lemon/karp.h
author Peter Kovacs <kpeter@inf.elte.hu>
Sat, 20 Feb 2010 18:39:03 +0100
changeset 839 f3bc4e9b5f3a
parent 771 8452ca46e29a
child 825 75e6020b19b1
permissions -rw-r--r--
New heuristics for MCF algorithms (#340)
and some implementation improvements.

- A useful heuristic is added to NetworkSimplex to make the
initial pivots faster.
- A powerful global update heuristic is added to CostScaling
and the implementation is reworked with various improvements.
- Better relabeling in CostScaling to improve numerical stability
and make the code faster.
- A small improvement is made in CapacityScaling for better
delta computation.
- Add notes to the classes about the usage of vector<char> instead
of vector<bool> for efficiency reasons.
     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 #ifdef DOXYGEN
   108   template <typename GR, typename LEN, typename TR>
   109 #else
   110   template < typename GR,
   111              typename LEN = typename GR::template ArcMap<int>,
   112              typename TR = KarpDefaultTraits<GR, LEN> >
   113 #endif
   114   class Karp
   115   {
   116   public:
   117 
   118     /// The type of the digraph
   119     typedef typename TR::Digraph Digraph;
   120     /// The type of the length map
   121     typedef typename TR::LengthMap LengthMap;
   122     /// The type of the arc lengths
   123     typedef typename TR::Value Value;
   124 
   125     /// \brief The large value type
   126     ///
   127     /// The large value type used for internal computations.
   128     /// Using the \ref KarpDefaultTraits "default traits class",
   129     /// it is \c long \c long if the \c Value type is integer,
   130     /// otherwise it is \c double.
   131     typedef typename TR::LargeValue LargeValue;
   132 
   133     /// The tolerance type
   134     typedef typename TR::Tolerance Tolerance;
   135 
   136     /// \brief The path type of the found cycles
   137     ///
   138     /// The path type of the found cycles.
   139     /// Using the \ref KarpDefaultTraits "default traits class",
   140     /// it is \ref lemon::Path "Path<Digraph>".
   141     typedef typename TR::Path Path;
   142 
   143     /// The \ref KarpDefaultTraits "traits class" of the algorithm
   144     typedef TR Traits;
   145 
   146   private:
   147 
   148     TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
   149 
   150     // Data sturcture for path data
   151     struct PathData
   152     {
   153       LargeValue dist;
   154       Arc pred;
   155       PathData(LargeValue d, Arc p = INVALID) :
   156         dist(d), pred(p) {}
   157     };
   158 
   159     typedef typename Digraph::template NodeMap<std::vector<PathData> >
   160       PathDataNodeMap;
   161 
   162   private:
   163 
   164     // The digraph the algorithm runs on
   165     const Digraph &_gr;
   166     // The length of the arcs
   167     const LengthMap &_length;
   168 
   169     // Data for storing the strongly connected components
   170     int _comp_num;
   171     typename Digraph::template NodeMap<int> _comp;
   172     std::vector<std::vector<Node> > _comp_nodes;
   173     std::vector<Node>* _nodes;
   174     typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
   175 
   176     // Data for the found cycle
   177     LargeValue _cycle_length;
   178     int _cycle_size;
   179     Node _cycle_node;
   180 
   181     Path *_cycle_path;
   182     bool _local_path;
   183 
   184     // Node map for storing path data
   185     PathDataNodeMap _data;
   186     // The processed nodes in the last round
   187     std::vector<Node> _process;
   188 
   189     Tolerance _tolerance;
   190     
   191     // Infinite constant
   192     const LargeValue INF;
   193 
   194   public:
   195 
   196     /// \name Named Template Parameters
   197     /// @{
   198 
   199     template <typename T>
   200     struct SetLargeValueTraits : public Traits {
   201       typedef T LargeValue;
   202       typedef lemon::Tolerance<T> Tolerance;
   203     };
   204 
   205     /// \brief \ref named-templ-param "Named parameter" for setting
   206     /// \c LargeValue type.
   207     ///
   208     /// \ref named-templ-param "Named parameter" for setting \c LargeValue
   209     /// type. It is used for internal computations in the algorithm.
