lemon/hao_orlin.h
author Peter Kovacs <kpeter@inf.elte.hu>
Fri, 13 Nov 2009 18:10:06 +0100
changeset 786 e20173729589
parent 596 293551ad254f
child 860 930ddeafdb20
permissions -rw-r--r--
Small doc fixes in several files (#331)
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     5  * Copyright (C) 2003-2009
     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_HAO_ORLIN_H
    20 #define LEMON_HAO_ORLIN_H
    21 
    22 #include <vector>
    23 #include <list>
    24 #include <limits>
    25 
    26 #include <lemon/maps.h>
    27 #include <lemon/core.h>
    28 #include <lemon/tolerance.h>
    29 
    30 /// \file
    31 /// \ingroup min_cut
    32 /// \brief Implementation of the Hao-Orlin algorithm.
    33 ///
    34 /// Implementation of the Hao-Orlin algorithm for finding a minimum cut 
    35 /// in a digraph.
    36 
    37 namespace lemon {
    38 
    39   /// \ingroup min_cut
    40   ///
    41   /// \brief Hao-Orlin algorithm for finding a minimum cut in a digraph.
    42   ///
    43   /// This class implements the Hao-Orlin algorithm for finding a minimum
    44   /// value cut in a directed graph \f$D=(V,A)\f$. 
    45   /// It takes a fixed node \f$ source \in V \f$ and
    46   /// consists of two phases: in the first phase it determines a
    47   /// minimum cut with \f$ source \f$ on the source-side (i.e. a set
    48   /// \f$ X\subsetneq V \f$ with \f$ source \in X \f$ and minimal outgoing
    49   /// capacity) and in the second phase it determines a minimum cut
    50   /// with \f$ source \f$ on the sink-side (i.e. a set
    51   /// \f$ X\subsetneq V \f$ with \f$ source \notin X \f$ and minimal outgoing
    52   /// capacity). Obviously, the smaller of these two cuts will be a
    53   /// minimum cut of \f$ D \f$. The algorithm is a modified
    54   /// preflow push-relabel algorithm. Our implementation calculates
    55   /// the minimum cut in \f$ O(n^2\sqrt{m}) \f$ time (we use the
    56   /// highest-label rule), or in \f$O(nm)\f$ for unit capacities. The
    57   /// purpose of such algorithm is e.g. testing network reliability.
    58   ///
    59   /// For an undirected graph you can run just the first phase of the
    60   /// algorithm or you can use the algorithm of Nagamochi and Ibaraki,
    61   /// which solves the undirected problem in \f$ O(nm + n^2 \log n) \f$ 
    62   /// time. It is implemented in the NagamochiIbaraki algorithm class.
    63   ///
    64   /// \tparam GR The type of the digraph the algorithm runs on.
    65   /// \tparam CAP The type of the arc map containing the capacities,
    66   /// which can be any numreric type. The default map type is
    67   /// \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
    68   /// \tparam TOL Tolerance class for handling inexact computations. The
    69   /// default tolerance type is \ref Tolerance "Tolerance<CAP::Value>".
    70 #ifdef DOXYGEN
    71   template <typename GR, typename CAP, typename TOL>
    72 #else
    73   template <typename GR,
    74             typename CAP = typename GR::template ArcMap<int>,
    75             typename TOL = Tolerance<typename CAP::Value> >
    76 #endif
    77   class HaoOrlin {
    78   public:
    79    
    80     /// The digraph type of the algorithm
    81     typedef GR Digraph;
    82     /// The capacity map type of the algorithm
    83     typedef CAP CapacityMap;
    84     /// The tolerance type of the algorithm
    85     typedef TOL Tolerance;
    86 
    87   private:
    88 
    89     typedef typename CapacityMap::Value Value;
    90 
    91     TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
    92 
    93     const Digraph& _graph;
    94     const CapacityMap* _capacity;
    95 
    96     typedef typename Digraph::template ArcMap<Value> FlowMap;
    97     FlowMap* _flow;
    98 
    99     Node _source;
   100 
   101     int _node_num;
   102 
   103     // Bucketing structure
   104     std::vector<Node> _first, _last;
   105     typename Digraph::template NodeMap<Node>* _next;
   106     typename Digraph::template NodeMap<Node>* _prev;
   107     typename Digraph::template NodeMap<bool>* _active;
   108     typename Digraph::template NodeMap<int>* _bucket;
   109 
   110     std::vector<bool> _dormant;
   111 
   112     std::list<std::list<int> > _sets;
   113     std::list<int>::iterator _highest;
   114 
   115     typedef typename Digraph::template NodeMap<Value> ExcessMap;
   116     ExcessMap* _excess;
   117 
   118     typedef typename Digraph::template NodeMap<bool> SourceSetMap;
   119     SourceSetMap* _source_set;
   120 
   121     Value _min_cut;
   122 
   123     typedef typename Digraph::template NodeMap<bool> MinCutMap;
   124     MinCutMap* _min_cut_map;
   125 
   126     Tolerance _tolerance;
   127 
   128   public:
   129 
   130     /// \brief Constructor
   131     ///
   132     /// Constructor of the algorithm class.
