alpar@877: /* -*- mode: C++; indent-tabs-mode: nil; -*-
kpeter@766:  *
alpar@877:  * This file is a part of LEMON, a generic C++ optimization library.
kpeter@766:  *
alpar@877:  * Copyright (C) 2003-2010
kpeter@766:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
kpeter@766:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
kpeter@766:  *
kpeter@766:  * Permission to use, modify and distribute this software is granted
kpeter@766:  * provided that this copyright notice appears in all copies. For
kpeter@766:  * precise terms see the accompanying LICENSE file.
kpeter@766:  *
kpeter@766:  * This software is provided "AS IS" with no warranty of any kind,
kpeter@766:  * express or implied, and with no claim as to its suitability for any
kpeter@766:  * purpose.
kpeter@766:  *
kpeter@766:  */
kpeter@766: 
kpeter@864: #ifndef LEMON_HARTMANN_ORLIN_MMC_H
kpeter@864: #define LEMON_HARTMANN_ORLIN_MMC_H
kpeter@766: 
kpeter@768: /// \ingroup min_mean_cycle
kpeter@766: ///
kpeter@766: /// \file
kpeter@766: /// \brief Hartmann-Orlin's algorithm for finding a minimum mean cycle.
kpeter@766: 
kpeter@766: #include <vector>
kpeter@766: #include <limits>
kpeter@766: #include <lemon/core.h>
kpeter@766: #include <lemon/path.h>
kpeter@766: #include <lemon/tolerance.h>
kpeter@766: #include <lemon/connectivity.h>
kpeter@766: 
kpeter@766: namespace lemon {
kpeter@766: 
kpeter@864:   /// \brief Default traits class of HartmannOrlinMmc class.
kpeter@766:   ///
kpeter@864:   /// Default traits class of HartmannOrlinMmc class.
kpeter@766:   /// \tparam GR The type of the digraph.
kpeter@864:   /// \tparam CM The type of the cost map.
kpeter@879:   /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
kpeter@766: #ifdef DOXYGEN
kpeter@864:   template <typename GR, typename CM>
kpeter@766: #else
kpeter@864:   template <typename GR, typename CM,
kpeter@864:     bool integer = std::numeric_limits<typename CM::Value>::is_integer>
kpeter@766: #endif
kpeter@864:   struct HartmannOrlinMmcDefaultTraits
kpeter@766:   {
kpeter@766:     /// The type of the digraph
kpeter@766:     typedef GR Digraph;
kpeter@864:     /// The type of the cost map
kpeter@864:     typedef CM CostMap;
kpeter@864:     /// The type of the arc costs
kpeter@864:     typedef typename CostMap::Value Cost;
kpeter@766: 
kpeter@864:     /// \brief The large cost type used for internal computations
kpeter@766:     ///
kpeter@864:     /// The large cost type used for internal computations.
kpeter@864:     /// It is \c long \c long if the \c Cost type is integer,
kpeter@766:     /// otherwise it is \c double.
kpeter@864:     /// \c Cost must be convertible to \c LargeCost.
kpeter@864:     typedef double LargeCost;
kpeter@766: 
kpeter@766:     /// The tolerance type used for internal computations
kpeter@864:     typedef lemon::Tolerance<LargeCost> Tolerance;
kpeter@766: 
kpeter@766:     /// \brief The path type of the found cycles
kpeter@766:     ///
kpeter@766:     /// The path type of the found cycles.
kpeter@766:     /// It must conform to the \ref lemon::concepts::Path "Path" concept
kpeter@772:     /// and it must have an \c addFront() function.