   210     template <typename T>
   211     struct SetLargeValue
   212       : public Karp<GR, LEN, SetLargeValueTraits<T> > {
   213       typedef Karp<GR, LEN, SetLargeValueTraits<T> > Create;
   214     };
   215 
   216     template <typename T>
   217     struct SetPathTraits : public Traits {
   218       typedef T Path;
   219     };
   220 
   221     /// \brief \ref named-templ-param "Named parameter" for setting
   222     /// \c %Path type.
   223     ///
   224     /// \ref named-templ-param "Named parameter" for setting the \c %Path
   225     /// type of the found cycles.
   226     /// It must conform to the \ref lemon::concepts::Path "Path" concept
   227     /// and it must have an \c addFront() function.
   228     template <typename T>
   229     struct SetPath
   230       : public Karp<GR, LEN, SetPathTraits<T> > {
   231       typedef Karp<GR, LEN, SetPathTraits<T> > Create;
   232     };
   233 
   234     /// @}
   235 
   236   public:
   237 
   238     /// \brief Constructor.
   239     ///
   240     /// The constructor of the class.
   241     ///
   242     /// \param digraph The digraph the algorithm runs on.
   243     /// \param length The lengths (costs) of the arcs.
   244     Karp( const Digraph &digraph,
   245           const LengthMap &length ) :
   246       _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph),
   247       _cycle_length(0), _cycle_size(1), _cycle_node(INVALID),
   248       _cycle_path(NULL), _local_path(false), _data(digraph),
   249       INF(std::numeric_limits<LargeValue>::has_infinity ?
   250           std::numeric_limits<LargeValue>::infinity() :
   251           std::numeric_limits<LargeValue>::max())
   252     {}
   253 
   254     /// Destructor.
   255     ~Karp() {
   256       if (_local_path) delete _cycle_path;
   257     }
   258 
   259     /// \brief Set the path structure for storing the found cycle.
   260     ///
   261     /// This function sets an external path structure for storing the
   262     /// found cycle.
   263     ///
   264     /// If you don't call this function before calling \ref run() or
   265     /// \ref findMinMean(), it will allocate a local \ref Path "path"
   266     /// structure. The destuctor deallocates this automatically
   267     /// allocated object, of course.
   268     ///
   269     /// \note The algorithm calls only the \ref lemon::Path::addFront()
   270     /// "addFront()" function of the given path structure.
   271     ///
   272     /// \return <tt>(*this)</tt>
   273     Karp& cycle(Path &path) {
   274       if (_local_path) {
   275         delete _cycle_path;
   276         _local_path = false;
   277       }
   278       _cycle_path = &path;
   279       return *this;
   280     }
   281 
   282     /// \brief Set the tolerance used by the algorithm.
   283     ///
   284     /// This function sets the tolerance object used by the algorithm.
   285     ///
   286     /// \return <tt>(*this)</tt>
   287     Karp& tolerance(const Tolerance& tolerance) {
   288       _tolerance = tolerance;
   289       return *this;
   290     }
   291 
   292     /// \brief Return a const reference to the tolerance.
   293     ///
   294     /// This function returns a const reference to the tolerance object
   295     /// used by the algorithm.
   296     const Tolerance& tolerance() const {
   297       return _tolerance;
   298     }
   299 
   300     /// \name Execution control
   301     /// The simplest way to execute the algorithm is to call the \ref run()
   302     /// function.\n
   303     /// If you only need the minimum mean length, you may call
   304     /// \ref findMinMean().
   305 
   306     /// @{
   307 
   308     /// \brief Run the algorithm.
   309     ///
   310     /// This function runs the algorithm.
   311     /// It can be called more than once (e.g. if the underlying digraph
   312     /// and/or the arc lengths have been modified).
   313     ///
   314     /// \return \c true if a directed cycle exists in the digraph.
   315     ///
   316     /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
   317     /// \code
   318     ///   return mmc.findMinMean() && mmc.findCycle();
   319     /// \endcode
   320     bool run() {
   321       return findMinMean() && findCycle();
   322     }
   323 
   324     /// \brief Find the minimum cycle mean.
   325     ///
   326     /// This function finds the minimum mean length of the directed
   327     /// cycles in the digraph.
   328     ///
   329     /// \return \c true if a directed cycle exists in the digraph.
