits class",
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    /// it is \ref lemon::Path "Path<Digraph>".
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    typedef typename TR::Path Path;
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    /// The \ref HowardMmcDefaultTraits "traits class" of the algorithm
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    typedef TR Traits;
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    /// \brief Constants for the causes of search termination.
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    ///
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    /// Enum type containing constants for the different causes of search
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    /// termination. The \ref findCycleMean() function returns one of
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    /// these values.
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    enum TerminationCause {
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      /// No directed cycle can be found in the digraph.
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      NO_CYCLE = 0,
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      /// Optimal solution (minimum cycle mean) is found.
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      OPTIMAL = 1,
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      /// The iteration count limit is reached.
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      ITERATION_LIMIT
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    };
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  private:
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    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
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    // The digraph the algorithm runs on
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    const Digraph &_gr;
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    // The cost of the arcs
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    const CostMap &_cost;
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    // Data for the found cycles
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    bool _curr_found, _best_found;
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    LargeCost _curr_cost, _best_cost;
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    int _curr_size, _best_size;
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    Node _curr_node, _best_node;
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    Path *_cycle_path;
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    bool _local_path;
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    // Internal data used by the algorithm
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    typename Digraph::template NodeMap<Arc> _policy;
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    typename Digraph::template NodeMap<bool> _reached;
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    typename Digraph::template NodeMap<int> _level;
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    typename Digraph::template NodeMap<LargeCost> _dist;
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    // Data for storing the strongly connected components
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    int _comp_num;
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    typename Digraph::template NodeMap<int> _comp;
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    std::vector<std::vector<Node> > _comp_nodes;
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    std::vector<Node>* _nodes;
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    typename Digraph::template NodeMap<std::vector<Arc> > _in_arcs;
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    // Queue used for BFS search
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    std::vector<Node> _queue;
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    int _qfront, _qback;
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    Tolerance _tolerance;
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    // Infinite constant
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    const LargeCost INF;
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  public:
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    /// \name Named Template Parameters
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    /// @{
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    template <typename T>
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    struct SetLargeCostTraits : public Traits {
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      typedef T LargeCost;
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      typedef lemon::Tolerance<T> Tolerance;
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    };
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    /// \brief \ref named-templ-param "Named parameter" for setting
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    /// \c LargeCost type.
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    ///
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    /// \ref named-templ-param "Named parameter" for setting \c LargeCost
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    /// type. It is used for internal computations in the algorithm.
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    template <typename T>
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    struct SetLargeCost
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      : public HowardMmc<GR, CM, SetLargeCostTraits<T> > {
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      typedef HowardMmc<GR, CM, SetLargeCostTraits<T> > Create;
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    };
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    template <typename T>
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    struct SetPathTraits : public Traits {
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      typedef T Path;
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    };
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    /// \brief \ref named-templ-param "Named parameter" for setting
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    /// \c %Path type.
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    ///
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    /// \ref named-templ-param "Named parameter" for setting the \c %Path
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    /// type of the found cycles.
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    /// It must conform to the \ref lemon::concepts::Path "Path" concept
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    /// and it must have an \c addBack() function.
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    template <typename T>
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    struct SetPath
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      : public HowardMmc<GR, CM, SetPathTraits<T> > {
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      typedef HowardMmc<GR, CM, SetPathTraits<T> > Create;
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    };
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    /// @}
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  protected:
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    HowardMmc() {}
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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 digraph The digraph the algorithm runs on.
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    /// \param cost The costs of the arcs.
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    HowardMmc( const Digraph &digraph,
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               const CostMap &cost ) :
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      _gr(digraph), _cost(cost), _best_found(false),
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      _best_cost(0), _best_size(1), _cycle_path(NULL), _local_path(false),
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      _policy(digraph), _reached(digraph), _level(digraph), _dist(digraph),
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      _comp(digraph), _in_arcs(digraph),
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      INF(std::numeric_limits<LargeCost>::has_infinity ?
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          std::numeric_limits<LargeCost>::infinity() :
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          std::numeric_limits<LargeCost>::max())
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    {}
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    /// Destructor.
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    ~HowardMmc() {
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      if (_local_path) delete _cycle_path;
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    }
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    /// \brief Set the path structure for storing the found cycle.
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    ///
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    /// This function sets an external path structure for storing the
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    /// found cycle.