kpeter@766:     typedef lemon::Path<Digraph> Path;
kpeter@766:   };
kpeter@766: 
kpeter@864:   // Default traits class for integer cost types
kpeter@864:   template <typename GR, typename CM>
kpeter@864:   struct HartmannOrlinMmcDefaultTraits<GR, CM, true>
kpeter@766:   {
kpeter@766:     typedef GR Digraph;
kpeter@864:     typedef CM CostMap;
kpeter@864:     typedef typename CostMap::Value Cost;
kpeter@766: #ifdef LEMON_HAVE_LONG_LONG
kpeter@864:     typedef long long LargeCost;
kpeter@766: #else
kpeter@864:     typedef long LargeCost;
kpeter@766: #endif
kpeter@864:     typedef lemon::Tolerance<LargeCost> Tolerance;
kpeter@766:     typedef lemon::Path<Digraph> Path;
kpeter@766:   };
kpeter@766: 
kpeter@766: 
kpeter@768:   /// \addtogroup min_mean_cycle
kpeter@766:   /// @{
kpeter@766: 
kpeter@766:   /// \brief Implementation of the Hartmann-Orlin algorithm for finding
kpeter@766:   /// a minimum mean cycle.
kpeter@766:   ///
kpeter@766:   /// This class implements the Hartmann-Orlin algorithm for finding
kpeter@864:   /// a directed cycle of minimum mean cost in a digraph
kpeter@1002:   /// \ref hartmann93finding, \ref dasdan98minmeancycle.
kpeter@1049:   /// This method is based on \ref KarpMmc "Karp"'s original algorithm, but
kpeter@1049:   /// applies an early termination scheme. It makes the algorithm
kpeter@1049:   /// significantly faster for some problem instances, but slower for others.
kpeter@1049:   /// The algorithm runs in time O(ne) and uses space O(n<sup>2</sup>+e).
kpeter@766:   ///
kpeter@766:   /// \tparam GR The type of the digraph the algorithm runs on.
kpeter@864:   /// \tparam CM The type of the cost map. The default
kpeter@766:   /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
kpeter@825:   /// \tparam TR The traits class that defines various types used by the
kpeter@864:   /// algorithm. By default, it is \ref HartmannOrlinMmcDefaultTraits
kpeter@864:   /// "HartmannOrlinMmcDefaultTraits<GR, CM>".
kpeter@825:   /// In most cases, this parameter should not be set directly,
kpeter@825:   /// consider to use the named template parameters instead.
kpeter@766: #ifdef DOXYGEN
kpeter@864:   template <typename GR, typename CM, typename TR>
kpeter@766: #else
kpeter@766:   template < typename GR,
kpeter@864:              typename CM = typename GR::template ArcMap<int>,
kpeter@864:              typename TR = HartmannOrlinMmcDefaultTraits<GR, CM> >
kpeter@766: #endif
kpeter@864:   class HartmannOrlinMmc
kpeter@766:   {
kpeter@766:   public:
kpeter@766: 
kpeter@766:     /// The type of the digraph
kpeter@766:     typedef typename TR::Digraph Digraph;
kpeter@864:     /// The type of the cost map
kpeter@864:     typedef typename TR::CostMap CostMap;
kpeter@864:     /// The type of the arc costs
kpeter@864:     typedef typename TR::Cost Cost;
kpeter@766: 
kpeter@864:     /// \brief The large cost type
kpeter@766:     ///
kpeter@864:     /// The large cost type used for internal computations.
kpeter@864:     /// By default, it is \c long \c long if the \c Cost type is integer,
kpeter@766:     /// otherwise it is \c double.
kpeter@864:     typedef typename TR::LargeCost LargeCost;
kpeter@766: 
kpeter@766:     /// The tolerance type
kpeter@766:     typedef typename TR::Tolerance Tolerance;
kpeter@766: 
kpeter@766:     /// \brief The path type of the found cycles
kpeter@766:     ///
kpeter@766:     /// The path type of the found cycles.
kpeter@864:     /// Using the \ref HartmannOrlinMmcDefaultTraits "default traits class",
kpeter@766:     /// it is \ref lemon::Path "Path<Digraph>".