   330     bool findMinMean() {
   331       // Initialization and find strongly connected components
   332       init();
   333       findComponents();
   334       
   335       // Find the minimum cycle mean in the components
   336       for (int comp = 0; comp < _comp_num; ++comp) {
   337         if (!initComponent(comp)) continue;
   338         processRounds();
   339         updateMinMean();
   340       }
   341       return (_cycle_node != INVALID);
   342     }
   343 
   344     /// \brief Find a minimum mean directed cycle.
   345     ///
   346     /// This function finds a directed cycle of minimum mean length
   347     /// in the digraph using the data computed by findMinMean().
   348     ///
   349     /// \return \c true if a directed cycle exists in the digraph.
   350     ///
   351     /// \pre \ref findMinMean() must be called before using this function.
   352     bool findCycle() {
   353       if (_cycle_node == INVALID) return false;
   354       IntNodeMap reached(_gr, -1);
   355       int r = _data[_cycle_node].size();
   356       Node u = _cycle_node;
   357       while (reached[u] < 0) {
   358         reached[u] = --r;
   359         u = _gr.source(_data[u][r].pred);
   360       }
   361       r = reached[u];
   362       Arc e = _data[u][r].pred;
   363       _cycle_path->addFront(e);
   364       _cycle_length = _length[e];
   365       _cycle_size = 1;
   366       Node v;
   367       while ((v = _gr.source(e)) != u) {
   368         e = _data[v][--r].pred;
   369         _cycle_path->addFront(e);
   370         _cycle_length += _length[e];
   371         ++_cycle_size;
   372       }
   373       return true;
   374     }
   375 
   376     /// @}
   377 
   378     /// \name Query Functions
   379     /// The results of the algorithm can be obtained using these
   380     /// functions.\n
   381     /// The algorithm should be executed before using them.
   382 
   383     /// @{
   384 
   385     /// \brief Return the total length of the found cycle.
   386     ///
   387     /// This function returns the total length of the found cycle.
   388     ///
   389     /// \pre \ref run() or \ref findMinMean() must be called before
   390     /// using this function.
   391     LargeValue cycleLength() const {
   392       return _cycle_length;
   393     }
   394 
   395     /// \brief Return the number of arcs on the found cycle.
   396     ///
   397     /// This function returns the number of arcs on the found cycle.
   398     ///
   399     /// \pre \ref run() or \ref findMinMean() must be called before
   400     /// using this function.
   401     int cycleArcNum() const {
   402       return _cycle_size;
   403     }
   404 
   405     /// \brief Return the mean length of the found cycle.
   406     ///
   407     /// This function returns the mean length of the found cycle.
   408     ///
   409     /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
   410     /// following code.
   411     /// \code
   412     ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
   413     /// \endcode
   414     ///
   415     /// \pre \ref run() or \ref findMinMean() must be called before
   416     /// using this function.
   417     double cycleMean() const {
   418       return static_cast<double>(_cycle_length) / _cycle_size;
   419     }
   420 
   421     /// \brief Return the found cycle.
   422     ///
   423     /// This function returns a const reference to the path structure
   424     /// storing the found cycle.
   425     ///
   426     /// \pre \ref run() or \ref findCycle() must be called before using
   427     /// this function.