   133     HaoOrlin(const Digraph& graph, const CapacityMap& capacity,
   134              const Tolerance& tolerance = Tolerance()) :
   135       _graph(graph), _capacity(&capacity), _flow(0), _source(),
   136       _node_num(), _first(), _last(), _next(0), _prev(0),
   137       _active(0), _bucket(0), _dormant(), _sets(), _highest(),
   138       _excess(0), _source_set(0), _min_cut(), _min_cut_map(0),
   139       _tolerance(tolerance) {}
   140 
   141     ~HaoOrlin() {
   142       if (_min_cut_map) {
   143         delete _min_cut_map;
   144       }
   145       if (_source_set) {
   146         delete _source_set;
   147       }
   148       if (_excess) {
   149         delete _excess;
   150       }
   151       if (_next) {
   152         delete _next;
   153       }
   154       if (_prev) {
   155         delete _prev;
   156       }
   157       if (_active) {
   158         delete _active;
   159       }
   160       if (_bucket) {
   161         delete _bucket;
   162       }
   163       if (_flow) {
   164         delete _flow;
   165       }
   166     }
   167 
   168   private:
   169 
   170     void activate(const Node& i) {
   171       (*_active)[i] = true;
   172 
   173       int bucket = (*_bucket)[i];
   174 
   175       if ((*_prev)[i] == INVALID || (*_active)[(*_prev)[i]]) return;
   176       //unlace
   177       (*_next)[(*_prev)[i]] = (*_next)[i];
   178       if ((*_next)[i] != INVALID) {
   179         (*_prev)[(*_next)[i]] = (*_prev)[i];
   180       } else {
   181         _last[bucket] = (*_prev)[i];
   182       }
   183       //lace
   184       (*_next)[i] = _first[bucket];
   185       (*_prev)[_first[bucket]] = i;
   186       (*_prev)[i] = INVALID;
   187       _first[bucket] = i;
   188     }
   189 
   190     void deactivate(const Node& i) {
   191       (*_active)[i] = false;
   192       int bucket = (*_bucket)[i];
   193 
   194       if ((*_next)[i] == INVALID || !(*_active)[(*_next)[i]]) return;
   195 
   196       //unlace
   197       (*_prev)[(*_next)[i]] = (*_prev)[i];
   198       if ((*_prev)[i] != INVALID) {
   199         (*_next)[(*_prev)[i]] = (*_next)[i];
   200       } else {
   201         _first[bucket] = (*_next)[i];
   202       }
   203       //lace
   204       (*_prev)[i] = _last[bucket];
   205       (*_next)[_last[bucket]] = i;
   206       (*_next)[i] = INVALID;
   207       _last[bucket] = i;
   208     }
   209 
   210     void addItem(const Node& i, int bucket) {
   211       (*_bucket)[i] = bucket;
   212       if (_last[bucket] != INVALID) {
   213         (*_prev)[i] = _last[bucket];
   214         (*_next)[_last[bucket]] = i;
   215         (*_next)[i] = INVALID;
   216         _last[bucket] = i;
   217       } else {
   218         (*_prev)[i] = INVALID;
   219         _first[bucket] = i;
   220         (*_next)[i] = INVALID;
   221         _last[bucket] = i;
   222       }
   223     }
   224 
   225     void findMinCutOut() {
   226 
   227       for (NodeIt n(_graph); n != INVALID; ++n) {
   228         (*_excess)[n] = 0;
   229         (*_source_set)[n] = false;
   230       }
   231 
   232       for (ArcIt a(_graph); a != INVALID; ++a) {
   233         (*_flow)[a] = 0;
   234       }
   235 
   236       int bucket_num = 0;
   237       std::vector<Node> queue(_node_num);
   238       int qfirst = 0, qlast = 0, qsep = 0;
   239 
   240       {
   241         typename Digraph::template NodeMap<bool> reached(_graph, false);
   242 
   243         reached[_source] = true;
   244         bool first_set = true;
   245 
   246         for (NodeIt t(_graph); t != INVALID; ++t) {
   247           if (reached[t]) continue;
   248           _sets.push_front(std::list<int>());
   249 
   250           queue[qlast++] = t;
   251           reached[t] = true;
   252 
   253           while (qfirst != qlast) {
   254             if (qsep == qfirst) {
   255               ++bucket_num;
   256               _sets.front().push_front(bucket_num);
   257               _dormant[bucket_num] = !first_set;
   258               _first[bucket_num] = _last[bucket_num] = INVALID;
   259               qsep = qlast;
   260             }
   261 
   262             Node n = queue[qfirst++];
   263             addItem(n, bucket_num);
   264 
   265             for (InArcIt a(_graph, n); a != INVALID; ++a) {
   266               Node u = _graph.source(a);
   267               if (!reached[u] && _tolerance.positive((*_capacity)[a])) {
   268                 reached[u] = true;
   269                 queue[qlast++] = u;
   270               }