kpeter@766:     typedef typename TR::Path Path;
kpeter@766: 
kpeter@864:     /// The \ref HartmannOrlinMmcDefaultTraits "traits class" of the algorithm
kpeter@766:     typedef TR Traits;
kpeter@766: 
kpeter@766:   private:
kpeter@766: 
kpeter@766:     TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
kpeter@766: 
kpeter@766:     // Data sturcture for path data
kpeter@766:     struct PathData
kpeter@766:     {
kpeter@864:       LargeCost dist;
kpeter@766:       Arc pred;
kpeter@864:       PathData(LargeCost d, Arc p = INVALID) :
kpeter@767:         dist(d), pred(p) {}
kpeter@766:     };
kpeter@766: 
kpeter@766:     typedef typename Digraph::template NodeMap<std::vector<PathData> >
kpeter@766:       PathDataNodeMap;
kpeter@766: 
kpeter@766:   private:
kpeter@766: 
kpeter@766:     // The digraph the algorithm runs on
kpeter@766:     const Digraph &_gr;
kpeter@864:     // The cost of the arcs
kpeter@864:     const CostMap &_cost;
kpeter@766: 
kpeter@766:     // Data for storing the strongly connected components
kpeter@766:     int _comp_num;
kpeter@766:     typename Digraph::template NodeMap<int> _comp;
kpeter@766:     std::vector<std::vector<Node> > _comp_nodes;
kpeter@766:     std::vector<Node>* _nodes;
kpeter@766:     typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
kpeter@766: 
kpeter@766:     // Data for the found cycles
kpeter@766:     bool _curr_found, _best_found;
kpeter@864:     LargeCost _curr_cost, _best_cost;
kpeter@766:     int _curr_size, _best_size;
kpeter@766:     Node _curr_node, _best_node;
kpeter@766:     int _curr_level, _best_level;
kpeter@766: 
kpeter@766:     Path *_cycle_path;
kpeter@766:     bool _local_path;
kpeter@766: 
kpeter@766:     // Node map for storing path data
kpeter@766:     PathDataNodeMap _data;
kpeter@766:     // The processed nodes in the last round
kpeter@766:     std::vector<Node> _process;
kpeter@766: 
kpeter@766:     Tolerance _tolerance;
kpeter@766: 
kpeter@767:     // Infinite constant
kpeter@864:     const LargeCost INF;
kpeter@767: 
kpeter@766:   public:
kpeter@766: 
kpeter@766:     /// \name Named Template Parameters
kpeter@766:     /// @{
kpeter@766: 
kpeter@766:     template <typename T>
kpeter@864:     struct SetLargeCostTraits : public Traits {
kpeter@864:       typedef T LargeCost;
kpeter@766:       typedef lemon::Tolerance<T> Tolerance;
kpeter@766:     };
kpeter@766: 
kpeter@766:     /// \brief \ref named-templ-param "Named parameter" for setting
kpeter@864:     /// \c LargeCost type.
kpeter@766:     ///
kpeter@864:     /// \ref named-templ-param "Named parameter" for setting \c LargeCost
kpeter@766:     /// type. It is used for internal computations in the algorithm.
kpeter@766:     template <typename T>
kpeter@864:     struct SetLargeCost
kpeter@864:       : public HartmannOrlinMmc<GR, CM, SetLargeCostTraits<T> > {
kpeter@864:       typedef HartmannOrlinMmc<GR, CM, SetLargeCostTraits<T> > Create;
kpeter@766:     };
kpeter@766: 
kpeter@766:     template <typename T>
kpeter@766:     struct SetPathTraits : public Traits {
kpeter@766:       typedef T Path;
kpeter@766:     };
kpeter@766: 
kpeter@766:     /// \brief \ref named-templ-param "Named parameter" for setting
kpeter@766:     /// \c %Path type.
kpeter@766:     ///
kpeter@766:     /// \ref named-templ-param "Named parameter" for setting the \c %Path
kpeter@766:     /// type of the found cycles.
