alpar@877: /* -*- mode: C++; indent-tabs-mode: nil; -*-
kpeter@765:  *
alpar@877:  * This file is a part of LEMON, a generic C++ optimization library.
kpeter@765:  *
alpar@877:  * Copyright (C) 2003-2010
kpeter@765:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
kpeter@765:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
kpeter@765:  *
kpeter@765:  * Permission to use, modify and distribute this software is granted
kpeter@765:  * provided that this copyright notice appears in all copies. For
kpeter@765:  * precise terms see the accompanying LICENSE file.
kpeter@765:  *
kpeter@765:  * This software is provided "AS IS" with no warranty of any kind,
kpeter@765:  * express or implied, and with no claim as to its suitability for any
kpeter@765:  * purpose.
kpeter@765:  *
kpeter@765:  */
kpeter@765: 
kpeter@864: #ifndef LEMON_KARP_MMC_H
kpeter@864: #define LEMON_KARP_MMC_H
kpeter@765: 
kpeter@768: /// \ingroup min_mean_cycle
kpeter@765: ///
kpeter@765: /// \file
kpeter@765: /// \brief Karp's algorithm for finding a minimum mean cycle.
kpeter@765: 
kpeter@765: #include <vector>
kpeter@765: #include <limits>
kpeter@765: #include <lemon/core.h>
kpeter@765: #include <lemon/path.h>
kpeter@765: #include <lemon/tolerance.h>
kpeter@765: #include <lemon/connectivity.h>
kpeter@765: 
kpeter@765: namespace lemon {
kpeter@765: 
kpeter@864:   /// \brief Default traits class of KarpMmc class.
kpeter@765:   ///
kpeter@864:   /// Default traits class of KarpMmc class.
kpeter@765:   /// \tparam GR The type of the digraph.
kpeter@864:   /// \tparam CM The type of the cost map.
kpeter@765:   /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
kpeter@765: #ifdef DOXYGEN
kpeter@864:   template <typename GR, typename CM>
kpeter@765: #else
kpeter@864:   template <typename GR, typename CM,
kpeter@864:     bool integer = std::numeric_limits<typename CM::Value>::is_integer>
kpeter@765: #endif
kpeter@864:   struct KarpMmcDefaultTraits
kpeter@765:   {
kpeter@765:     /// The type of the digraph
kpeter@765:     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@765: 
kpeter@864:     /// \brief The large cost type used for internal computations
kpeter@765:     ///
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@765:     /// otherwise it is \c double.
kpeter@864:     /// \c Cost must be convertible to \c LargeCost.
kpeter@864:     typedef double LargeCost;
kpeter@765: 
kpeter@765:     /// The tolerance type used for internal computations
kpeter@864:     typedef lemon::Tolerance<LargeCost> Tolerance;
kpeter@765: 
kpeter@765:     /// \brief The path type of the found cycles
kpeter@765:     ///
kpeter@765:     /// The path type of the found cycles.
kpeter@765:     /// It must conform to the \ref lemon::concepts::Path "Path" concept
kpeter@772:     /// and it must have an \c addFront() function.
kpeter@765:     typedef lemon::Path<Digraph> Path;
kpeter@765:   };
kpeter@765: 
kpeter@864:   // Default traits class for integer cost types
kpeter@864:   template <typename GR, typename CM>
kpeter@864:   struct KarpMmcDefaultTraits<GR, CM, true>
kpeter@765:   {
kpeter@765:     typedef GR Digraph;
kpeter@864:     typedef CM CostMap;
kpeter@864:     typedef typename CostMap::Value Cost;
kpeter@765: #ifdef LEMON_HAVE_LONG_LONG
kpeter@864:     typedef long long LargeCost;
kpeter@765: #else
kpeter@864:     typedef long LargeCost;
kpeter@765: #endif
kpeter@864:     typedef lemon::Tolerance<LargeCost> Tolerance;
kpeter@765:     typedef lemon::Path<Digraph> Path;
kpeter@765:   };
kpeter@765: 
kpeter@765: 
kpeter@768:   /// \addtogroup min_mean_cycle
kpeter@765:   /// @{
kpeter@765: 
kpeter@765:   /// \brief Implementation of Karp's algorithm for finding a minimum
kpeter@765:   /// mean cycle.
