kpeter@813: /* -*- C++ -*-
kpeter@813:  *
kpeter@813:  * This file is a part of LEMON, a generic C++ optimization library
kpeter@813:  *
kpeter@813:  * Copyright (C) 2003-2008
kpeter@813:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
kpeter@813:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
kpeter@813:  *
kpeter@813:  * Permission to use, modify and distribute this software is granted
kpeter@813:  * provided that this copyright notice appears in all copies. For
kpeter@813:  * precise terms see the accompanying LICENSE file.
kpeter@813:  *
kpeter@813:  * This software is provided "AS IS" with no warranty of any kind,
kpeter@813:  * express or implied, and with no claim as to its suitability for any
kpeter@813:  * purpose.
kpeter@813:  *
kpeter@813:  */
kpeter@813: 
kpeter@813: #ifndef LEMON_HARTMANN_ORLIN_H
kpeter@813: #define LEMON_HARTMANN_ORLIN_H
kpeter@813: 
kpeter@815: /// \ingroup min_mean_cycle
kpeter@813: ///
kpeter@813: /// \file
kpeter@813: /// \brief Hartmann-Orlin's algorithm for finding a minimum mean cycle.
kpeter@813: 
kpeter@813: #include <vector>
kpeter@813: #include <limits>
kpeter@813: #include <lemon/core.h>
kpeter@813: #include <lemon/path.h>
kpeter@813: #include <lemon/tolerance.h>
kpeter@813: #include <lemon/connectivity.h>
kpeter@813: 
kpeter@813: namespace lemon {
kpeter@813: 
kpeter@813:   /// \brief Default traits class of HartmannOrlin algorithm.
kpeter@813:   ///
kpeter@813:   /// Default traits class of HartmannOrlin algorithm.
kpeter@813:   /// \tparam GR The type of the digraph.
kpeter@813:   /// \tparam LEN The type of the length map.
kpeter@813:   /// It must conform to the \ref concepts::Rea_data "Rea_data" concept.
kpeter@813: #ifdef DOXYGEN
kpeter@813:   template <typename GR, typename LEN>
kpeter@813: #else
kpeter@813:   template <typename GR, typename LEN,
kpeter@813:     bool integer = std::numeric_limits<typename LEN::Value>::is_integer>
kpeter@813: #endif
kpeter@813:   struct HartmannOrlinDefaultTraits
kpeter@813:   {
kpeter@813:     /// The type of the digraph
kpeter@813:     typedef GR Digraph;
kpeter@813:     /// The type of the length map
kpeter@813:     typedef LEN LengthMap;
kpeter@813:     /// The type of the arc lengths
kpeter@813:     typedef typename LengthMap::Value Value;
kpeter@813: 
kpeter@813:     /// \brief The large value type used for internal computations
kpeter@813:     ///
kpeter@813:     /// The large value type used for internal computations.
kpeter@813:     /// It is \c long \c long if the \c Value type is integer,
kpeter@813:     /// otherwise it is \c double.
kpeter@813:     /// \c Value must be convertible to \c LargeValue.
kpeter@813:     typedef double LargeValue;
kpeter@813: 
kpeter@813:     /// The tolerance type used for internal computations
kpeter@813:     typedef lemon::Tolerance<LargeValue> Tolerance;
kpeter@813: 
kpeter@813:     /// \brief The path type of the found cycles
kpeter@813:     ///
kpeter@813:     /// The path type of the found cycles.
kpeter@813:     /// It must conform to the \ref lemon::concepts::Path "Path" concept
kpeter@819:     /// and it must have an \c addFront() function.
kpeter@813:     typedef lemon::Path<Digraph> Path;
kpeter@813:   };
kpeter@813: 
kpeter@813:   // Default traits class for integer value types
kpeter@813:   template <typename GR, typename LEN>
kpeter@813:   struct HartmannOrlinDefaultTraits<GR, LEN, true>
kpeter@813:   {
kpeter@813:     typedef GR Digraph;
kpeter@813:     typedef LEN LengthMap;
kpeter@813:     typedef typename LengthMap::Value Value;
kpeter@813: #ifdef LEMON_HAVE_LONG_LONG
kpeter@813:     typedef long long LargeValue;
kpeter@813: #else
kpeter@813:     typedef long LargeValue;
kpeter@813: #endif
kpeter@813:     typedef lemon::Tolerance<LargeValue> Tolerance;
kpeter@813:     typedef lemon::Path<Digraph> Path;
kpeter@813:   };
kpeter@813: 
kpeter@813: 
kpeter@815:   /// \addtogroup min_mean_cycle
kpeter@813:   /// @{
kpeter@813: 
kpeter@813:   /// \brief Implementation of the Hartmann-Orlin algorithm for finding
kpeter@813:   /// a minimum mean cycle.