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    ///
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    /// If you don't call this function before calling \ref run() or
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    /// \ref findCycleMean(), it will allocate a local \ref Path "path"
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    /// structure. The destuctor deallocates this automatically
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    /// allocated object, of course.
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    ///
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    /// \note The algorithm calls only the \ref lemon::Path::addBack()
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    /// "addBack()" function of the given path structure.
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    ///
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    /// \return <tt>(*this)</tt>
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    HowardMmc& cycle(Path &path) {
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      if (_local_path) {
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        delete _cycle_path;
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        _local_path = false;
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      }
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      _cycle_path = &path;
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      return *this;
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    }
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    /// \brief Set the tolerance used by the algorithm.
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    ///
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    /// This function sets the tolerance object used by the algorithm.
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    ///
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    /// \return <tt>(*this)</tt>
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    HowardMmc& tolerance(const Tolerance& tolerance) {
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      _tolerance = tolerance;
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      return *this;
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    }
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    /// \brief Return a const reference to the tolerance.
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    ///
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    /// This function returns a const reference to the tolerance object
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    /// used by the algorithm.
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    const Tolerance& tolerance() const {
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      return _tolerance;
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    }
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    /// \name Execution control
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    /// The simplest way to execute the algorithm is to call the \ref run()
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    /// function.\n
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    /// If you only need the minimum mean cost, you may call
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    /// \ref findCycleMean().
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    /// @{
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    /// \brief Run the algorithm.
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    ///
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    /// This function runs the algorithm.
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    /// It can be called more than once (e.g. if the underlying digraph
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    /// and/or the arc costs have been modified).
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    ///
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    /// \return \c true if a directed cycle exists in the digraph.
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    ///
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    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
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    /// \code
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    ///   return mmc.findCycleMean() && mmc.findCycle();
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    /// \endcode
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    bool run() {
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      return findCycleMean() && findCycle();
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    }
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    /// \brief Find the minimum cycle mean (or an upper bound).
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    ///
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    /// This function finds the minimum mean cost of the directed
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    /// cycles in the digraph (or an upper bound for it).
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    ///
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    /// By default, the function finds the exact minimum cycle mean,
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    /// but an optional limit can also be specified for the number of
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    /// iterations performed during the search process.
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    /// The return value indicates if the optimal solution is found
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    /// or the iteration limit is reached. In the latter case, an
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    /// approximate solution is provided, which corresponds to a directed
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    /// cycle whose mean cost is relatively small, but not necessarily
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    /// minimal.
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    ///
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    /// \param limit  The maximum allowed number of iterations during
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    /// the search process. Its default value implies that the algorithm 
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    /// runs until it finds the exact optimal solution.
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    ///
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    /// \return The termination cause of the search process.
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    /// For more information, see \ref TerminationCause. 
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    TerminationCause findCycleMean(int limit = std::numeric_limits<int>::max()) {
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      // Initialize and find strongly connected components
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      init();
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      findComponents();
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      // Find the minimum cycle mean in the components
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      int iter_count = 0;
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      bool iter_limit_reached = false;
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      for (int comp = 0; comp < _comp_num; ++comp) {
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        // Find the minimum mean cycle in the current component
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        if (!buildPolicyGraph(comp)) continue;
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        while (true) {
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          if (++iter_count > limit) {
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            iter_limit_reached = true;
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            break;
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          }
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          findPolicyCycle();
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          if (!computeNodeDistances()) break;
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        }
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        // Update the best cycle (global minimum mean cycle)
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        if ( _curr_found && (!_best_found ||
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             _curr_cost * _best_size < _best_cost * _curr_size) ) {
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          _best_found = true;
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          _best_cost = _curr_cost;
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          _best_size = _curr_size;
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          _best_node = _curr_node;
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        }
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        if (iter_limit_reached) break;
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      }
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      if (iter_limit_reached) {
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        return ITERATION_LIMIT;
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      } else {
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        return _best_found ? OPTIMAL : NO_CYCLE;
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      }
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    }
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    /// \brief Find a minimum mean directed cycle.
kpeter@758
   404
    ///
kpeter@864
   405
    /// This function finds a directed cycle of minimum mean cost
kpeter@864
   406
    /// in the digraph using the data computed by findCycleMean().