kpeter@765:   ///
kpeter@765:   /// This class implements Karp's algorithm for finding a directed
kpeter@864:   /// cycle of minimum mean cost in a digraph
kpeter@771:   /// \ref amo93networkflows, \ref dasdan98minmeancycle.
kpeter@768:   /// It runs in time O(ne) and uses space O(n<sup>2</sup>+e).
kpeter@765:   ///
kpeter@765:   /// \tparam GR The type of the digraph the algorithm runs on.
kpeter@864:   /// \tparam CM The type of the cost map. The default
kpeter@765:   /// 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 KarpMmcDefaultTraits
kpeter@864:   /// "KarpMmcDefaultTraits<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@765: #ifdef DOXYGEN
kpeter@864:   template <typename GR, typename CM, typename TR>
kpeter@765: #else
kpeter@765:   template < typename GR,
kpeter@864:              typename CM = typename GR::template ArcMap<int>,
kpeter@864:              typename TR = KarpMmcDefaultTraits<GR, CM> >
kpeter@765: #endif
kpeter@864:   class KarpMmc
kpeter@765:   {
kpeter@765:   public:
kpeter@765: 
kpeter@765:     /// The type of the digraph
kpeter@765:     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@765: 
kpeter@864:     /// \brief The large cost type
kpeter@765:     ///
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@765:     /// otherwise it is \c double.
kpeter@864:     typedef typename TR::LargeCost LargeCost;
kpeter@765: 
kpeter@765:     /// The tolerance type
kpeter@765:     typedef typename TR::Tolerance Tolerance;
kpeter@765: 
kpeter@765:     /// \brief The path type of the found cycles
kpeter@765:     ///
kpeter@765:     /// The path type of the found cycles.
kpeter@864:     /// Using the \ref KarpMmcDefaultTraits "default traits class",
kpeter@765:     /// it is \ref lemon::Path "Path<Digraph>".
kpeter@765:     typedef typename TR::Path Path;
kpeter@765: 
kpeter@864:     /// The \ref KarpMmcDefaultTraits "traits class" of the algorithm
kpeter@765:     typedef TR Traits;
kpeter@765: 
kpeter@765:   private:
kpeter@765: 
kpeter@765:     TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
kpeter@765: 
kpeter@765:     // Data sturcture for path data
kpeter@765:     struct PathData
kpeter@765:     {
kpeter@864:       LargeCost dist;
kpeter@765:       Arc pred;
kpeter@864:       PathData(LargeCost d, Arc p = INVALID) :
kpeter@767:         dist(d), pred(p) {}
kpeter@765:     };
kpeter@765: 
kpeter@765:     typedef typename Digraph::template NodeMap<std::vector<PathData> >
kpeter@765:       PathDataNodeMap;
kpeter@765: 
kpeter@765:   private:
kpeter@765: 
kpeter@765:     // The digraph the algorithm runs on
kpeter@765:     const Digraph &_gr;
kpeter@864:     // The cost of the arcs
kpeter@864:     const CostMap &_cost;
kpeter@765: 
kpeter@765:     // Data for storing the strongly connected components
kpeter@765:     int _comp_num;
kpeter@765:     typename Digraph::template NodeMap<int> _comp;
kpeter@765:     std::vector<std::vector<Node> > _comp_nodes;
kpeter@765:     std::vector<Node>* _nodes;
kpeter@765:     typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
kpeter@765: 
kpeter@765:     // Data for the found cycle
kpeter@864:     LargeCost _cycle_cost;
kpeter@765:     int _cycle_size;
kpeter@765:     Node _cycle_node;
kpeter@765: 
kpeter@765:     Path *_cycle_path;
kpeter@765:     bool _local_path;
kpeter@765: 
kpeter@765:     // Node map for storing path data
kpeter@765:     PathDataNodeMap _data;
kpeter@765:     // The processed nodes in the last round
kpeter@765:     std::vector<Node> _process;
kpeter@765: 
kpeter@765:     Tolerance _tolerance;
alpar@877: 
kpeter@767:     // Infinite constant
kpeter@864:     const LargeCost INF;
kpeter@765: 
kpeter@765:   public:
kpeter@765: 
kpeter@765:     /// \name Named Template Parameters
kpeter@765:     /// @{
kpeter@765: 
kpeter@765:     template <typename T>
kpeter@864:     struct SetLargeCostTraits : public Traits {
kpeter@864:       typedef T LargeCost;
kpeter@765:       typedef lemon::Tolerance<T> Tolerance;
kpeter@765:     };
kpeter@765: 
kpeter@765:     /// \brief \ref named-templ-param "Named parameter" for setting
kpeter@864:     /// \c LargeCost type.