kpeter@813:   ///
kpeter@813:   /// This class implements the Hartmann-Orlin algorithm for finding
kpeter@818:   /// a directed cycle of minimum mean length (cost) in a digraph
kpeter@818:   /// \ref amo93networkflows, \ref dasdan98minmeancycle.
kpeter@815:   /// It is an improved version of \ref Karp "Karp"'s original algorithm,
kpeter@813:   /// it applies an efficient early termination scheme.
kpeter@815:   /// It runs in time O(ne) and uses space O(n<sup>2</sup>+e).
kpeter@813:   ///
kpeter@813:   /// \tparam GR The type of the digraph the algorithm runs on.
kpeter@813:   /// \tparam LEN The type of the length map. The default
kpeter@813:   /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
kpeter@891:   /// \tparam TR The traits class that defines various types used by the
kpeter@891:   /// algorithm. By default, it is \ref HartmannOrlinDefaultTraits
kpeter@891:   /// "HartmannOrlinDefaultTraits<GR, LEN>".
kpeter@891:   /// In most cases, this parameter should not be set directly,
kpeter@891:   /// consider to use the named template parameters instead.
kpeter@813: #ifdef DOXYGEN
kpeter@813:   template <typename GR, typename LEN, typename TR>
kpeter@813: #else
kpeter@813:   template < typename GR,
kpeter@813:              typename LEN = typename GR::template ArcMap<int>,
kpeter@813:              typename TR = HartmannOrlinDefaultTraits<GR, LEN> >
kpeter@813: #endif
kpeter@813:   class HartmannOrlin
kpeter@813:   {
kpeter@813:   public:
kpeter@813: 
kpeter@813:     /// The type of the digraph
kpeter@813:     typedef typename TR::Digraph Digraph;
kpeter@813:     /// The type of the length map
kpeter@813:     typedef typename TR::LengthMap LengthMap;
kpeter@813:     /// The type of the arc lengths
kpeter@813:     typedef typename TR::Value Value;
kpeter@813: 
kpeter@813:     /// \brief The large value type
kpeter@813:     ///
kpeter@813:     /// The large value type used for internal computations.
kpeter@891:     /// By default, it is \c long \c long if the \c Value type is integer,
kpeter@813:     /// otherwise it is \c double.
kpeter@813:     typedef typename TR::LargeValue LargeValue;
kpeter@813: 
kpeter@813:     /// The tolerance type
kpeter@813:     typedef typename TR::Tolerance Tolerance;
kpeter@813: 
kpeter@813:     /// \brief The path type of the found cycles
kpeter@813:     ///
kpeter@813:     /// The path type of the found cycles.
kpeter@813:     /// Using the \ref HartmannOrlinDefaultTraits "default traits class",
kpeter@813:     /// it is \ref lemon::Path "Path<Digraph>".