kpeter@758
   407
    ///
kpeter@758
   408
    /// \return \c true if a directed cycle exists in the digraph.
kpeter@758
   409
    ///
kpeter@864
   410
    /// \pre \ref findCycleMean() must be called before using this function.
kpeter@758
   411
    bool findCycle() {
kpeter@760
   412
      if (!_best_found) return false;
kpeter@760
   413
      _cycle_path->addBack(_policy[_best_node]);
kpeter@760
   414
      for ( Node v = _best_node;
kpeter@760
   415
            (v = _gr.target(_policy[v])) != _best_node; ) {
kpeter@758
   416
        _cycle_path->addBack(_policy[v]);
kpeter@758
   417
      }
kpeter@758
   418
      return true;
kpeter@758
   419
    }
kpeter@758
   420
kpeter@758
   421
    /// @}
kpeter@758
   422
kpeter@758
   423
    /// \name Query Functions
kpeter@759
   424
    /// The results of the algorithm can be obtained using these
kpeter@758
   425
    /// functions.\n
kpeter@758
   426
    /// The algorithm should be executed before using them.
kpeter@758
   427
kpeter@758
   428
    /// @{
kpeter@758
   429
kpeter@864
   430
    /// \brief Return the total cost of the found cycle.
kpeter@758
   431
    ///
kpeter@864
   432
    /// This function returns the total cost of the found cycle.
kpeter@758
   433
    ///
kpeter@864
   434
    /// \pre \ref run() or \ref findCycleMean() must be called before
kpeter@758
   435
    /// using this function.
kpeter@864
   436
    Cost cycleCost() const {
kpeter@864
   437
      return static_cast<Cost>(_best_cost);
kpeter@758
   438
    }
kpeter@758
   439
kpeter@758
   440
    /// \brief Return the number of arcs on the found cycle.
kpeter@758
   441
    ///
kpeter@758
   442
    /// This function returns the number of arcs on the found cycle.
kpeter@758
   443
    ///
kpeter@864
   444
    /// \pre \ref run() or \ref findCycleMean() must be called before
kpeter@758
   445
    /// using this function.
kpeter@864
   446
    int cycleSize() const {
kpeter@760
   447
      return _best_size;
kpeter@758
   448
    }
kpeter@758
   449
kpeter@864
   450
    /// \brief Return the mean cost of the found cycle.
kpeter@758
   451
    ///
kpeter@864
   452
    /// This function returns the mean cost of the found cycle.
kpeter@758
   453
    ///
kpeter@760
   454
    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
kpeter@758
   455
    /// following code.
kpeter@758
   456
    /// \code
kpeter@864
   457
    ///   return static_cast<double>(alg.cycleCost()) / alg.cycleSize();
kpeter@758
   458
    /// \endcode
kpeter@758
   459
    ///
kpeter@864
   460
    /// \pre \ref run() or \ref findCycleMean() must be called before
kpeter@758
   461
    /// using this function.
kpeter@758
   462
    double cycleMean() const {
kpeter@864
   463
      return static_cast<double>(_best_cost) / _best_size;
kpeter@758
   464
    }
kpeter@758
   465
kpeter@758
   466
    /// \brief Return the found cycle.
kpeter@758
   467
    ///
kpeter@758
   468
    /// This function returns a const reference to the path structure
kpeter@758
   469
    /// storing the found cycle.
kpeter@758
   470
    ///
kpeter@758
   471
    /// \pre \ref run() or \ref findCycle() must be called before using
kpeter@758
   472
    /// this function.