kpeter@765:     ///
kpeter@864:     /// \ref named-templ-param "Named parameter" for setting \c LargeCost
kpeter@765:     /// type. It is used for internal computations in the algorithm.
kpeter@765:     template <typename T>
kpeter@864:     struct SetLargeCost
kpeter@864:       : public KarpMmc<GR, CM, SetLargeCostTraits<T> > {
kpeter@864:       typedef KarpMmc<GR, CM, SetLargeCostTraits<T> > Create;
kpeter@765:     };
kpeter@765: 
kpeter@765:     template <typename T>
kpeter@765:     struct SetPathTraits : public Traits {
kpeter@765:       typedef T Path;
kpeter@765:     };
kpeter@765: 
kpeter@765:     /// \brief \ref named-templ-param "Named parameter" for setting
kpeter@765:     /// \c %Path type.
kpeter@765:     ///
kpeter@765:     /// \ref named-templ-param "Named parameter" for setting the \c %Path
kpeter@765:     /// type of the found cycles.
kpeter@765:     /// It must conform to the \ref lemon::concepts::Path "Path" concept
kpeter@765:     /// and it must have an \c addFront() function.
kpeter@765:     template <typename T>
kpeter@765:     struct SetPath
kpeter@864:       : public KarpMmc<GR, CM, SetPathTraits<T> > {
kpeter@864:       typedef KarpMmc<GR, CM, SetPathTraits<T> > Create;
kpeter@765:     };
kpeter@765: 
kpeter@765:     /// @}
kpeter@765: 
kpeter@863:   protected:
kpeter@863: 
kpeter@864:     KarpMmc() {}
kpeter@863: 
kpeter@765:   public:
kpeter@765: 
kpeter@765:     /// \brief Constructor.
kpeter@765:     ///
kpeter@765:     /// The constructor of the class.
kpeter@765:     ///
kpeter@765:     /// \param digraph The digraph the algorithm runs on.
kpeter@864:     /// \param cost The costs of the arcs.
kpeter@864:     KarpMmc( const Digraph &digraph,
kpeter@864:              const CostMap &cost ) :
kpeter@864:       _gr(digraph), _cost(cost), _comp(digraph), _out_arcs(digraph),
kpeter@864:       _cycle_cost(0), _cycle_size(1), _cycle_node(INVALID),
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@765:     {}
kpeter@765: 
kpeter@765:     /// Destructor.
kpeter@864:     ~KarpMmc() {
kpeter@765:       if (_local_path) delete _cycle_path;
kpeter@765:     }
kpeter@765: 
kpeter@765:     /// \brief Set the path structure for storing the found cycle.
kpeter@765:     ///
kpeter@765:     /// This function sets an external path structure for storing the
kpeter@765:     /// found cycle.
kpeter@765:     ///
kpeter@765:     /// If you don't call this function before calling \ref run() or
kpeter@864:     /// \ref findCycleMean(), it will allocate a local \ref Path "path"
kpeter@765:     /// structure. The destuctor deallocates this automatically
kpeter@765:     /// allocated object, of course.
kpeter@765:     ///
kpeter@765:     /// \note The algorithm calls only the \ref lemon::Path::addFront()
kpeter@765:     /// "addFront()" function of the given path structure.