kpeter@813:     typedef typename TR::Path Path;
kpeter@813: 
kpeter@813:     /// The \ref HartmannOrlinDefaultTraits "traits class" of the algorithm
kpeter@813:     typedef TR Traits;
kpeter@813: 
kpeter@813:   private:
kpeter@813: 
kpeter@813:     TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
kpeter@813: 
kpeter@813:     // Data sturcture for path data
kpeter@813:     struct PathData
kpeter@813:     {
kpeter@813:       LargeValue dist;
kpeter@813:       Arc pred;
kpeter@814:       PathData(LargeValue d, Arc p = INVALID) :
kpeter@814:         dist(d), pred(p) {}
kpeter@813:     };
kpeter@813: 
kpeter@813:     typedef typename Digraph::template NodeMap<std::vector<PathData> >
kpeter@813:       PathDataNodeMap;
kpeter@813: 
kpeter@813:   private:
kpeter@813: 
kpeter@813:     // The digraph the algorithm runs on
kpeter@813:     const Digraph &_gr;
kpeter@813:     // The length of the arcs
kpeter@813:     const LengthMap &_length;
kpeter@813: 
kpeter@813:     // Data for storing the strongly connected components
kpeter@813:     int _comp_num;
kpeter@813:     typename Digraph::template NodeMap<int> _comp;
kpeter@813:     std::vector<std::vector<Node> > _comp_nodes;
kpeter@813:     std::vector<Node>* _nodes;
kpeter@813:     typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
kpeter@813: 
kpeter@813:     // Data for the found cycles
kpeter@813:     bool _curr_found, _best_found;
kpeter@813:     LargeValue _curr_length, _best_length;
kpeter@813:     int _curr_size, _best_size;
kpeter@813:     Node _curr_node, _best_node;
kpeter@813:     int _curr_level, _best_level;
kpeter@813: 
kpeter@813:     Path *_cycle_path;
kpeter@813:     bool _local_path;
kpeter@813: 
kpeter@813:     // Node map for storing path data
kpeter@813:     PathDataNodeMap _data;
kpeter@813:     // The processed nodes in the last round
kpeter@813:     std::vector<Node> _process;
kpeter@813: 
kpeter@813:     Tolerance _tolerance;
kpeter@813: 
kpeter@814:     // Infinite constant
kpeter@814:     const LargeValue INF;
kpeter@814: 
kpeter@813:   public:
kpeter@813: 
kpeter@813:     /// \name Named Template Parameters
kpeter@813:     /// @{
kpeter@813: 
kpeter@813:     template <typename T>
kpeter@813:     struct SetLargeValueTraits : public Traits {
kpeter@813:       typedef T LargeValue;
kpeter@813:       typedef lemon::Tolerance<T> Tolerance;
kpeter@813:     };
kpeter@813: 
kpeter@813:     /// \brief \ref named-templ-param "Named parameter" for setting
kpeter@813:     /// \c LargeValue type.
kpeter@813:     ///
kpeter@813:     /// \ref named-templ-param "Named parameter" for setting \c LargeValue
kpeter@813:     /// type. It is used for internal computations in the algorithm.
kpeter@813:     template <typename T>
kpeter@813:     struct SetLargeValue
kpeter@813:       : public HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > {
kpeter@813:       typedef HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > Create;
kpeter@813:     };
kpeter@813: 
kpeter@813:     template <typename T>
kpeter@813:     struct SetPathTraits : public Traits {
kpeter@813:       typedef T Path;
kpeter@813:     };
kpeter@813: 
kpeter@813:     /// \brief \ref named-templ-param "Named parameter" for setting
kpeter@813:     /// \c %Path type.
kpeter@813:     ///
kpeter@813:     /// \ref named-templ-param "Named parameter" for setting the \c %Path
kpeter@813:     /// type of the found cycles.
kpeter@813:     /// It must conform to the \ref lemon::concepts::Path "Path" concept
kpeter@813:     /// and it must have an \c addFront() function.
kpeter@813:     template <typename T>
kpeter@813:     struct SetPath
kpeter@813:       : public HartmannOrlin<GR, LEN, SetPathTraits<T> > {
kpeter@813:       typedef HartmannOrlin<GR, LEN, SetPathTraits<T> > Create;
kpeter@813:     };
kpeter@813: 
kpeter@813:     /// @}
kpeter@813: 
kpeter@941:   protected:
kpeter@941: 
kpeter@941:     HartmannOrlin() {}
kpeter@941: 
kpeter@813:   public:
kpeter@813: 
kpeter@813:     /// \brief Constructor.
kpeter@813:     ///
kpeter@813:     /// The constructor of the class.
kpeter@813:     ///
kpeter@813:     /// \param digraph The digraph the algorithm runs on.
kpeter@813:     /// \param length The lengths (costs) of the arcs.
kpeter@813:     HartmannOrlin( const Digraph &digraph,
kpeter@813:                    const LengthMap &length ) :
kpeter@813:       _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph),
kpeter@813:       _best_found(false), _best_length(0), _best_size(1),
kpeter@814:       _cycle_path(NULL), _local_path(false), _data(digraph),
kpeter@814:       INF(std::numeric_limits<LargeValue>::has_infinity ?
kpeter@814:           std::numeric_limits<LargeValue>::infinity() :
kpeter@814:           std::numeric_limits<LargeValue>::max())
kpeter@813:     {}
kpeter@813: 
kpeter@813:     /// Destructor.
kpeter@813:     ~HartmannOrlin() {
kpeter@813:       if (_local_path) delete _cycle_path;
kpeter@813:     }
kpeter@813: 
kpeter@813:     /// \brief Set the path structure for storing the found cycle.