kpeter@766:     /// It must conform to the \ref lemon::concepts::Path "Path" concept
kpeter@766:     /// and it must have an \c addFront() function.
kpeter@766:     template <typename T>
kpeter@766:     struct SetPath
kpeter@864:       : public HartmannOrlinMmc<GR, CM, SetPathTraits<T> > {
kpeter@864:       typedef HartmannOrlinMmc<GR, CM, SetPathTraits<T> > Create;
kpeter@766:     };
kpeter@766: 
kpeter@766:     /// @}
kpeter@766: 
kpeter@863:   protected:
kpeter@863: 
kpeter@864:     HartmannOrlinMmc() {}
kpeter@863: 
kpeter@766:   public:
kpeter@766: 
kpeter@766:     /// \brief Constructor.
kpeter@766:     ///
kpeter@766:     /// The constructor of the class.
kpeter@766:     ///
kpeter@766:     /// \param digraph The digraph the algorithm runs on.
kpeter@864:     /// \param cost The costs of the arcs.
kpeter@864:     HartmannOrlinMmc( const Digraph &digraph,
kpeter@864:                       const CostMap &cost ) :
kpeter@864:       _gr(digraph), _cost(cost), _comp(digraph), _out_arcs(digraph),
kpeter@864:       _best_found(false), _best_cost(0), _best_size(1),
kpeter@767:       _cycle_path(NULL), _local_path(false), _data(digraph),
kpeter@864:       INF(std::numeric_limits<LargeCost>::has_infinity ?
kpeter@864:           std::numeric_limits<LargeCost>::infinity() :
kpeter@864:           std::numeric_limits<LargeCost>::max())
kpeter@766:     {}
kpeter@766: 
kpeter@766:     /// Destructor.
kpeter@864:     ~HartmannOrlinMmc() {
kpeter@766:       if (_local_path) delete _cycle_path;
kpeter@766:     }
kpeter@766: 
kpeter@766:     /// \brief Set the path structure for storing the found cycle.
kpeter@766:     ///
kpeter@766:     /// This function sets an external path structure for storing the
kpeter@766:     /// found cycle.
kpeter@766:     ///
kpeter@766:     /// If you don't call this function before calling \ref run() or
kpeter@1049:     /// \ref findCycleMean(), a local \ref Path "path" structure
kpeter@1049:     /// will be allocated. The destuctor deallocates this automatically
kpeter@766:     /// allocated object, of course.
kpeter@766:     ///
kpeter@766:     /// \note The algorithm calls only the \ref lemon::Path::addFront()
kpeter@766:     /// "addFront()" function of the given path structure.
kpeter@766:     ///
kpeter@766:     /// \return <tt>(*this)</tt>
kpeter@864:     HartmannOrlinMmc& cycle(Path &path) {
kpeter@766:       if (_local_path) {
kpeter@766:         delete _cycle_path;
kpeter@766:         _local_path = false;
kpeter@766:       }
kpeter@766:       _cycle_path = &path;
kpeter@766:       return *this;
kpeter@766:     }
kpeter@766: 
kpeter@769:     /// \brief Set the tolerance used by the algorithm.
kpeter@769:     ///
kpeter@769:     /// This function sets the tolerance object used by the algorithm.
kpeter@769:     ///
kpeter@769:     /// \return <tt>(*this)</tt>
kpeter@864:     HartmannOrlinMmc& tolerance(const Tolerance& tolerance) {
kpeter@769:       _tolerance = tolerance;
kpeter@769:       return *this;
kpeter@769:     }
kpeter@769: 
kpeter@769:     /// \brief Return a const reference to the tolerance.
kpeter@769:     ///
kpeter@769:     /// This function returns a const reference to the tolerance object
kpeter@769:     /// used by the algorithm.
kpeter@769:     const Tolerance& tolerance() const {
kpeter@769:       return _tolerance;
kpeter@769:     }
kpeter@769: 
kpeter@766:     /// \name Execution control
kpeter@766:     /// The simplest way to execute the algorithm is to call the \ref run()
kpeter@766:     /// function.\n
kpeter@864:     /// If you only need the minimum mean cost, you may call
kpeter@864:     /// \ref findCycleMean().