kpeter@758
   473
    const Path& cycle() const {
kpeter@758
   474
      return *_cycle_path;
kpeter@758
   475
    }
kpeter@758
   476
kpeter@758
   477
    ///@}
kpeter@758
   478
kpeter@758
   479
  private:
kpeter@758
   480
kpeter@760
   481
    // Initialize
kpeter@760
   482
    void init() {
kpeter@760
   483
      if (!_cycle_path) {
kpeter@760
   484
        _local_path = true;
kpeter@760
   485
        _cycle_path = new Path;
kpeter@758
   486
      }
kpeter@760
   487
      _queue.resize(countNodes(_gr));
kpeter@760
   488
      _best_found = false;
kpeter@864
   489
      _best_cost = 0;
kpeter@760
   490
      _best_size = 1;
kpeter@760
   491
      _cycle_path->clear();
kpeter@760
   492
    }
alpar@877
   493
kpeter@760
   494
    // Find strongly connected components and initialize _comp_nodes
kpeter@760
   495
    // and _in_arcs
kpeter@760
   496
    void findComponents() {
kpeter@760
   497
      _comp_num = stronglyConnectedComponents(_gr, _comp);
kpeter@760
   498
      _comp_nodes.resize(_comp_num);
kpeter@760
   499
      if (_comp_num == 1) {
kpeter@760
   500
        _comp_nodes[0].clear();
kpeter@760
   501
        for (NodeIt n(_gr); n != INVALID; ++n) {
kpeter@760
   502
          _comp_nodes[0].push_back(n);
kpeter@760
   503
          _in_arcs[n].clear();
kpeter@760
   504
          for (InArcIt a(_gr, n); a != INVALID; ++a) {
kpeter@760
   505
            _in_arcs[n].push_back(a);
kpeter@760
   506
          }
kpeter@760
   507
        }
kpeter@760
   508
      } else {
kpeter@760
   509
        for (int i = 0; i < _comp_num; ++i)
kpeter@760
   510
          _comp_nodes[i].clear();
kpeter@760
   511
        for (NodeIt n(_gr); n != INVALID; ++n) {
kpeter@760
   512
          int k = _comp[n];
kpeter@760
   513
          _comp_nodes[k].push_back(n);
kpeter@760
   514
          _in_arcs[n].clear();
kpeter@760
   515
          for (InArcIt a(_gr, n); a != INVALID; ++a) {
kpeter@760
   516
            if (_comp[_gr.source(a)] == k) _in_arcs[n].push_back(a);
kpeter@760
   517
          }
kpeter@760
   518
        }
kpeter@758
   519
      }
kpeter@760
   520
    }
kpeter@760
   521
kpeter@760
   522
    // Build the policy graph in the given strongly connected component
kpeter@760
   523
    // (the out-degree of every node is 1)
kpeter@760
   524
    bool buildPolicyGraph(int comp) {
kpeter@760
   525
      _nodes = &(_comp_nodes[comp]);
kpeter@760
   526
      if (_nodes->size() < 1 ||
kpeter@760
   527
          (_nodes->size() == 1 && _in_arcs[(*_nodes)[0]].size() == 0)) {
kpeter@760
   528
        return false;
kpeter@758
   529
      }
kpeter@760
   530
      for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@767
   531
        _dist[(*_nodes)[i]] = INF;
kpeter@760
   532
      }
kpeter@760
   533
      Node u, v;
kpeter@760
   534
      Arc e;
kpeter@760
   535
      for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@760
   536
        v = (*_nodes)[i];
kpeter@760
   537
        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
kpeter@760
   538
          e = _in_arcs[v][j];
kpeter@760
   539
          u = _gr.source(e);
kpeter@864
   540
          if (_cost[e] < _dist[u]) {
kpeter@864
   541
            _dist[u] = _cost[e];
kpeter@760
   542
            _policy[u] = e;
kpeter@760
   543
          }
kpeter@758
   544
        }
kpeter@758
   545
      }
kpeter@758
   546
      return true;
kpeter@758
   547
    }
kpeter@758
   548
kpeter@760
   549
    // Find the minimum mean cycle in the policy graph
kpeter@760
   550
    void findPolicyCycle() {
kpeter@760
   551
      for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@760
   552
        _level[(*_nodes)[i]] = -1;
kpeter@760
   553
      }
kpeter@864
   554
      LargeCost ccost;
kpeter@758
   555
      int csize;
kpeter@758
   556
      Node u, v;
kpeter@760
   557
      _curr_found = false;
kpeter@760
   558
      for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@760
   559
        u = (*_nodes)[i];
kpeter@760
   560
        if (_level[u] >= 0) continue;
kpeter@760
   561
        for (; _level[u] < 0; u = _gr.target(_policy[u])) {
kpeter@760