kpeter@813:     ///
kpeter@813:     /// This function sets an external path structure for storing the
kpeter@813:     /// found cycle.
kpeter@813:     ///
kpeter@813:     /// If you don't call this function before calling \ref run() or
kpeter@813:     /// \ref findMinMean(), it will allocate a local \ref Path "path"
kpeter@813:     /// structure. The destuctor deallocates this automatically
kpeter@813:     /// allocated object, of course.
kpeter@813:     ///
kpeter@813:     /// \note The algorithm calls only the \ref lemon::Path::addFront()
kpeter@813:     /// "addFront()" function of the given path structure.
kpeter@813:     ///
kpeter@813:     /// \return <tt>(*this)</tt>
kpeter@813:     HartmannOrlin& cycle(Path &path) {
kpeter@813:       if (_local_path) {
kpeter@813:         delete _cycle_path;
kpeter@813:         _local_path = false;
kpeter@813:       }
kpeter@813:       _cycle_path = &path;
kpeter@813:       return *this;
kpeter@813:     }
kpeter@813: 
kpeter@816:     /// \brief Set the tolerance used by the algorithm.
kpeter@816:     ///
kpeter@816:     /// This function sets the tolerance object used by the algorithm.
kpeter@816:     ///
kpeter@816:     /// \return <tt>(*this)</tt>
kpeter@816:     HartmannOrlin& tolerance(const Tolerance& tolerance) {
kpeter@816:       _tolerance = tolerance;
kpeter@816:       return *this;
kpeter@816:     }
kpeter@816: 
kpeter@816:     /// \brief Return a const reference to the tolerance.
kpeter@816:     ///
kpeter@816:     /// This function returns a const reference to the tolerance object
kpeter@816:     /// used by the algorithm.
kpeter@816:     const Tolerance& tolerance() const {
kpeter@816:       return _tolerance;
kpeter@816:     }
kpeter@816: 
kpeter@813:     /// \name Execution control
kpeter@813:     /// The simplest way to execute the algorithm is to call the \ref run()
kpeter@813:     /// function.\n
kpeter@813:     /// If you only need the minimum mean length, you may call
kpeter@813:     /// \ref findMinMean().
kpeter@813: 
kpeter@813:     /// @{
kpeter@813: 
kpeter@813:     /// \brief Run the algorithm.
kpeter@813:     ///
kpeter@813:     /// This function runs the algorithm.
kpeter@813:     /// It can be called more than once (e.g. if the underlying digraph
kpeter@813:     /// and/or the arc lengths have been modified).
kpeter@813:     ///
kpeter@813:     /// \return \c true if a directed cycle exists in the digraph.
kpeter@813:     ///
kpeter@813:     /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
kpeter@813:     /// \code
kpeter@813:     ///   return mmc.findMinMean() && mmc.findCycle();
kpeter@813:     /// \endcode
kpeter@813:     bool run() {
kpeter@813:       return findMinMean() && findCycle();
kpeter@813:     }
kpeter@813: 
kpeter@813:     /// \brief Find the minimum cycle mean.
kpeter@813:     ///
kpeter@813:     /// This function finds the minimum mean length of the directed
kpeter@813:     /// cycles in the digraph.
kpeter@813:     ///
kpeter@813:     /// \return \c true if a directed cycle exists in the digraph.
kpeter@813:     bool findMinMean() {
kpeter@813:       // Initialization and find strongly connected components
kpeter@813:       init();
kpeter@813:       findComponents();
kpeter@813:       
kpeter@813:       // Find the minimum cycle mean in the components
kpeter@813:       for (int comp = 0; comp < _comp_num; ++comp) {
kpeter@813:         if (!initComponent(comp)) continue;
kpeter@813:         processRounds();
kpeter@813:         
kpeter@813:         // Update the best cycle (global minimum mean cycle)
kpeter@813:         if ( _curr_found && (!_best_found || 
kpeter@813:              _curr_length * _best_size < _best_length * _curr_size) ) {
kpeter@813:           _best_found = true;
kpeter@813:           _best_length = _curr_length;
kpeter@813:           _best_size = _curr_size;
kpeter@813:           _best_node = _curr_node;
kpeter@813:           _best_level = _curr_level;
kpeter@813:         }
kpeter@813:       }
kpeter@813:       return _best_found;
kpeter@813:     }
kpeter@813: 
kpeter@813:     /// \brief Find a minimum mean directed cycle.