   271             }
   272           }
   273           first_set = false;
   274         }
   275 
   276         ++bucket_num;
   277         (*_bucket)[_source] = 0;
   278         _dormant[0] = true;
   279       }
   280       (*_source_set)[_source] = true;
   281 
   282       Node target = _last[_sets.back().back()];
   283       {
   284         for (OutArcIt a(_graph, _source); a != INVALID; ++a) {
   285           if (_tolerance.positive((*_capacity)[a])) {
   286             Node u = _graph.target(a);
   287             (*_flow)[a] = (*_capacity)[a];
   288             (*_excess)[u] += (*_capacity)[a];
   289             if (!(*_active)[u] && u != _source) {
   290               activate(u);
   291             }
   292           }
   293         }
   294 
   295         if ((*_active)[target]) {
   296           deactivate(target);
   297         }
   298 
   299         _highest = _sets.back().begin();
   300         while (_highest != _sets.back().end() &&
   301                !(*_active)[_first[*_highest]]) {
   302           ++_highest;
   303         }
   304       }
   305 
   306       while (true) {
   307         while (_highest != _sets.back().end()) {
   308           Node n = _first[*_highest];
   309           Value excess = (*_excess)[n];
   310           int next_bucket = _node_num;
   311 
   312           int under_bucket;
   313           if (++std::list<int>::iterator(_highest) == _sets.back().end()) {
   314             under_bucket = -1;
   315           } else {
   316             under_bucket = *(++std::list<int>::iterator(_highest));
   317           }
   318 
   319           for (OutArcIt a(_graph, n); a != INVALID; ++a) {
   320             Node v = _graph.target(a);
   321             if (_dormant[(*_bucket)[v]]) continue;
   322             Value rem = (*_capacity)[a] - (*_flow)[a];
   323             if (!_tolerance.positive(rem)) continue;
   324             if ((*_bucket)[v] == under_bucket) {
   325               if (!(*_active)[v] && v != target) {
   326                 activate(v);
   327               }
   328               if (!_tolerance.less(rem, excess)) {
   329                 (*_flow)[a] += excess;
   330                 (*_excess)[v] += excess;
   331                 excess = 0;
   332                 goto no_more_push;
   333               } else {
   334                 excess -= rem;
   335                 (*_excess)[v] += rem;
   336                 (*_flow)[a] = (*_capacity)[a];
   337               }
   338             } else if (next_bucket > (*_bucket)[v]) {
   339               next_bucket = (*_bucket)[v];
   340             }
   341           }
   342 
   343           for (InArcIt a(_graph, n); a != INVALID; ++a) {
   344             Node v = _graph.source(a);
   345             if (_dormant[(*_bucket)[v]]) continue;
   346             Value rem = (*_flow)[a];
   347             if (!_tolerance.positive(rem)) continue;
   348             if ((*_bucket)[v] == under_bucket) {
   349               if (!(*_active)[v] && v != target) {
   350                 activate(v);
   351               }
   352               if (!_tolerance.less(rem, excess)) {
   353                 (*_flow)[a] -= excess;
   354                 (*_excess)[v] += excess;
   355                 excess = 0;
   356                 goto no_more_push;
   357               } else {
   358                 excess -= rem;
   359                 (*_excess)[v] += rem;
   360                 (*_flow)[a] = 0;
   361               }
   362             } else if (next_bucket > (*_bucket)[v]) {
   363               next_bucket = (*_bucket)[v];
   364             }
   365           }
   366 
   367         no_more_push:
   368 
   369           (*_excess)[n] = excess;
   370 
   371           if (excess != 0) {
   372             if ((*_next)[n] == INVALID) {
   373               typename std::list<std::list<int> >::iterator new_set =
   374                 _sets.insert(--_sets.end(), std::list<int>());
   375               new_set->splice(new_set->end(), _sets.back(),
   376                               _sets.back().begin(), ++_highest);
   377               for (std::list<int>::iterator it = new_set->begin();
   378                    it != new_set->end(); ++it) {
   379                 _dormant[*it] = true;
   380               }
   381               while (_highest != _sets.back().end() &&
   382                      !(*_active)[_first[*_highest]]) {
   383                 ++_highest;
   384               }
   385             } else if (next_bucket == _node_num) {