   562
          _level[u] = i;
kpeter@760
   563
        }
kpeter@760
   564
        if (_level[u] == i) {
kpeter@760
   565
          // A cycle is found
kpeter@864
   566
          ccost = _cost[_policy[u]];
kpeter@760
   567
          csize = 1;
kpeter@760
   568
          for (v = u; (v = _gr.target(_policy[v])) != u; ) {
kpeter@864
   569
            ccost += _cost[_policy[v]];
kpeter@760
   570
            ++csize;
kpeter@758
   571
          }
kpeter@760
   572
          if ( !_curr_found ||
kpeter@864
   573
               (ccost * _curr_size < _curr_cost * csize) ) {
kpeter@760
   574
            _curr_found = true;
kpeter@864
   575
            _curr_cost = ccost;
kpeter@760
   576
            _curr_size = csize;
kpeter@760
   577
            _curr_node = u;
kpeter@758
   578
          }
kpeter@758
   579
        }
kpeter@758
   580
      }
kpeter@758
   581
    }
kpeter@758
   582
kpeter@760
   583
    // Contract the policy graph and compute node distances
kpeter@758
   584
    bool computeNodeDistances() {
kpeter@760
   585
      // Find the component of the main cycle and compute node distances
kpeter@760
   586
      // using reverse BFS
kpeter@760
   587
      for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@760
   588
        _reached[(*_nodes)[i]] = false;
kpeter@760
   589
      }
kpeter@760
   590
      _qfront = _qback = 0;
kpeter@760
   591
      _queue[0] = _curr_node;
kpeter@760
   592
      _reached[_curr_node] = true;
kpeter@760
   593
      _dist[_curr_node] = 0;
kpeter@758
   594
      Node u, v;
kpeter@760
   595
      Arc e;
kpeter@760
   596
      while (_qfront <= _qback) {
kpeter@760
   597
        v = _queue[_qfront++];
kpeter@760
   598
        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
kpeter@760
   599
          e = _in_arcs[v][j];
kpeter@758
   600
          u = _gr.source(e);
kpeter@760
   601
          if (_policy[u] == e && !_reached[u]) {
kpeter@760
   602
            _reached[u] = true;
kpeter@864
   603
            _dist[u] = _dist[v] + _cost[e] * _curr_size - _curr_cost;
kpeter@760
   604
            _queue[++_qback] = u;
kpeter@758
   605
          }
kpeter@758
   606
        }
kpeter@758
   607
      }
kpeter@760
   608
kpeter@760
   609
      // Connect all other nodes to this component and compute node
kpeter@760
   610
      // distances using reverse BFS
kpeter@760
   611
      _qfront = 0;
kpeter@760
   612
      while (_qback < int(_nodes->size())-1) {
kpeter@760
   613
        v = _queue[_qfront++];
kpeter@760
   614
        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
kpeter@760
   615
          e = _in_arcs[v][j];
kpeter@760
   616
          u = _gr.source(e);
kpeter@760
   617
          if (!_reached[u]) {
kpeter@760
   618
            _reached[u] = true;
kpeter@760
   619
            _policy[u] = e;
kpeter@864
   620
            _dist[u] = _dist[v] + _cost[e] * _curr_size - _curr_cost;
kpeter@760
   621
            _queue[++_qback] = u;
kpeter@760
   622
          }
kpeter@760
   623
        }
kpeter@760
   624
      }
kpeter@760
   625
kpeter@760
   626
      // Improve node distances
kpeter@758
   627
      bool improved = false;
kpeter@760
   628
      for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@760
   629
        v = (*_nodes)[i];
kpeter@760
   630
        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
kpeter@760
   631
          e = _in_arcs[v][j];
kpeter@760
   632
          u = _gr.source(e);
kpeter@864
   633
          LargeCost delta = _dist[v] + _cost[e] * _curr_size - _curr_cost;
kpeter@761
   634
          if (_tolerance.less(delta, _dist[u])) {
kpeter@760
   635
            _dist[u] = delta;
kpeter@760
   636
            _policy[u] = e;
kpeter@760
   637
            improved = true;
kpeter@760
   638
          }
kpeter@758
   639
        }
kpeter@758
   640
      }
kpeter@758
   641
      return improved;
kpeter@758
   642
    }
kpeter@758
   643
kpeter@864
   644
  }; //class HowardMmc
kpeter@758
   645
kpeter@758
   646
  ///@}
kpeter@758
   647
kpeter@758
   648
} //namespace lemon
kpeter@758
   649
kpeter@864
   650
#endif //LEMON_HOWARD_MMC_H