lemon/karp.h
author Peter Kovacs <kpeter@inf.elte.hu>
Fri, 19 Feb 2010 14:08:32 +0100
changeset 844 a6eb9698c321
parent 772 f964a00b9068
child 841 aa8c9008b3de
permissions -rw-r--r--
Support tolerance technique for BellmanFord (#51)

A new operation traits class BellmanFordToleranceOperationTraits
is introduced, which uses the tolerance technique in its less()
function. This class can be used with the SetOperationTraits
named template parameter.
     1 /* -*- C++ -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library
     4  *
     5  * Copyright (C) 2003-2008
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    19 #ifndef LEMON_KARP_H
    20 #define LEMON_KARP_H
    21 
    22 /// \ingroup min_mean_cycle
    23 ///
    24 /// \file
    25 /// \brief Karp's algorithm for finding a minimum mean cycle.
    26 
    27 #include <vector>
    28 #include <limits>
    29 #include <lemon/core.h>
    30 #include <lemon/path.h>
    31 #include <lemon/tolerance.h>
    32 #include <lemon/connectivity.h>
    33 
    34 namespace lemon {
    35 
    36   /// \brief Default traits class of Karp algorithm.
    37   ///
    38   /// Default traits class of Karp algorithm.
    39   /// \tparam GR The type of the digraph.
    40   /// \tparam LEN The type of the length map.
    41   /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
    42 #ifdef DOXYGEN
    43   template <typename GR, typename LEN>
    44 #else
    45   template <typename GR, typename LEN,
    46     bool integer = std::numeric_limits<typename LEN::Value>::is_integer>
    47 #endif
    48   struct KarpDefaultTraits
    49   {
    50     /// The type of the digraph
    51     typedef GR Digraph;
    52     /// The type of the length map
    53     typedef LEN LengthMap;
    54     /// The type of the arc lengths
    55     typedef typename LengthMap::Value Value;
    56 
    57     /// \brief The large value type used for internal computations
    58     ///
    59     /// The large value type used for internal computations.
    60     /// It is \c long \c long if the \c Value type is integer,
    61     /// otherwise it is \c double.
    62     /// \c Value must be convertible to \c LargeValue.
    63     typedef double LargeValue;
    64 
    65     /// The tolerance type used for internal computations
    66     typedef lemon::Tolerance<LargeValue> Tolerance;
    67 
    68     /// \brief The path type of the found cycles
    69     ///
    70     /// The path type of the found cycles.
    71     /// It must conform to the \ref lemon::concepts::Path "Path" concept
    72     /// and it must have an \c addFront() function.
    73     typedef lemon::Path<Digraph> Path;
    74   };
    75 
    76   // Default traits class for integer value types
    77   template <typename GR, typename LEN>
    78   struct KarpDefaultTraits<GR, LEN, true>
    79   {
    80     typedef GR Digraph;
    81     typedef LEN LengthMap;
    82     typedef typename LengthMap::Value Value;
    83 #ifdef LEMON_HAVE_LONG_LONG
    84     typedef long long LargeValue;
    85 #else
    86     typedef long LargeValue;
    87 #endif
    88     typedef lemon::Tolerance<LargeValue> Tolerance;
    89     typedef lemon::Path<Digraph> Path;
    90   };
    91 
    92 
    93   /// \addtogroup min_mean_cycle
    94   /// @{
    95 
    96   /// \brief Implementation of Karp's algorithm for finding a minimum
    97   /// mean cycle.
    98   ///
    99   /// This class implements Karp's algorithm for finding a directed
   100   /// cycle of minimum mean length (cost) in a digraph
   101   /// \ref amo93networkflows, \ref dasdan98minmeancycle.
   102   /// It runs in time O(ne) and uses space O(n<sup>2</sup>+e).
   103   ///
   104   /// \tparam GR The type of the digraph the algorithm runs on.
   105   /// \tparam LEN The type of the length map. The default
   106   /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
   107   /// \tparam TR The traits class that defines various types used by the
   108   /// algorithm. By default, it is \ref KarpDefaultTraits
   109   /// "KarpDefaultTraits<GR, LEN>".