   386               _first[(*_bucket)[n]] = (*_next)[n];
   387               (*_prev)[(*_next)[n]] = INVALID;
   388 
   389               std::list<std::list<int> >::iterator new_set =
   390                 _sets.insert(--_sets.end(), std::list<int>());
   391 
   392               new_set->push_front(bucket_num);
   393               (*_bucket)[n] = bucket_num;
   394               _first[bucket_num] = _last[bucket_num] = n;
   395               (*_next)[n] = INVALID;
   396               (*_prev)[n] = INVALID;
   397               _dormant[bucket_num] = true;
   398               ++bucket_num;
   399 
   400               while (_highest != _sets.back().end() &&
   401                      !(*_active)[_first[*_highest]]) {
   402                 ++_highest;
   403               }
   404             } else {
   405               _first[*_highest] = (*_next)[n];
   406               (*_prev)[(*_next)[n]] = INVALID;
   407 
   408               while (next_bucket != *_highest) {
   409                 --_highest;
   410               }
   411 
   412               if (_highest == _sets.back().begin()) {
   413                 _sets.back().push_front(bucket_num);
   414                 _dormant[bucket_num] = false;
   415                 _first[bucket_num] = _last[bucket_num] = INVALID;
   416                 ++bucket_num;
   417               }
   418               --_highest;
   419 
   420               (*_bucket)[n] = *_highest;
   421               (*_next)[n] = _first[*_highest];
   422               if (_first[*_highest] != INVALID) {
   423                 (*_prev)[_first[*_highest]] = n;
   424               } else {
   425                 _last[*_highest] = n;
   426               }
   427               _first[*_highest] = n;
   428             }
   429           } else {
   430 
   431             deactivate(n);
   432             if (!(*_active)[_first[*_highest]]) {
   433               ++_highest;
   434               if (_highest != _sets.back().end() &&
   435                   !(*_active)[_first[*_highest]]) {
   436                 _highest = _sets.back().end();
   437               }
   438             }
   439           }
   440         }
   441 
   442         if ((*_excess)[target] < _min_cut) {
   443           _min_cut = (*_excess)[target];
   444           for (NodeIt i(_graph); i != INVALID; ++i) {
   445             (*_min_cut_map)[i] = true;
   446           }
   447           for (std::list<int>::iterator it = _sets.back().begin();
   448                it != _sets.back().end(); ++it) {
   449             Node n = _first[*it];
   450             while (n != INVALID) {
   451               (*_min_cut_map)[n] = false;
   452               n = (*_next)[n];
   453             }
   454           }
   455         }
   456 
   457         {
   458           Node new_target;
   459           if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) {
   460             if ((*_next)[target] == INVALID) {
   461               _last[(*_bucket)[target]] = (*_prev)[target];
   462               new_target = (*_prev)[target];
   463             } else {
   464               (*_prev)[(*_next)[target]] = (*_prev)[target];
   465               new_target = (*_next)[target];
   466             }
   467             if ((*_prev)[target] == INVALID) {
   468               _first[(*_bucket)[target]] = (*_next)[target];
   469             } else {
   470               (*_next)[(*_prev)[target]] = (*_next)[target];
   471             }
   472           } else {
   473             _sets.back().pop_back();
   474             if (_sets.back().empty()) {
   475               _sets.pop_back();
   476               if (_sets.empty())
   477                 break;
   478               for (std::list<int>::iterator it = _sets.back().begin();
   479                    it != _sets.back().end(); ++it) {
   480                 _dormant[*it] = false;
   481               }
   482             }
   483             new_target = _last[_sets.back().back()];
   484           }
   485 
   486           (*_bucket)[target] = 0;
   487 
   488           (*_source_set)[target] = true;
   489           for (OutArcIt a(_graph, target); a != INVALID; ++a) {
   490             Value rem = (*_capacity)[a] - (*_flow)[a];
   491             if (!_tolerance.positive(rem)) continue;
   492             Node v = _graph.target(a);
   493             if (!(*_active)[v] && !(*_source_set)[v]) {
   494               activate(v);
   495             }
   496             (*_excess)[v] += rem;
   497             (*_flow)[a] = (*_capacity)[a];
   498           }