kpeter@766: 
kpeter@766:     /// @{
kpeter@766: 
kpeter@766:     /// \brief Run the algorithm.
kpeter@766:     ///
kpeter@766:     /// This function runs the algorithm.
kpeter@766:     /// It can be called more than once (e.g. if the underlying digraph
kpeter@864:     /// and/or the arc costs have been modified).
kpeter@766:     ///
kpeter@766:     /// \return \c true if a directed cycle exists in the digraph.
kpeter@766:     ///
kpeter@766:     /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
kpeter@766:     /// \code
kpeter@864:     ///   return mmc.findCycleMean() && mmc.findCycle();
kpeter@766:     /// \endcode
kpeter@766:     bool run() {
kpeter@864:       return findCycleMean() && findCycle();
kpeter@766:     }
kpeter@766: 
kpeter@766:     /// \brief Find the minimum cycle mean.
kpeter@766:     ///
kpeter@864:     /// This function finds the minimum mean cost of the directed
kpeter@766:     /// cycles in the digraph.
kpeter@766:     ///
kpeter@766:     /// \return \c true if a directed cycle exists in the digraph.
kpeter@864:     bool findCycleMean() {
kpeter@766:       // Initialization and find strongly connected components
kpeter@766:       init();
kpeter@766:       findComponents();
alpar@877: 
kpeter@766:       // Find the minimum cycle mean in the components
kpeter@766:       for (int comp = 0; comp < _comp_num; ++comp) {
kpeter@766:         if (!initComponent(comp)) continue;
kpeter@766:         processRounds();
alpar@877: 
kpeter@766:         // Update the best cycle (global minimum mean cycle)
alpar@877:         if ( _curr_found && (!_best_found ||
kpeter@864:              _curr_cost * _best_size < _best_cost * _curr_size) ) {
kpeter@766:           _best_found = true;
kpeter@864:           _best_cost = _curr_cost;
kpeter@766:           _best_size = _curr_size;
kpeter@766:           _best_node = _curr_node;
kpeter@766:           _best_level = _curr_level;
kpeter@766:         }
kpeter@766:       }
kpeter@766:       return _best_found;
kpeter@766:     }
kpeter@766: 
kpeter@766:     /// \brief Find a minimum mean directed cycle.
kpeter@766:     ///
kpeter@864:     /// This function finds a directed cycle of minimum mean cost
kpeter@864:     /// in the digraph using the data computed by findCycleMean().
kpeter@766:     ///
kpeter@766:     /// \return \c true if a directed cycle exists in the digraph.
kpeter@766:     ///
kpeter@864:     /// \pre \ref findCycleMean() must be called before using this function.
kpeter@766:     bool findCycle() {
kpeter@766:       if (!_best_found) return false;
kpeter@766:       IntNodeMap reached(_gr, -1);
kpeter@766:       int r = _best_level + 1;
kpeter@766:       Node u = _best_node;
kpeter@766:       while (reached[u] < 0) {
kpeter@766:         reached[u] = --r;
kpeter@766:         u = _gr.source(_data[u][r].pred);
kpeter@766:       }
kpeter@766:       r = reached[u];
kpeter@766:       Arc e = _data[u][r].pred;
kpeter@766:       _cycle_path->addFront(e);
kpeter@864:       _best_cost = _cost[e];
kpeter@766:       _best_size = 1;
kpeter@766:       Node v;
kpeter@766:       while ((v = _gr.source(e)) != u) {
kpeter@766:         e = _data[v][--r].pred;
kpeter@766:         _cycle_path->addFront(e);
kpeter@864:         _best_cost += _cost[e];
kpeter@766:         ++_best_size;
kpeter@766:       }
kpeter@766:       return true;
kpeter@766:     }
kpeter@766: 
kpeter@766:     /// @}
kpeter@766: 
kpeter@766:     /// \name Query Functions
kpeter@766:     /// The results of the algorithm can be obtained using these
kpeter@766:     /// functions.\n
kpeter@766:     /// The algorithm should be executed before using them.