kpeter@765:     ///
kpeter@765:     /// \return <tt>(*this)</tt>
kpeter@864:     KarpMmc& cycle(Path &path) {
kpeter@765:       if (_local_path) {
kpeter@765:         delete _cycle_path;
kpeter@765:         _local_path = false;
kpeter@765:       }
kpeter@765:       _cycle_path = &path;
kpeter@765:       return *this;
kpeter@765:     }
kpeter@765: 
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:     KarpMmc& 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@765:     /// \name Execution control
kpeter@765:     /// The simplest way to execute the algorithm is to call the \ref run()
kpeter@765:     /// function.\n
kpeter@864:     /// If you only need the minimum mean cost, you may call
kpeter@864:     /// \ref findCycleMean().
kpeter@765: 
kpeter@765:     /// @{
kpeter@765: 
kpeter@765:     /// \brief Run the algorithm.
kpeter@765:     ///
kpeter@765:     /// This function runs the algorithm.
kpeter@765:     /// It can be called more than once (e.g. if the underlying digraph
kpeter@864:     /// and/or the arc costs have been modified).
kpeter@765:     ///
kpeter@765:     /// \return \c true if a directed cycle exists in the digraph.
kpeter@765:     ///
kpeter@765:     /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
kpeter@765:     /// \code
kpeter@864:     ///   return mmc.findCycleMean() && mmc.findCycle();
kpeter@765:     /// \endcode
kpeter@765:     bool run() {
kpeter@864:       return findCycleMean() && findCycle();
kpeter@765:     }
kpeter@765: 
kpeter@765:     /// \brief Find the minimum cycle mean.
kpeter@765:     ///
kpeter@864:     /// This function finds the minimum mean cost of the directed
kpeter@765:     /// cycles in the digraph.
kpeter@765:     ///
kpeter@765:     /// \return \c true if a directed cycle exists in the digraph.
kpeter@864:     bool findCycleMean() {
kpeter@765:       // Initialization and find strongly connected components
kpeter@765:       init();
kpeter@765:       findComponents();
alpar@877: 
kpeter@765:       // Find the minimum cycle mean in the components
kpeter@765:       for (int comp = 0; comp < _comp_num; ++comp) {
kpeter@765:         if (!initComponent(comp)) continue;
kpeter@765:         processRounds();
kpeter@765:         updateMinMean();
kpeter@765:       }
kpeter@765:       return (_cycle_node != INVALID);
kpeter@765:     }
kpeter@765: 
kpeter@765:     /// \brief Find a minimum mean directed cycle.
kpeter@765:     ///
kpeter@864:     /// This function finds a directed cycle of minimum mean cost
kpeter@864:     /// in the digraph using the data computed by findCycleMean().
kpeter@765:     ///
kpeter@765:     /// \return \c true if a directed cycle exists in the digraph.
kpeter@765:     ///
kpeter@864:     /// \pre \ref findCycleMean() must be called before using this function.
kpeter@765:     bool findCycle() {
kpeter@765:       if (_cycle_node == INVALID) return false;
kpeter@765:       IntNodeMap reached(_gr, -1);
kpeter@765:       int r = _data[_cycle_node].size();
kpeter@765:       Node u = _cycle_node;
kpeter@765:       while (reached[u] < 0) {
kpeter@765:         reached[u] = --r;
kpeter@765:         u = _gr.source(_data[u][r].pred);
kpeter@765:       }
kpeter@765:       r = reached[u];
kpeter@765:       Arc e = _data[u][r].pred;
kpeter@765:       _cycle_path->addFront(e);
kpeter@864:       _cycle_cost = _cost[e];
kpeter@765:       _cycle_size = 1;
kpeter@765:       Node v;
kpeter@765:       while ((v = _gr.source(e)) != u) {
kpeter@765:         e = _data[v][--r].pred;
kpeter@765:         _cycle_path->addFront(e);
kpeter@864:         _cycle_cost += _cost[e];
kpeter@765:         ++_cycle_size;
kpeter@765:       }
kpeter@765:       return true;
kpeter@765:     }
kpeter@765: 
kpeter@765:     /// @}
kpeter@765: 
kpeter@765:     /// \name Query Functions
kpeter@765:     /// The results of the algorithm can be obtained using these
kpeter@765:     /// functions.\n
kpeter@765:     /// The algorithm should be executed before using them.
kpeter@765: 
kpeter@765:     /// @{
kpeter@765: 
kpeter@864:     /// \brief Return the total cost of the found cycle.