   499 
   500           for (InArcIt a(_graph, target); a != INVALID; ++a) {
   501             Value rem = (*_flow)[a];
   502             if (!_tolerance.positive(rem)) continue;
   503             Node v = _graph.source(a);
   504             if (!(*_active)[v] && !(*_source_set)[v]) {
   505               activate(v);
   506             }
   507             (*_excess)[v] += rem;
   508             (*_flow)[a] = 0;
   509           }
   510 
   511           target = new_target;
   512           if ((*_active)[target]) {
   513             deactivate(target);
   514           }
   515 
   516           _highest = _sets.back().begin();
   517           while (_highest != _sets.back().end() &&
   518                  !(*_active)[_first[*_highest]]) {
   519             ++_highest;
   520           }
   521         }
   522       }
   523     }
   524 
   525     void findMinCutIn() {
   526 
   527       for (NodeIt n(_graph); n != INVALID; ++n) {
   528         (*_excess)[n] = 0;
   529         (*_source_set)[n] = false;
   530       }
   531 
   532       for (ArcIt a(_graph); a != INVALID; ++a) {
   533         (*_flow)[a] = 0;
   534       }
   535 
   536       int bucket_num = 0;
   537       std::vector<Node> queue(_node_num);
   538       int qfirst = 0, qlast = 0, qsep = 0;
   539 
   540       {
   541         typename Digraph::template NodeMap<bool> reached(_graph, false);
   542 
   543         reached[_source] = true;
   544 
   545         bool first_set = true;
   546 
   547         for (NodeIt t(_graph); t != INVALID; ++t) {
   548           if (reached[t]) continue;
   549           _sets.push_front(std::list<int>());
   550 
   551           queue[qlast++] = t;
   552           reached[t] = true;
   553 
   554           while (qfirst != qlast) {
   555             if (qsep == qfirst) {
   556               ++bucket_num;
   557               _sets.front().push_front(bucket_num);
   558               _dormant[bucket_num] = !first_set;
   559               _first[bucket_num] = _last[bucket_num] = INVALID;
   560               qsep = qlast;
   561             }
   562 
   563             Node n = queue[qfirst++];
   564             addItem(n, bucket_num);
   565 
   566             for (OutArcIt a(_graph, n); a != INVALID; ++a) {
   567               Node u = _graph.target(a);
   568               if (!reached[u] && _tolerance.positive((*_capacity)[a])) {
   569                 reached[u] = true;
   570                 queue[qlast++] = u;
   571               }
   572             }
   573           }
   574           first_set = false;
   575         }
   576 
   577         ++bucket_num;
   578         (*_bucket)[_source] = 0;
   579         _dormant[0] = true;
   580       }
   581       (*_source_set)[_source] = true;
   582 
   583       Node target = _last[_sets.back().back()];
   584       {
   585         for (InArcIt a(_graph, _source); a != INVALID; ++a) {
   586           if (_tolerance.positive((*_capacity)[a])) {
   587             Node u = _graph.source(a);
   588             (*_flow)[a] = (*_capacity)[a];
   589             (*_excess)[u] += (*_capacity)[a];
   590             if (!(*_active)[u] && u != _source) {
   591               activate(u);
   592             }
   593           }
   594         }
   595         if ((*_active)[target]) {
   596           deactivate(target);
   597         }
   598 
   599         _highest = _sets.back().begin();
   600         while (_highest != _sets.back().end() &&
   601                !(*_active)[_first[*_highest]]) {
   602           ++_highest;
   603         }
   604       }
   605 
   606 
   607       while (true) {
   608         while (_highest != _sets.back().end()) {
   609           Node n = _first[*_highest];
   610           Value excess = (*_excess)[n];
   611           int next_bucket = _node_num;
   612 
   613           int under_bucket;
   614           if (++std::list<int>::iterator(_highest) == _sets.back().end()) {
   615             under_bucket = -1;
   616           } else {
   617             under_bucket = *(++std::list<int>::iterator(_highest));
   618           }
   619 
   620           for (InArcIt a(_graph, n); a != INVALID; ++a) {
   621             Node v = _graph.source(a);
   622             if (_dormant[(*_bucket)[v]]) continue;
   623             Value rem = (*_capacity)[a] - (*_flow)[a];
   624             if (!_tolerance.positive(rem)) continue;
   625             if ((*_bucket)[v] == under_bucket) {
   626               if (!(*_active)[v] && v != target) {
   627                 activate(v);