   110   /// In most cases, this parameter should not be set directly,
   111   /// consider to use the named template parameters instead.
   112 #ifdef DOXYGEN
   113   template <typename GR, typename LEN, typename TR>
   114 #else
   115   template < typename GR,
   116              typename LEN = typename GR::template ArcMap<int>,
   117              typename TR = KarpDefaultTraits<GR, LEN> >
   118 #endif
   119   class Karp
   120   {
   121   public:
   122 
   123     /// The type of the digraph
   124     typedef typename TR::Digraph Digraph;
   125     /// The type of the length map
   126     typedef typename TR::LengthMap LengthMap;
   127     /// The type of the arc lengths
   128     typedef typename TR::Value Value;
   129 
   130     /// \brief The large value type
   131     ///
   132     /// The large value type used for internal computations.
   133     /// By default, it is \c long \c long if the \c Value type is integer,
   134     /// otherwise it is \c double.
   135     typedef typename TR::LargeValue LargeValue;
   136 
   137     /// The tolerance type
   138     typedef typename TR::Tolerance Tolerance;
   139 
   140     /// \brief The path type of the found cycles
   141     ///
   142     /// The path type of the found cycles.
   143     /// Using the \ref KarpDefaultTraits "default traits class",
   144     /// it is \ref lemon::Path "Path<Digraph>".
   145     typedef typename TR::Path Path;
   146 
   147     /// The \ref KarpDefaultTraits "traits class" of the algorithm
   148     typedef TR Traits;
   149 
   150   private:
   151 
   152     TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
   153 
   154     // Data sturcture for path data
   155     struct PathData
   156     {
   157       LargeValue dist;
   158       Arc pred;
   159       PathData(LargeValue d, Arc p = INVALID) :
   160         dist(d), pred(p) {}
   161     };
   162 
   163     typedef typename Digraph::template NodeMap<std::vector<PathData> >
   164       PathDataNodeMap;
   165 
   166   private:
   167 
   168     // The digraph the algorithm runs on
   169     const Digraph &_gr;
   170     // The length of the arcs
   171     const LengthMap &_length;
   172 
   173     // Data for storing the strongly connected components
   174     int _comp_num;
   175     typename Digraph::template NodeMap<int> _comp;
   176     std::vector<std::vector<Node> > _comp_nodes;
   177     std::vector<Node>* _nodes;
   178     typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
   179 
   180     // Data for the found cycle
   181     LargeValue _cycle_length;
   182     int _cycle_size;
   183     Node _cycle_node;
   184 
   185     Path *_cycle_path;
   186     bool _local_path;
   187 
   188     // Node map for storing path data
   189     PathDataNodeMap _data;
   190     // The processed nodes in the last round
   191     std::vector<Node> _process;
   192 
   193     Tolerance _tolerance;
   194     
   195     // Infinite constant
   196     const LargeValue INF;
   197 
   198   public:
   199 
   200     /// \name Named Template Parameters
   201     /// @{
   202 
   203     template <typename T>
   204     struct SetLargeValueTraits : public Traits {
   205       typedef T LargeValue;
   206       typedef lemon::Tolerance<T> Tolerance;
   207     };
   208 
   209     /// \brief \ref named-templ-param "Named parameter" for setting
   210     /// \c LargeValue type.
   211     ///
   212     /// \ref named-templ-param "Named parameter" for setting \c LargeValue
   213     /// type. It is used for internal computations in the algorithm.
   214     template <typename T>
   215     struct SetLargeValue
   216       : public Karp<GR, LEN, SetLargeValueTraits<T> > {
   217       typedef Karp<GR, LEN, SetLargeValueTraits<T> > Create;
   218     };
   219 
   220     template <typename T>
   221     struct SetPathTraits : public Traits {
   222       typedef T Path;
   223     };
   224 
   225     /// \brief \ref named-templ-param "Named parameter" for setting
   226     /// \c %Path type.
   227     ///
   228     /// \ref named-templ-param "Named parameter" for setting the \c %Path
   229     /// type of the found cycles.