kpeter@765:     ///
kpeter@864:     /// This function returns the total cost of the found cycle.
kpeter@765:     ///
kpeter@864:     /// \pre \ref run() or \ref findCycleMean() must be called before
kpeter@765:     /// using this function.
kpeter@864:     Cost cycleCost() const {
kpeter@864:       return static_cast<Cost>(_cycle_cost);
kpeter@765:     }
kpeter@765: 
kpeter@765:     /// \brief Return the number of arcs on the found cycle.
kpeter@765:     ///
kpeter@765:     /// This function returns the number of arcs on the found cycle.
kpeter@765:     ///
kpeter@864:     /// \pre \ref run() or \ref findCycleMean() must be called before
kpeter@765:     /// using this function.
kpeter@864:     int cycleSize() const {
kpeter@765:       return _cycle_size;
kpeter@765:     }
kpeter@765: 
kpeter@864:     /// \brief Return the mean cost of the found cycle.
kpeter@765:     ///
kpeter@864:     /// This function returns the mean cost of the found cycle.
kpeter@765:     ///
kpeter@765:     /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
kpeter@765:     /// following code.
kpeter@765:     /// \code
kpeter@864:     ///   return static_cast<double>(alg.cycleCost()) / alg.cycleSize();
kpeter@765:     /// \endcode
kpeter@765:     ///
kpeter@864:     /// \pre \ref run() or \ref findCycleMean() must be called before
kpeter@765:     /// using this function.
kpeter@765:     double cycleMean() const {
kpeter@864:       return static_cast<double>(_cycle_cost) / _cycle_size;
kpeter@765:     }
kpeter@765: 
kpeter@765:     /// \brief Return the found cycle.
kpeter@765:     ///
kpeter@765:     /// This function returns a const reference to the path structure
kpeter@765:     /// storing the found cycle.
kpeter@765:     ///
kpeter@765:     /// \pre \ref run() or \ref findCycle() must be called before using
kpeter@765:     /// this function.
kpeter@765:     const Path& cycle() const {
kpeter@765:       return *_cycle_path;
kpeter@765:     }
kpeter@765: 
kpeter@765:     ///@}
kpeter@765: 
kpeter@765:   private:
kpeter@765: 
kpeter@765:     // Initialization
kpeter@765:     void init() {
kpeter@765:       if (!_cycle_path) {
kpeter@765:         _local_path = true;
kpeter@765:         _cycle_path = new Path;
kpeter@765:       }
kpeter@765:       _cycle_path->clear();
kpeter@864:       _cycle_cost = 0;
kpeter@765:       _cycle_size = 1;
kpeter@765:       _cycle_node = INVALID;
kpeter@765:       for (NodeIt u(_gr); u != INVALID; ++u)
kpeter@765:         _data[u].clear();
kpeter@765:     }
kpeter@765: 
kpeter@765:     // Find strongly connected components and initialize _comp_nodes
kpeter@765:     // and _out_arcs
kpeter@765:     void findComponents() {
kpeter@765:       _comp_num = stronglyConnectedComponents(_gr, _comp);
kpeter@765:       _comp_nodes.resize(_comp_num);
kpeter@765:       if (_comp_num == 1) {
kpeter@765:         _comp_nodes[0].clear();
kpeter@765:         for (NodeIt n(_gr); n != INVALID; ++n) {
kpeter@765:           _comp_nodes[0].push_back(n);
kpeter@765:           _out_arcs[n].clear();
kpeter@765:           for (OutArcIt a(_gr, n); a != INVALID; ++a) {
kpeter@765:             _out_arcs[n].push_back(a);
kpeter@765:           }
kpeter@765:         }
kpeter@765:       } else {
kpeter@765:         for (int i = 0; i < _comp_num; ++i)
kpeter@765:           _comp_nodes[i].clear();
kpeter@765:         for (NodeIt n(_gr); n != INVALID; ++n) {
kpeter@765:           int k = _comp[n];
kpeter@765:           _comp_nodes[k].push_back(n);
kpeter@765:           _out_arcs[n].clear();
kpeter@765:           for (OutArcIt a(_gr, n); a != INVALID; ++a) {
kpeter@765:             if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
kpeter@765:           }
kpeter@765:         }
kpeter@765:       }
kpeter@765:     }
kpeter@765: 
kpeter@765:     // Initialize path data for the current component
kpeter@765:     bool initComponent(int comp) {
kpeter@765:       _nodes = &(_comp_nodes[comp]);
kpeter@765:       int n = _nodes->size();
kpeter@765:       if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
kpeter@765:         return false;
alpar@877:       }
kpeter@765:       for (int i = 0; i < n; ++i) {
kpeter@767:         _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
kpeter@765:       }
kpeter@765:       return true;
kpeter@765:     }
kpeter@765: 
kpeter@765:     // 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@765:     // node to node v containing exactly k arcs.