kpeter@766: 
kpeter@766:     /// @{
kpeter@766: 
kpeter@864:     /// \brief Return the total cost of the found cycle.
kpeter@766:     ///
kpeter@864:     /// This function returns the total cost of the found cycle.
kpeter@766:     ///
kpeter@864:     /// \pre \ref run() or \ref findCycleMean() must be called before
kpeter@766:     /// using this function.
kpeter@864:     Cost cycleCost() const {
kpeter@864:       return static_cast<Cost>(_best_cost);
kpeter@766:     }
kpeter@766: 
kpeter@766:     /// \brief Return the number of arcs on the found cycle.
kpeter@766:     ///
kpeter@766:     /// This function returns the number of arcs on the found cycle.
kpeter@766:     ///
kpeter@864:     /// \pre \ref run() or \ref findCycleMean() must be called before
kpeter@766:     /// using this function.
kpeter@864:     int cycleSize() const {
kpeter@766:       return _best_size;
kpeter@766:     }
kpeter@766: 
kpeter@864:     /// \brief Return the mean cost of the found cycle.
kpeter@766:     ///
kpeter@864:     /// This function returns the mean cost of the found cycle.
kpeter@766:     ///
kpeter@766:     /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
kpeter@766:     /// following code.
kpeter@766:     /// \code
kpeter@864:     ///   return static_cast<double>(alg.cycleCost()) / alg.cycleSize();
kpeter@766:     /// \endcode
kpeter@766:     ///
kpeter@864:     /// \pre \ref run() or \ref findCycleMean() must be called before
kpeter@766:     /// using this function.
kpeter@766:     double cycleMean() const {
kpeter@864:       return static_cast<double>(_best_cost) / _best_size;
kpeter@766:     }
kpeter@766: 
kpeter@766:     /// \brief Return the found cycle.
kpeter@766:     ///
kpeter@766:     /// This function returns a const reference to the path structure
kpeter@766:     /// storing the found cycle.
kpeter@766:     ///
kpeter@766:     /// \pre \ref run() or \ref findCycle() must be called before using
kpeter@766:     /// this function.
kpeter@766:     const Path& cycle() const {
kpeter@766:       return *_cycle_path;
kpeter@766:     }
kpeter@766: 
kpeter@766:     ///@}
kpeter@766: 
kpeter@766:   private:
kpeter@766: 
kpeter@766:     // Initialization
kpeter@766:     void init() {
kpeter@766:       if (!_cycle_path) {
kpeter@766:         _local_path = true;
kpeter@766:         _cycle_path = new Path;
kpeter@766:       }
kpeter@766:       _cycle_path->clear();
kpeter@766:       _best_found = false;
kpeter@864:       _best_cost = 0;
kpeter@766:       _best_size = 1;
kpeter@766:       _cycle_path->clear();
kpeter@766:       for (NodeIt u(_gr); u != INVALID; ++u)
kpeter@766:         _data[u].clear();
kpeter@766:     }
kpeter@766: 
kpeter@766:     // Find strongly connected components and initialize _comp_nodes
kpeter@766:     // and _out_arcs
kpeter@766:     void findComponents() {
kpeter@766:       _comp_num = stronglyConnectedComponents(_gr, _comp);
kpeter@766:       _comp_nodes.resize(_comp_num);
kpeter@766:       if (_comp_num == 1) {
kpeter@766:         _comp_nodes[0].clear();
kpeter@766:         for (NodeIt n(_gr); n != INVALID; ++n) {
kpeter@766:           _comp_nodes[0].push_back(n);
kpeter@766:           _out_arcs[n].clear();
kpeter@766:           for (OutArcIt a(_gr, n); a != INVALID; ++a) {
kpeter@766:             _out_arcs[n].push_back(a);
kpeter@766:           }
kpeter@766:         }
kpeter@766:       } else {
kpeter@766:         for (int i = 0; i < _comp_num; ++i)