   230     /// It must conform to the \ref lemon::concepts::Path "Path" concept
   231     /// and it must have an \c addFront() function.
   232     template <typename T>
   233     struct SetPath
   234       : public Karp<GR, LEN, SetPathTraits<T> > {
   235       typedef Karp<GR, LEN, SetPathTraits<T> > Create;
   236     };
   237 
   238     /// @}
   239 
   240   public:
   241 
   242     /// \brief Constructor.
   243     ///
   244     /// The constructor of the class.
   245     ///
   246     /// \param digraph The digraph the algorithm runs on.
   247     /// \param length The lengths (costs) of the arcs.
   248     Karp( const Digraph &digraph,
   249           const LengthMap &length ) :
   250       _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph),
   251       _cycle_length(0), _cycle_size(1), _cycle_node(INVALID),
   252       _cycle_path(NULL), _local_path(false), _data(digraph),
   253       INF(std::numeric_limits<LargeValue>::has_infinity ?
   254           std::numeric_limits<LargeValue>::infinity() :
   255           std::numeric_limits<LargeValue>::max())
   256     {}
   257 
   258     /// Destructor.
   259     ~Karp() {
   260       if (_local_path) delete _cycle_path;
   261     }
   262 
   263     /// \brief Set the path structure for storing the found cycle.
   264     ///
   265     /// This function sets an external path structure for storing the
   266     /// found cycle.
   267     ///
   268     /// If you don't call this function before calling \ref run() or
   269     /// \ref findMinMean(), it will allocate a local \ref Path "path"
   270     /// structure. The destuctor deallocates this automatically
   271     /// allocated object, of course.
   272     ///
   273     /// \note The algorithm calls only the \ref lemon::Path::addFront()
   274     /// "addFront()" function of the given path structure.
   275     ///
   276     /// \return <tt>(*this)</tt>
   277     Karp& cycle(Path &path) {
   278       if (_local_path) {
   279         delete _cycle_path;
   280         _local_path = false;
   281       }
   282       _cycle_path = &path;
   283       return *this;
   284     }
   285 
   286     /// \brief Set the tolerance used by the algorithm.
   287     ///
   288     /// This function sets the tolerance object used by the algorithm.
   289     ///
   290     /// \return <tt>(*this)</tt>
   291     Karp& tolerance(const Tolerance& tolerance) {
   292       _tolerance = tolerance;
   293       return *this;
   294     }
   295 
   296     /// \brief Return a const reference to the tolerance.
   297     ///
   298     /// This function returns a const reference to the tolerance object
   299     /// used by the algorithm.
   300     const Tolerance& tolerance() const {
   301       return _tolerance;
   302     }
   303 
   304     /// \name Execution control
   305     /// The simplest way to execute the algorithm is to call the \ref run()
   306     /// function.\n
   307     /// If you only need the minimum mean length, you may call
   308     /// \ref findMinMean().
   309 
   310     /// @{
   311 
   312     /// \brief Run the algorithm.
   313     ///
   314     /// This function runs the algorithm.
   315     /// It can be called more than once (e.g. if the underlying digraph
   316     /// and/or the arc lengths have been modified).
   317     ///
   318     /// \return \c true if a directed cycle exists in the digraph.
   319     ///
   320     /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
   321     /// \code
   322     ///   return mmc.findMinMean() && mmc.findCycle();
   323     /// \endcode
   324     bool run() {
   325       return findMinMean() && findCycle();
   326     }
   327 
   328     /// \brief Find the minimum cycle mean.
   329     ///
   330     /// This function finds the minimum mean length of the directed
   331     /// cycles in the digraph.
   332     ///
   333     /// \return \c true if a directed cycle exists in the digraph.
   334     bool findMinMean() {
   335       // Initialization and find strongly connected components
   336       init();
   337       findComponents();
   338       
   339       // Find the minimum cycle mean in the components
   340       for (int comp = 0; comp < _comp_num; ++comp) {
   341         if (!initComponent(comp)) continue;
   342         processRounds();
   343         updateMinMean();
   344       }
   345       return (_cycle_node != INVALID);
   346     }
   347 
   348     /// \brief Find a minimum mean directed cycle.