kpeter@765:     void processRounds() {
kpeter@765:       Node start = (*_nodes)[0];
kpeter@767:       _data[start][0] = PathData(0);
kpeter@765:       _process.clear();
kpeter@765:       _process.push_back(start);
kpeter@765: 
kpeter@765:       int k, n = _nodes->size();
kpeter@765:       for (k = 1; k <= n && int(_process.size()) < n; ++k) {
kpeter@765:         processNextBuildRound(k);
kpeter@765:       }
kpeter@765:       for ( ; k <= n; ++k) {
kpeter@765:         processNextFullRound(k);
kpeter@765:       }
kpeter@765:     }
kpeter@765: 
kpeter@765:     // Process one round and rebuild _process
kpeter@765:     void processNextBuildRound(int k) {
kpeter@765:       std::vector<Node> next;
kpeter@765:       Node u, v;
kpeter@765:       Arc e;
kpeter@864:       LargeCost d;
kpeter@765:       for (int i = 0; i < int(_process.size()); ++i) {
kpeter@765:         u = _process[i];
kpeter@765:         for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
kpeter@765:           e = _out_arcs[u][j];
kpeter@765:           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@765:           }
kpeter@765:         }
kpeter@765:       }
kpeter@765:       _process.swap(next);
kpeter@765:     }
kpeter@765: 
kpeter@765:     // Process one round using _nodes instead of _process
kpeter@765:     void processNextFullRound(int k) {
kpeter@765:       Node u, v;
kpeter@765:       Arc e;
kpeter@864:       LargeCost d;
kpeter@765:       for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@765:         u = (*_nodes)[i];
kpeter@765:         for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
kpeter@765:           e = _out_arcs[u][j];
kpeter@765:           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@765:           }
kpeter@765:         }
kpeter@765:       }
kpeter@765:     }
kpeter@765: 
kpeter@765:     // Update the minimum cycle mean
kpeter@765:     void updateMinMean() {
kpeter@765:       int n = _nodes->size();
kpeter@765:       for (int i = 0; i < n; ++i) {
kpeter@765:         Node u = (*_nodes)[i];
kpeter@767:         if (_data[u][n].dist == INF) continue;
kpeter@864:         LargeCost cost, max_cost = 0;
kpeter@765:         int size, max_size = 1;
kpeter@765:         bool found_curr = false;
kpeter@765:         for (int k = 0; k < n; ++k) {
kpeter@767:           if (_data[u][k].dist == INF) continue;
kpeter@864:           cost = _data[u][n].dist - _data[u][k].dist;
kpeter@765:           size = n - k;
kpeter@864:           if (!found_curr || cost * max_size > max_cost * size) {
kpeter@765:             found_curr = true;
kpeter@864:             max_cost = cost;
kpeter@765:             max_size = size;
kpeter@765:           }
kpeter@765:         }
kpeter@765:         if ( found_curr && (_cycle_node == INVALID ||
kpeter@864:              max_cost * _cycle_size < _cycle_cost * max_size) ) {
kpeter@864:           _cycle_cost = max_cost;
kpeter@765:           _cycle_size = max_size;
kpeter@765:           _cycle_node = u;
kpeter@765:         }
kpeter@765:       }
kpeter@765:     }
kpeter@765: 
kpeter@864:   }; //class KarpMmc
kpeter@765: 
kpeter@765:   ///@}
kpeter@765: 
kpeter@765: } //namespace lemon
kpeter@765: 
kpeter@864: #endif //LEMON_KARP_MMC_H