   628               }
   629               if (!_tolerance.less(rem, excess)) {
   630                 (*_flow)[a] += excess;
   631                 (*_excess)[v] += excess;
   632                 excess = 0;
   633                 goto no_more_push;
   634               } else {
   635                 excess -= rem;
   636                 (*_excess)[v] += rem;
   637                 (*_flow)[a] = (*_capacity)[a];
   638               }
   639             } else if (next_bucket > (*_bucket)[v]) {
   640               next_bucket = (*_bucket)[v];
   641             }
   642           }
   643 
   644           for (OutArcIt a(_graph, n); a != INVALID; ++a) {
   645             Node v = _graph.target(a);
   646             if (_dormant[(*_bucket)[v]]) continue;
   647             Value rem = (*_flow)[a];
   648             if (!_tolerance.positive(rem)) continue;
   649             if ((*_bucket)[v] == under_bucket) {
   650               if (!(*_active)[v] && v != target) {
   651                 activate(v);
   652               }
   653               if (!_tolerance.less(rem, excess)) {
   654                 (*_flow)[a] -= excess;
   655                 (*_excess)[v] += excess;
   656                 excess = 0;
   657                 goto no_more_push;
   658               } else {
   659                 excess -= rem;
   660                 (*_excess)[v] += rem;
   661                 (*_flow)[a] = 0;
   662               }
   663             } else if (next_bucket > (*_bucket)[v]) {
   664               next_bucket = (*_bucket)[v];
   665             }
   666           }
   667 
   668         no_more_push:
   669 
   670           (*_excess)[n] = excess;
   671 
   672           if (excess != 0) {
   673             if ((*_next)[n] == INVALID) {
   674               typename std::list<std::list<int> >::iterator new_set =
   675                 _sets.insert(--_sets.end(), std::list<int>());
   676               new_set->splice(new_set->end(), _sets.back(),
   677                               _sets.back().begin(), ++_highest);
   678               for (std::list<int>::iterator it = new_set->begin();
   679                    it != new_set->end(); ++it) {
   680                 _dormant[*it] = true;
   681               }
   682               while (_highest != _sets.back().end() &&
   683                      !(*_active)[_first[*_highest]]) {
   684                 ++_highest;
   685               }
   686             } else if (next_bucket == _node_num) {
   687               _first[(*_bucket)[n]] = (*_next)[n];
   688               (*_prev)[(*_next)[n]] = INVALID;
   689 
   690               std::list<std::list<int> >::iterator new_set =
   691                 _sets.insert(--_sets.end(), std::list<int>());
   692 
   693               new_set->push_front(bucket_num);
   694               (*_bucket)[n] = bucket_num;
   695               _first[bucket_num] = _last[bucket_num] = n;
   696               (*_next)[n] = INVALID;
   697               (*_prev)[n] = INVALID;
   698               _dormant[bucket_num] = true;
   699               ++bucket_num;
   700 
   701               while (_highest != _sets.back().end() &&
   702                      !(*_active)[_first[*_highest]]) {
   703                 ++_highest;
   704               }
   705             } else {
   706               _first[*_highest] = (*_next)[n];
   707               (*_prev)[(*_next)[n]] = INVALID;
   708 
   709               while (next_bucket != *_highest) {
   710                 --_highest;
   711               }
   712               if (_highest == _sets.back().begin()) {
   713                 _sets.back().push_front(bucket_num);
   714                 _dormant[bucket_num] = false;
   715                 _first[bucket_num] = _last[bucket_num] = INVALID;
   716                 ++bucket_num;
   717               }
   718               --_highest;
   719 
   720               (*_bucket)[n] = *_highest;
   721               (*_next)[n] = _first[*_highest];
   722               if (_first[*_highest] != INVALID) {
   723                 (*_prev)[_first[*_highest]] = n;
   724               } else {
   725                 _last[*_highest] = n;
   726               }
   727               _first[*_highest] = n;
   728             }
   729           } else {
   730 
   731             deactivate(n);
   732             if (!(*_active)[_first[*_highest]]) {
   733               ++_highest;
   734               if (_highest != _sets.back().end() &&
   735                   !(*_active)[_first[*_highest]]) {