   349     ///
   350     /// This function finds a directed cycle of minimum mean length
   351     /// in the digraph using the data computed by findMinMean().
   352     ///
   353     /// \return \c true if a directed cycle exists in the digraph.
   354     ///
   355     /// \pre \ref findMinMean() must be called before using this function.
   356     bool findCycle() {
   357       if (_cycle_node == INVALID) return false;
   358       IntNodeMap reached(_gr, -1);
   359       int r = _data[_cycle_node].size();
   360       Node u = _cycle_node;
   361       while (reached[u] < 0) {
   362         reached[u] = --r;
   363         u = _gr.source(_data[u][r].pred);
   364       }
   365       r = reached[u];
   366       Arc e = _data[u][r].pred;
   367       _cycle_path->addFront(e);
   368       _cycle_length = _length[e];
   369       _cycle_size = 1;
   370       Node v;
   371       while ((v = _gr.source(e)) != u) {
   372         e = _data[v][--r].pred;
   373         _cycle_path->addFront(e);
   374         _cycle_length += _length[e];
   375         ++_cycle_size;
   376       }
   377       return true;
   378     }
   379 
   380     /// @}
   381 
   382     /// \name Query Functions
   383     /// The results of the algorithm can be obtained using these
   384     /// functions.\n
   385     /// The algorithm should be executed before using them.
   386 
   387     /// @{
   388 
   389     /// \brief Return the total length of the found cycle.
   390     ///
   391     /// This function returns the total length of the found cycle.
   392     ///
   393     /// \pre \ref run() or \ref findMinMean() must be called before
   394     /// using this function.
   395     LargeValue cycleLength() const {
   396       return _cycle_length;
   397     }
   398 
   399     /// \brief Return the number of arcs on the found cycle.
   400     ///
   401     /// This function returns the number of arcs on the found cycle.
   402     ///
   403     /// \pre \ref run() or \ref findMinMean() must be called before
   404     /// using this function.
   405     int cycleArcNum() const {
   406       return _cycle_size;
   407     }
   408 
   409     /// \brief Return the mean length of the found cycle.
   410     ///
   411     /// This function returns the mean length of the found cycle.
   412     ///
   413     /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
   414     /// following code.
   415     /// \code
   416     ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
   417     /// \endcode
   418     ///
   419     /// \pre \ref run() or \ref findMinMean() must be called before
   420     /// using this function.
   421     double cycleMean() const {
   422       return static_cast<double>(_cycle_length) / _cycle_size;
   423     }
   424 
   425     /// \brief Return the found cycle.
   426     ///
   427     /// This function returns a const reference to the path structure
   428     /// storing the found cycle.
   429     ///
   430     /// \pre \ref run() or \ref findCycle() must be called before using
   431     /// this function.
   432     const Path& cycle() const {
   433       return *_cycle_path;
   434     }
   435 
   436     ///@}
   437 
   438   private:
   439 
   440     // Initialization
   441     void init() {
   442       if (!_cycle_path) {
   443         _local_path = true;
   444         _cycle_path = new Path;
   445       }
   446       _cycle_path->clear();
   447       _cycle_length = 0;
   448       _cycle_size = 1;
   449       _cycle_node = INVALID;
   450       for (NodeIt u(_gr); u != INVALID; ++u)
   451         _data[u].clear();
   452     }
   453 
   454     // Find strongly connected components and initialize _comp_nodes
   455     // and _out_arcs
   456     void findComponents() {
   457       _comp_num = stronglyConnectedComponents(_gr, _comp);
   458       _comp_nodes.resize(_comp_num);
   459       if (_comp_num == 1) {
   460         _comp_nodes[0].clear();
   461         for (NodeIt n(_gr); n != INVALID; ++n) {
   462           _comp_nodes[0].push_back(n);
   463           _out_arcs[n].clear();
   464           for (OutArcIt a(_gr, n); a != INVALID; ++a) {
   465             _out_arcs[n].push_back(a);
   466           }
   467         }
   468       } else {
   469         for (int i = 0; i < _comp_num; ++i)
   470           _comp_nodes[i].clear();
   471         for (NodeIt n(_gr); n != INVALID; ++n) {
   472           int k = _comp[n];
   473           _comp_nodes[k].push_back(n);
   474           _out_arcs[n].clear();
   475           for (OutArcIt a(_gr, n); a != INVALID; ++a) {
   476             if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
   477           }
   478         }
   479       }
   480     }
   481 
   482     // Initialize path data for the current component
   483     bool initComponent(int comp) {
   484       _nodes = &(_comp_nodes[comp]);
   485       int n = _nodes->size();
   486       if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
   487         return false;
   488       }      
   489       for (int i = 0; i < n; ++i) {
   490         _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
   491       }
   492       return true;
   493     }
   494 
   495     // Process all rounds of computing path data for the current component.