kpeter@766:           _comp_nodes[i].clear();
kpeter@766:         for (NodeIt n(_gr); n != INVALID; ++n) {
kpeter@766:           int k = _comp[n];
kpeter@766:           _comp_nodes[k].push_back(n);
kpeter@766:           _out_arcs[n].clear();
kpeter@766:           for (OutArcIt a(_gr, n); a != INVALID; ++a) {
kpeter@766:             if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
kpeter@766:           }
kpeter@766:         }
kpeter@766:       }
kpeter@766:     }
kpeter@766: 
kpeter@766:     // Initialize path data for the current component
kpeter@766:     bool initComponent(int comp) {
kpeter@766:       _nodes = &(_comp_nodes[comp]);
kpeter@766:       int n = _nodes->size();
kpeter@766:       if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
kpeter@766:         return false;
alpar@877:       }
kpeter@766:       for (int i = 0; i < n; ++i) {
kpeter@767:         _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
kpeter@766:       }
kpeter@766:       return true;
kpeter@766:     }
kpeter@766: 
kpeter@766:     // Process all rounds of computing path data for the current component.
kpeter@864:     // _data[v][k] is the cost of a shortest directed walk from the root
kpeter@766:     // node to node v containing exactly k arcs.
kpeter@766:     void processRounds() {
kpeter@766:       Node start = (*_nodes)[0];
kpeter@767:       _data[start][0] = PathData(0);
kpeter@766:       _process.clear();
kpeter@766:       _process.push_back(start);
kpeter@766: 
kpeter@766:       int k, n = _nodes->size();
kpeter@766:       int next_check = 4;
kpeter@766:       bool terminate = false;
kpeter@766:       for (k = 1; k <= n && int(_process.size()) < n && !terminate; ++k) {
kpeter@766:         processNextBuildRound(k);
kpeter@766:         if (k == next_check || k == n) {
kpeter@766:           terminate = checkTermination(k);
kpeter@766:           next_check = next_check * 3 / 2;
kpeter@766:         }
kpeter@766:       }
kpeter@766:       for ( ; k <= n && !terminate; ++k) {
kpeter@766:         processNextFullRound(k);
kpeter@766:         if (k == next_check || k == n) {
kpeter@766:           terminate = checkTermination(k);
kpeter@766:           next_check = next_check * 3 / 2;
kpeter@766:         }
kpeter@766:       }
kpeter@766:     }
kpeter@766: 
kpeter@766:     // Process one round and rebuild _process
kpeter@766:     void processNextBuildRound(int k) {
kpeter@766:       std::vector<Node> next;
kpeter@766:       Node u, v;
kpeter@766:       Arc e;
kpeter@864:       LargeCost d;
kpeter@766:       for (int i = 0; i < int(_process.size()); ++i) {
kpeter@766:         u = _process[i];
kpeter@766:         for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
kpeter@766:           e = _out_arcs[u][j];
kpeter@766:           v = _gr.target(e);
kpeter@864:           d = _data[u][k-1].dist + _cost[e];
kpeter@767:           if (_tolerance.less(d, _data[v][k].dist)) {
kpeter@767:             if (_data[v][k].dist == INF) next.push_back(v);
kpeter@767:             _data[v][k] = PathData(d, e);
kpeter@766:           }
kpeter@766:         }
kpeter@766:       }
kpeter@766:       _process.swap(next);
kpeter@766:     }
kpeter@766: 
kpeter@766:     // Process one round using _nodes instead of _process
kpeter@766:     void processNextFullRound(int k) {
kpeter@766:       Node u, v;
kpeter@766:       Arc e;
kpeter@864:       LargeCost d;
kpeter@766:       for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@766:         u = (*_nodes)[i];