   736                 _highest = _sets.back().end();
   737               }
   738             }
   739           }
   740         }
   741 
   742         if ((*_excess)[target] < _min_cut) {
   743           _min_cut = (*_excess)[target];
   744           for (NodeIt i(_graph); i != INVALID; ++i) {
   745             (*_min_cut_map)[i] = false;
   746           }
   747           for (std::list<int>::iterator it = _sets.back().begin();
   748                it != _sets.back().end(); ++it) {
   749             Node n = _first[*it];
   750             while (n != INVALID) {
   751               (*_min_cut_map)[n] = true;
   752               n = (*_next)[n];
   753             }
   754           }
   755         }
   756 
   757         {
   758           Node new_target;
   759           if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) {
   760             if ((*_next)[target] == INVALID) {
   761               _last[(*_bucket)[target]] = (*_prev)[target];
   762               new_target = (*_prev)[target];
   763             } else {
   764               (*_prev)[(*_next)[target]] = (*_prev)[target];
   765               new_target = (*_next)[target];
   766             }
   767             if ((*_prev)[target] == INVALID) {
   768               _first[(*_bucket)[target]] = (*_next)[target];
   769             } else {
   770               (*_next)[(*_prev)[target]] = (*_next)[target];
   771             }
   772           } else {
   773             _sets.back().pop_back();
   774             if (_sets.back().empty()) {
   775               _sets.pop_back();
   776               if (_sets.empty())
   777                 break;
   778               for (std::list<int>::iterator it = _sets.back().begin();
   779                    it != _sets.back().end(); ++it) {
   780                 _dormant[*it] = false;
   781               }
   782             }
   783             new_target = _last[_sets.back().back()];
   784           }
   785 
   786           (*_bucket)[target] = 0;
   787 
   788           (*_source_set)[target] = true;
   789           for (InArcIt a(_graph, target); a != INVALID; ++a) {
   790             Value rem = (*_capacity)[a] - (*_flow)[a];
   791             if (!_tolerance.positive(rem)) continue;
   792             Node v = _graph.source(a);
   793             if (!(*_active)[v] && !(*_source_set)[v]) {
   794               activate(v);
   795             }
   796             (*_excess)[v] += rem;
   797             (*_flow)[a] = (*_capacity)[a];
   798           }
   799 
   800           for (OutArcIt a(_graph, target); a != INVALID; ++a) {
   801             Value rem = (*_flow)[a];
   802             if (!_tolerance.positive(rem)) continue;
   803             Node v = _graph.target(a);
   804             if (!(*_active)[v] && !(*_source_set)[v]) {
   805               activate(v);
   806             }
   807             (*_excess)[v] += rem;
   808             (*_flow)[a] = 0;
   809           }
   810 
   811           target = new_target;
   812           if ((*_active)[target]) {
   813             deactivate(target);
   814           }
   815 
   816           _highest = _sets.back().begin();
   817           while (_highest != _sets.back().end() &&
   818                  !(*_active)[_first[*_highest]]) {
   819             ++_highest;
   820           }
   821         }
   822       }
   823     }
   824 
   825   public:
   826 
   827     /// \name Execution Control
   828     /// The simplest way to execute the algorithm is to use
   829     /// one of the member functions called \ref run().
   830     /// \n
   831     /// If you need better control on the execution,
   832     /// you have to call one of the \ref init() functions first, then
   833     /// \ref calculateOut() and/or \ref calculateIn().
   834 
   835     /// @{
   836 
   837     /// \brief Initialize the internal data structures.
   838     ///
   839     /// This function initializes the internal data structures. It creates
   840     /// the maps and some bucket structures for the algorithm.
   841     /// The first node is used as the source node for the push-relabel
   842     /// algorithm.
   843     void init() {
   844       init(NodeIt(_graph));
   845     }
   846 
   847     /// \brief Initialize the internal data structures.
   848     ///
   849     /// This function initializes the internal data structures. It creates
   850     /// the maps and some bucket structures for the algorithm. 
   851     /// The given node is used as the source node for the push-relabel
   852     /// algorithm.