kpeter@813:     ///
kpeter@813:     /// This function finds a directed cycle of minimum mean length
kpeter@813:     /// in the digraph using the data computed by findMinMean().
kpeter@813:     ///
kpeter@813:     /// \return \c true if a directed cycle exists in the digraph.
kpeter@813:     ///
kpeter@813:     /// \pre \ref findMinMean() must be called before using this function.
kpeter@813:     bool findCycle() {
kpeter@813:       if (!_best_found) return false;
kpeter@813:       IntNodeMap reached(_gr, -1);
kpeter@813:       int r = _best_level + 1;
kpeter@813:       Node u = _best_node;
kpeter@813:       while (reached[u] < 0) {
kpeter@813:         reached[u] = --r;
kpeter@813:         u = _gr.source(_data[u][r].pred);
kpeter@813:       }
kpeter@813:       r = reached[u];
kpeter@813:       Arc e = _data[u][r].pred;
kpeter@813:       _cycle_path->addFront(e);
kpeter@813:       _best_length = _length[e];
kpeter@813:       _best_size = 1;
kpeter@813:       Node v;
kpeter@813:       while ((v = _gr.source(e)) != u) {
kpeter@813:         e = _data[v][--r].pred;
kpeter@813:         _cycle_path->addFront(e);
kpeter@813:         _best_length += _length[e];
kpeter@813:         ++_best_size;
kpeter@813:       }
kpeter@813:       return true;
kpeter@813:     }
kpeter@813: 
kpeter@813:     /// @}
kpeter@813: 
kpeter@813:     /// \name Query Functions
kpeter@813:     /// The results of the algorithm can be obtained using these
kpeter@813:     /// functions.\n
kpeter@813:     /// The algorithm should be executed before using them.
kpeter@813: 
kpeter@813:     /// @{
kpeter@813: 
kpeter@813:     /// \brief Return the total length of the found cycle.
kpeter@813:     ///
kpeter@813:     /// This function returns the total length of the found cycle.
kpeter@813:     ///
kpeter@813:     /// \pre \ref run() or \ref findMinMean() must be called before
kpeter@813:     /// using this function.
kpeter@914:     Value cycleLength() const {
kpeter@914:       return static_cast<Value>(_best_length);
kpeter@813:     }
kpeter@813: 
kpeter@813:     /// \brief Return the number of arcs on the found cycle.
kpeter@813:     ///
kpeter@813:     /// This function returns the number of arcs on the found cycle.
kpeter@813:     ///
kpeter@813:     /// \pre \ref run() or \ref findMinMean() must be called before
kpeter@813:     /// using this function.
kpeter@813:     int cycleArcNum() const {
kpeter@813:       return _best_size;
kpeter@813:     }
kpeter@813: 
kpeter@813:     /// \brief Return the mean length of the found cycle.
kpeter@813:     ///
kpeter@813:     /// This function returns the mean length of the found cycle.
kpeter@813:     ///
kpeter@813:     /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
kpeter@813:     /// following code.
kpeter@813:     /// \code
kpeter@813:     ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
kpeter@813:     /// \endcode
kpeter@813:     ///
kpeter@813:     /// \pre \ref run() or \ref findMinMean() must be called before
kpeter@813:     /// using this function.
kpeter@813:     double cycleMean() const {
kpeter@813:       return static_cast<double>(_best_length) / _best_size;
kpeter@813:     }
kpeter@813: 
kpeter@813:     /// \brief Return the found cycle.
kpeter@813:     ///
kpeter@813:     /// This function returns a const reference to the path structure
kpeter@813:     /// storing the found cycle.
kpeter@813:     ///
kpeter@813:     /// \pre \ref run() or \ref findCycle() must be called before using
kpeter@813:     /// this function.