kpeter@766:         for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
kpeter@766:           e = _out_arcs[u][j];
kpeter@766:           v = _gr.target(e);
kpeter@864:           d = _data[u][k-1].dist + _cost[e];
kpeter@767:           if (_tolerance.less(d, _data[v][k].dist)) {
kpeter@767:             _data[v][k] = PathData(d, e);
kpeter@766:           }
kpeter@766:         }
kpeter@766:       }
kpeter@766:     }
alpar@877: 
kpeter@766:     // Check early termination
kpeter@766:     bool checkTermination(int k) {
kpeter@766:       typedef std::pair<int, int> Pair;
kpeter@766:       typename GR::template NodeMap<Pair> level(_gr, Pair(-1, 0));
kpeter@864:       typename GR::template NodeMap<LargeCost> pi(_gr);
kpeter@766:       int n = _nodes->size();
kpeter@864:       LargeCost cost;
kpeter@766:       int size;
kpeter@766:       Node u;
alpar@877: 
kpeter@766:       // Search for cycles that are already found
kpeter@766:       _curr_found = false;
kpeter@766:       for (int i = 0; i < n; ++i) {
kpeter@766:         u = (*_nodes)[i];
kpeter@767:         if (_data[u][k].dist == INF) continue;
kpeter@766:         for (int j = k; j >= 0; --j) {
kpeter@766:           if (level[u].first == i && level[u].second > 0) {
kpeter@766:             // A cycle is found
kpeter@864:             cost = _data[u][level[u].second].dist - _data[u][j].dist;
kpeter@766:             size = level[u].second - j;
kpeter@864:             if (!_curr_found || cost * _curr_size < _curr_cost * size) {
kpeter@864:               _curr_cost = cost;
kpeter@766:               _curr_size = size;
kpeter@766:               _curr_node = u;
kpeter@766:               _curr_level = level[u].second;
kpeter@766:               _curr_found = true;
kpeter@766:             }
kpeter@766:           }
kpeter@766:           level[u] = Pair(i, j);
deba@795:           if (j != 0) {
alpar@877:             u = _gr.source(_data[u][j].pred);
alpar@877:           }
kpeter@766:         }
kpeter@766:       }
kpeter@766: 
kpeter@766:       // If at least one cycle is found, check the optimality condition
kpeter@864:       LargeCost d;
kpeter@766:       if (_curr_found && k < n) {
kpeter@766:         // Find node potentials
kpeter@766:         for (int i = 0; i < n; ++i) {
kpeter@766:           u = (*_nodes)[i];
kpeter@767:           pi[u] = INF;
kpeter@766:           for (int j = 0; j <= k; ++j) {
kpeter@767:             if (_data[u][j].dist < INF) {
kpeter@864:               d = _data[u][j].dist * _curr_size - j * _curr_cost;
kpeter@767:               if (_tolerance.less(d, pi[u])) pi[u] = d;
kpeter@766:             }
kpeter@766:           }
kpeter@766:         }
kpeter@766: 
kpeter@766:         // Check the optimality condition for all arcs
kpeter@766:         bool done = true;
kpeter@766:         for (ArcIt a(_gr); a != INVALID; ++a) {
kpeter@864:           if (_tolerance.less(_cost[a] * _curr_size - _curr_cost,
kpeter@766:                               pi[_gr.target(a)] - pi[_gr.source(a)]) ) {
kpeter@766:             done = false;
kpeter@766:             break;
kpeter@766:           }
kpeter@766:         }
kpeter@766:         return done;
kpeter@766:       }
kpeter@766:       return (k == n);
kpeter@766:     }
kpeter@766: 
kpeter@864:   }; //class HartmannOrlinMmc
kpeter@766: 
kpeter@766:   ///@}
kpeter@766: 
kpeter@766: } //namespace lemon
kpeter@766: 
kpeter@864: #endif //LEMON_HARTMANN_ORLIN_MMC_H