   853     void init(const Node& source) {
   854       _source = source;
   855 
   856       _node_num = countNodes(_graph);
   857 
   858       _first.resize(_node_num);
   859       _last.resize(_node_num);
   860 
   861       _dormant.resize(_node_num);
   862 
   863       if (!_flow) {
   864         _flow = new FlowMap(_graph);
   865       }
   866       if (!_next) {
   867         _next = new typename Digraph::template NodeMap<Node>(_graph);
   868       }
   869       if (!_prev) {
   870         _prev = new typename Digraph::template NodeMap<Node>(_graph);
   871       }
   872       if (!_active) {
   873         _active = new typename Digraph::template NodeMap<bool>(_graph);
   874       }
   875       if (!_bucket) {
   876         _bucket = new typename Digraph::template NodeMap<int>(_graph);
   877       }
   878       if (!_excess) {
   879         _excess = new ExcessMap(_graph);
   880       }
   881       if (!_source_set) {
   882         _source_set = new SourceSetMap(_graph);
   883       }
   884       if (!_min_cut_map) {
   885         _min_cut_map = new MinCutMap(_graph);
   886       }
   887 
   888       _min_cut = std::numeric_limits<Value>::max();
   889     }
   890 
   891 
   892     /// \brief Calculate a minimum cut with \f$ source \f$ on the
   893     /// source-side.
   894     ///
   895     /// This function calculates a minimum cut with \f$ source \f$ on the
   896     /// source-side (i.e. a set \f$ X\subsetneq V \f$ with
   897     /// \f$ source \in X \f$ and minimal outgoing capacity).
   898     ///
   899     /// \pre \ref init() must be called before using this function.
   900     void calculateOut() {
   901       findMinCutOut();
   902     }
   903 
   904     /// \brief Calculate a minimum cut with \f$ source \f$ on the
   905     /// sink-side.
   906     ///
   907     /// This function calculates a minimum cut with \f$ source \f$ on the
   908     /// sink-side (i.e. a set \f$ X\subsetneq V \f$ with
   909     /// \f$ source \notin X \f$ and minimal outgoing capacity).
   910     ///
   911     /// \pre \ref init() must be called before using this function.
   912     void calculateIn() {
   913       findMinCutIn();
   914     }
   915 
   916 
   917     /// \brief Run the algorithm.
   918     ///
   919     /// This function runs the algorithm. It finds nodes \c source and
   920     /// \c target arbitrarily and then calls \ref init(), \ref calculateOut()
   921     /// and \ref calculateIn().
   922     void run() {
   923       init();
   924       calculateOut();
   925       calculateIn();
   926     }
   927 
   928     /// \brief Run the algorithm.
   929     ///
   930     /// This function runs the algorithm. It uses the given \c source node, 
   931     /// finds a proper \c target node and then calls the \ref init(),
   932     /// \ref calculateOut() and \ref calculateIn().
   933     void run(const Node& s) {
   934       init(s);
   935       calculateOut();
   936       calculateIn();
   937     }
   938 
   939     /// @}
   940 
   941     /// \name Query Functions
   942     /// The result of the %HaoOrlin algorithm
   943     /// can be obtained using these functions.\n
   944     /// \ref run(), \ref calculateOut() or \ref calculateIn() 
   945     /// should be called before using them.
   946 
   947     /// @{
   948 
   949     /// \brief Return the value of the minimum cut.
   950     ///
   951     /// This function returns the value of the minimum cut.
   952     ///
   953     /// \pre \ref run(), \ref calculateOut() or \ref calculateIn() 
   954     /// must be called before using this function.
   955     Value minCutValue() const {
   956       return _min_cut;
   957     }
   958 
   959 
   960     /// \brief Return a minimum cut.
   961     ///
   962     /// This function sets \c cutMap to the characteristic vector of a
   963     /// minimum value cut: it will give a non-empty set \f$ X\subsetneq V \f$
   964     /// with minimal outgoing capacity (i.e. \c cutMap will be \c true exactly
   965     /// for the nodes of \f$ X \f$).
   966     ///
   967     /// \param cutMap A \ref concepts::WriteMap "writable" node map with
   968     /// \c bool (or convertible) value type.
   969     ///
   970     /// \return The value of the minimum cut.
   971     ///
   972     /// \pre \ref run(), \ref calculateOut() or \ref calculateIn() 
   973     /// must be called before using this function.
   974     template <typename CutMap>
   975     Value minCutMap(CutMap& cutMap) const {
   976       for (NodeIt it(_graph); it != INVALID; ++it) {
   977         cutMap.set(it, (*_min_cut_map)[it]);
   978       }
   979       return _min_cut;
   980     }
   981 
   982     /// @}
   983 
   984   }; //class HaoOrlin
   985 
   986 } //namespace lemon
   987 
   988 #endif //LEMON_HAO_ORLIN_H