   496     // _data[v][k] is the length of a shortest directed walk from the root
   497     // node to node v containing exactly k arcs.
   498     void processRounds() {
   499       Node start = (*_nodes)[0];
   500       _data[start][0] = PathData(0);
   501       _process.clear();
   502       _process.push_back(start);
   503 
   504       int k, n = _nodes->size();
   505       for (k = 1; k <= n && int(_process.size()) < n; ++k) {
   506         processNextBuildRound(k);
   507       }
   508       for ( ; k <= n; ++k) {
   509         processNextFullRound(k);
   510       }
   511     }
   512 
   513     // Process one round and rebuild _process
   514     void processNextBuildRound(int k) {
   515       std::vector<Node> next;
   516       Node u, v;
   517       Arc e;
   518       LargeValue d;
   519       for (int i = 0; i < int(_process.size()); ++i) {
   520         u = _process[i];
   521         for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
   522           e = _out_arcs[u][j];
   523           v = _gr.target(e);
   524           d = _data[u][k-1].dist + _length[e];
   525           if (_tolerance.less(d, _data[v][k].dist)) {
   526             if (_data[v][k].dist == INF) next.push_back(v);
   527             _data[v][k] = PathData(d, e);
   528           }
   529         }
   530       }
   531       _process.swap(next);
   532     }
   533 
   534     // Process one round using _nodes instead of _process
   535     void processNextFullRound(int k) {
   536       Node u, v;
   537       Arc e;
   538       LargeValue d;
   539       for (int i = 0; i < int(_nodes->size()); ++i) {
   540         u = (*_nodes)[i];
   541         for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
   542           e = _out_arcs[u][j];
   543           v = _gr.target(e);
   544           d = _data[u][k-1].dist + _length[e];
   545           if (_tolerance.less(d, _data[v][k].dist)) {
   546             _data[v][k] = PathData(d, e);
   547           }
   548         }
   549       }
   550     }
   551 
   552     // Update the minimum cycle mean
   553     void updateMinMean() {
   554       int n = _nodes->size();
   555       for (int i = 0; i < n; ++i) {
   556         Node u = (*_nodes)[i];
   557         if (_data[u][n].dist == INF) continue;
   558         LargeValue length, max_length = 0;
   559         int size, max_size = 1;
   560         bool found_curr = false;
   561         for (int k = 0; k < n; ++k) {
   562           if (_data[u][k].dist == INF) continue;
   563           length = _data[u][n].dist - _data[u][k].dist;
   564           size = n - k;
   565           if (!found_curr || length * max_size > max_length * size) {
   566             found_curr = true;
   567             max_length = length;
   568             max_size = size;
   569           }
   570         }
   571         if ( found_curr && (_cycle_node == INVALID ||
   572              max_length * _cycle_size < _cycle_length * max_size) ) {
   573           _cycle_length = max_length;
   574           _cycle_size = max_size;
   575           _cycle_node = u;
   576         }
   577       }
   578     }
   579 
   580   }; //class Karp
   581 
   582   ///@}
   583 
   584 } //namespace lemon
   585 
   586 #endif //LEMON_KARP_H