   428     const Path& cycle() const {
   429       return *_cycle_path;
   430     }
   431 
   432     ///@}
   433 
   434   private:
   435 
   436     // Initialization
   437     void init() {
   438       if (!_cycle_path) {
   439         _local_path = true;
   440         _cycle_path = new Path;
   441       }
   442       _cycle_path->clear();
   443       _cycle_length = 0;
   444       _cycle_size = 1;
   445       _cycle_node = INVALID;
   446       for (NodeIt u(_gr); u != INVALID; ++u)
   447         _data[u].clear();
   448     }
   449 
   450     // Find strongly connected components and initialize _comp_nodes
   451     // and _out_arcs
   452     void findComponents() {
   453       _comp_num = stronglyConnectedComponents(_gr, _comp);
   454       _comp_nodes.resize(_comp_num);
   455       if (_comp_num == 1) {
   456         _comp_nodes[0].clear();
   457         for (NodeIt n(_gr); n != INVALID; ++n) {
   458           _comp_nodes[0].push_back(n);
   459           _out_arcs[n].clear();
   460           for (OutArcIt a(_gr, n); a != INVALID; ++a) {
   461             _out_arcs[n].push_back(a);
   462           }
   463         }
   464       } else {
   465         for (int i = 0; i < _comp_num; ++i)
   466           _comp_nodes[i].clear();
   467         for (NodeIt n(_gr); n != INVALID; ++n) {
   468           int k = _comp[n];
   469           _comp_nodes[k].push_back(n);
   470           _out_arcs[n].clear();
   471           for (OutArcIt a(_gr, n); a != INVALID; ++a) {
   472             if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
   473           }
   474         }
   475       }
   476     }
   477 
   478     // Initialize path data for the current component
   479     bool initComponent(int comp) {
   480       _nodes = &(_comp_nodes[comp]);
   481       int n = _nodes->size();
   482       if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
   483         return false;
   484       }      
   485       for (int i = 0; i < n; ++i) {
   486         _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
   487       }
   488       return true;
   489     }
   490 
   491     // Process all rounds of computing path data for the current component.
   492     // _data[v][k] is the length of a shortest directed walk from the root
   493     // node to node v containing exactly k arcs.
   494     void processRounds() {
   495       Node start = (*_nodes)[0];
   496       _data[start][0] = PathData(0);
   497       _process.clear();
   498       _process.push_back(start);
   499 
   500       int k, n = _nodes->size();
   501       for (k = 1; k <= n && int(_process.size()) < n; ++k) {
   502         processNextBuildRound(k);
   503       }
   504       for ( ; k <= n; ++k) {
   505         processNextFullRound(k);
   506       }
   507     }
   508 
   509     // Process one round and rebuild _process
   510     void processNextBuildRound(int k) {
   511       std::vector<Node> next;
   512       Node u, v;
   513       Arc e;
   514       LargeValue d;
   515       for (int i = 0; i < int(_process.size()); ++i) {
   516         u = _process[i];
   517         for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
   518           e = _out_arcs[u][j];
   519           v = _gr.target(e);
   520           d = _data[u][k-1].dist + _length[e];
   521           if (_tolerance.less(d, _data[v][k].dist)) {
   522             if (_data[v][k].dist == INF) next.push_back(v);
   523             _data[v][k] = PathData(d, e);
   524           }
   525         }
   526       }
   527       _process.swap(next);
   528     }
   529 
   530     // Process one round using _nodes instead of _process
   531     void processNextFullRound(int k) {
   532       Node u, v;
   533       Arc e;
   534       LargeValue d;
   535       for (int i = 0; i < int(_nodes->size()); ++i) {
   536         u = (*_nodes)[i];
   537         for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
   538           e = _out_arcs[u][j];
   539           v = _gr.target(e);
   540           d = _data[u][k-1].dist + _length[e];
   541           if (_tolerance.less(d, _data[v][k].dist)) {
   542             _data[v][k] = PathData(d, e);
   543           }
   544         }
   545       }
   546     }
   547 
   548     // Update the minimum cycle mean
   549     void updateMinMean() {
   550       int n = _nodes->size();
   551       for (int i = 0; i < n; ++i) {
   552         Node u = (*_nodes)[i];
   553         if (_data[u][n].dist == INF) continue;
   554         LargeValue length, max_length = 0;
   555         int size, max_size = 1;
   556         bool found_curr = false;
   557         for (int k = 0; k < n; ++k) {
   558           if (_data[u][k].dist == INF) continue;
   559           length = _data[u][n].dist - _data[u][k].dist;
   560           size = n - k;
   561           if (!found_curr || length * max_size > max_length * size) {
   562             found_curr = true;
   563             max_length = length;
   564             max_size = size;
   565           }
   566         }
   567         if ( found_curr && (_cycle_node == INVALID ||
   568              max_length * _cycle_size < _cycle_length * max_size) ) {
   569           _cycle_length = max_length;
   570           _cycle_size = max_size;
   571           _cycle_node = u;
   572         }
   573       }
   574     }
   575 
   576   }; //class Karp
   577 
   578   ///@}
   579 
   580 } //namespace lemon
   581 
   582 #endif //LEMON_KARP_H