kpeter@813:     const Path& cycle() const {
kpeter@813:       return *_cycle_path;
kpeter@813:     }
kpeter@813: 
kpeter@813:     ///@}
kpeter@813: 
kpeter@813:   private:
kpeter@813: 
kpeter@813:     // Initialization
kpeter@813:     void init() {
kpeter@813:       if (!_cycle_path) {
kpeter@813:         _local_path = true;
kpeter@813:         _cycle_path = new Path;
kpeter@813:       }
kpeter@813:       _cycle_path->clear();
kpeter@813:       _best_found = false;
kpeter@813:       _best_length = 0;
kpeter@813:       _best_size = 1;
kpeter@813:       _cycle_path->clear();
kpeter@813:       for (NodeIt u(_gr); u != INVALID; ++u)
kpeter@813:         _data[u].clear();
kpeter@813:     }
kpeter@813: 
kpeter@813:     // Find strongly connected components and initialize _comp_nodes
kpeter@813:     // and _out_arcs
kpeter@813:     void findComponents() {
kpeter@813:       _comp_num = stronglyConnectedComponents(_gr, _comp);
kpeter@813:       _comp_nodes.resize(_comp_num);
kpeter@813:       if (_comp_num == 1) {
kpeter@813:         _comp_nodes[0].clear();
kpeter@813:         for (NodeIt n(_gr); n != INVALID; ++n) {
kpeter@813:           _comp_nodes[0].push_back(n);
kpeter@813:           _out_arcs[n].clear();
kpeter@813:           for (OutArcIt a(_gr, n); a != INVALID; ++a) {
kpeter@813:             _out_arcs[n].push_back(a);
kpeter@813:           }
kpeter@813:         }
kpeter@813:       } else {
kpeter@813:         for (int i = 0; i < _comp_num; ++i)
kpeter@813:           _comp_nodes[i].clear();
kpeter@813:         for (NodeIt n(_gr); n != INVALID; ++n) {
kpeter@813:           int k = _comp[n];
kpeter@813:           _comp_nodes[k].push_back(n);
kpeter@813:           _out_arcs[n].clear();
kpeter@813:           for (OutArcIt a(_gr, n); a != INVALID; ++a) {
kpeter@813:             if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
kpeter@813:           }
kpeter@813:         }
kpeter@813:       }
kpeter@813:     }
kpeter@813: 
kpeter@813:     // Initialize path data for the current component
kpeter@813:     bool initComponent(int comp) {
kpeter@813:       _nodes = &(_comp_nodes[comp]);
kpeter@813:       int n = _nodes->size();
kpeter@813:       if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
kpeter@813:         return false;
kpeter@813:       }      
kpeter@813:       for (int i = 0; i < n; ++i) {
kpeter@814:         _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
kpeter@813:       }
kpeter@813:       return true;
kpeter@813:     }
kpeter@813: 
kpeter@813:     // Process all rounds of computing path data for the current component.
kpeter@813:     // _data[v][k] is the length of a shortest directed walk from the root
kpeter@813:     // node to node v containing exactly k arcs.
kpeter@813:     void processRounds() {
kpeter@813:       Node start = (*_nodes)[0];
kpeter@814:       _data[start][0] = PathData(0);
kpeter@813:       _process.clear();
kpeter@813:       _process.push_back(start);
kpeter@813: 
kpeter@813:       int k, n = _nodes->size();
kpeter@813:       int next_check = 4;
kpeter@813:       bool terminate = false;
kpeter@813:       for (k = 1; k <= n && int(_process.size()) < n && !terminate; ++k) {
kpeter@813:         processNextBuildRound(k);
kpeter@813:         if (k == next_check || k == n) {
kpeter@813:           terminate = checkTermination(k);
kpeter@813:           next_check = next_check * 3 / 2;
kpeter@813:         }
kpeter@813:       }
kpeter@813:       for ( ; k <= n && !terminate; ++k) {
kpeter@813:         processNextFullRound(k);
kpeter@813:         if (k == next_check || k == n) {
kpeter@813:           terminate = checkTermination(k);
kpeter@813:           next_check = next_check * 3 / 2;
kpeter@813:         }
kpeter@813:       }
kpeter@813:     }
kpeter@813: 
kpeter@813:     // Process one round and rebuild _process
kpeter@813:     void processNextBuildRound(int k) {
kpeter@813:       std::vector<Node> next;
kpeter@813:       Node u, v;
kpeter@813:       Arc e;
kpeter@813:       LargeValue d;
kpeter@813:       for (int i = 0; i < int(_process.size()); ++i) {
kpeter@813:         u = _process[i];
kpeter@813:         for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
kpeter@813:           e = _out_arcs[u][j];
kpeter@813:           v = _gr.target(e);
kpeter@813:           d = _data[u][k-1].dist + _length[e];
kpeter@814:           if (_tolerance.less(d, _data[v][k].dist)) {
kpeter@814:             if (_data[v][k].dist == INF) next.push_back(v);
kpeter@814:             _data[v][k] = PathData(d, e);
kpeter@813:           }
kpeter@813:         }
kpeter@813:       }
kpeter@813:       _process.swap(next);
kpeter@813:     }
kpeter@813: 
kpeter@813:     // Process one round using _nodes instead of _process
kpeter@813:     void processNextFullRound(int k) {
kpeter@813:       Node u, v;
kpeter@813:       Arc e;
kpeter@813:       LargeValue d;
kpeter@813:       for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@813:         u = (*_nodes)[i];
kpeter@813:         for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
kpeter@813:           e = _out_arcs[u][j];
kpeter@813:           v = _gr.target(e);
kpeter@813:           d = _data[u][k-1].dist + _length[e];
kpeter@814:           if (_tolerance.less(d, _data[v][k].dist)) {
kpeter@814:             _data[v][k] = PathData(d, e);
kpeter@813:           }
kpeter@813:         }
kpeter@813:       }
kpeter@813:     }
kpeter@813:     
kpeter@813:     // Check early termination
kpeter@813:     bool checkTermination(int k) {
kpeter@813:       typedef std::pair<int, int> Pair;
kpeter@813:       typename GR::template NodeMap<Pair> level(_gr, Pair(-1, 0));
kpeter@813:       typename GR::template NodeMap<LargeValue> pi(_gr);
kpeter@813:       int n = _nodes->size();
kpeter@813:       LargeValue length;
kpeter@813:       int size;
kpeter@813:       Node u;
kpeter@813:       
kpeter@813:       // Search for cycles that are already found
kpeter@813:       _curr_found = false;
kpeter@813:       for (int i = 0; i < n; ++i) {
kpeter@813:         u = (*_nodes)[i];
kpeter@814:         if (_data[u][k].dist == INF) continue;
kpeter@813:         for (int j = k; j >= 0; --j) {
kpeter@813:           if (level[u].first == i && level[u].second > 0) {
kpeter@813:             // A cycle is found
kpeter@813:             length = _data[u][level[u].second].dist - _data[u][j].dist;
kpeter@813:             size = level[u].second - j;
kpeter@813:             if (!_curr_found || length * _curr_size < _curr_length * size) {
kpeter@813:               _curr_length = length;
kpeter@813:               _curr_size = size;
kpeter@813:               _curr_node = u;
kpeter@813:               _curr_level = level[u].second;
kpeter@813:               _curr_found = true;
kpeter@813:             }
kpeter@813:           }
kpeter@813:           level[u] = Pair(i, j);
deba@859:           if (j != 0) {
deba@859: 	    u = _gr.source(_data[u][j].pred);
deba@859: 	  }
kpeter@813:         }
kpeter@813:       }
kpeter@813: 
kpeter@813:       // If at least one cycle is found, check the optimality condition
kpeter@813:       LargeValue d;
kpeter@813:       if (_curr_found && k < n) {
kpeter@813:         // Find node potentials
kpeter@813:         for (int i = 0; i < n; ++i) {
kpeter@813:           u = (*_nodes)[i];
kpeter@814:           pi[u] = INF;
kpeter@813:           for (int j = 0; j <= k; ++j) {
kpeter@814:             if (_data[u][j].dist < INF) {
kpeter@814:               d = _data[u][j].dist * _curr_size - j * _curr_length;
kpeter@814:               if (_tolerance.less(d, pi[u])) pi[u] = d;
kpeter@813:             }
kpeter@813:           }
kpeter@813:         }
kpeter@813: 
kpeter@813:         // Check the optimality condition for all arcs
kpeter@813:         bool done = true;
kpeter@813:         for (ArcIt a(_gr); a != INVALID; ++a) {
kpeter@813:           if (_tolerance.less(_length[a] * _curr_size - _curr_length,
kpeter@813:                               pi[_gr.target(a)] - pi[_gr.source(a)]) ) {
kpeter@813:             done = false;
kpeter@813:             break;
kpeter@813:           }
kpeter@813:         }
kpeter@813:         return done;
kpeter@813:       }
kpeter@813:       return (k == n);
kpeter@813:     }
kpeter@813: 
kpeter@813:   }; //class HartmannOrlin
kpeter@813: 
kpeter@813:   ///@}
kpeter@813: 
kpeter@813: } //namespace lemon
kpeter@813: 
kpeter@813: #endif //LEMON_HARTMANN_ORLIN_H