lemon/hao_orlin.h
author Alpar Juttner <alpar@cs.elte.hu>
Mon, 18 Mar 2013 17:41:19 +0100
changeset 1053 1c978b5bcc65
parent 877 141f9c0db4a3
child 1092 dceba191c00d
permissions -rw-r--r--
Use doxygen's own bibtex support (#456)
     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) 2003-2010
     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. A notable
    57   /// use of this algorithm is 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     /// \brief Set the tolerance used by the algorithm.
   169     ///
   170     /// This function sets the tolerance object used by the algorithm.
   171     /// \return <tt>(*this)</tt>
   172     HaoOrlin& tolerance(const Tolerance& tolerance) {
   173       _tolerance = tolerance;
   174       return *this;
   175     }
   176 
   177     /// \brief Returns a const reference to the tolerance.
   178     ///
   179     /// This function returns a const reference to the tolerance object
   180     /// used by the algorithm.
   181     const Tolerance& tolerance() const {
   182       return _tolerance;
   183     }
   184 
   185   private:
   186 
   187     void activate(const Node& i) {
   188       (*_active)[i] = true;
   189 
   190       int bucket = (*_bucket)[i];
   191 
   192       if ((*_prev)[i] == INVALID || (*_active)[(*_prev)[i]]) return;
   193       //unlace
   194       (*_next)[(*_prev)[i]] = (*_next)[i];
   195       if ((*_next)[i] != INVALID) {
   196         (*_prev)[(*_next)[i]] = (*_prev)[i];
   197       } else {
   198         _last[bucket] = (*_prev)[i];
   199       }
   200       //lace
   201       (*_next)[i] = _first[bucket];
   202       (*_prev)[_first[bucket]] = i;
   203       (*_prev)[i] = INVALID;
   204       _first[bucket] = i;
   205     }
   206 
   207     void deactivate(const Node& i) {
   208       (*_active)[i] = false;
   209       int bucket = (*_bucket)[i];
   210 
   211       if ((*_next)[i] == INVALID || !(*_active)[(*_next)[i]]) return;
   212 
   213       //unlace
   214       (*_prev)[(*_next)[i]] = (*_prev)[i];
   215       if ((*_prev)[i] != INVALID) {
   216         (*_next)[(*_prev)[i]] = (*_next)[i];
   217       } else {
   218         _first[bucket] = (*_next)[i];
   219       }
   220       //lace
   221       (*_prev)[i] = _last[bucket];
   222       (*_next)[_last[bucket]] = i;
   223       (*_next)[i] = INVALID;
   224       _last[bucket] = i;
   225     }
   226 
   227     void addItem(const Node& i, int bucket) {
   228       (*_bucket)[i] = bucket;
   229       if (_last[bucket] != INVALID) {
   230         (*_prev)[i] = _last[bucket];
   231         (*_next)[_last[bucket]] = i;
   232         (*_next)[i] = INVALID;
   233         _last[bucket] = i;
   234       } else {
   235         (*_prev)[i] = INVALID;
   236         _first[bucket] = i;
   237         (*_next)[i] = INVALID;
   238         _last[bucket] = i;
   239       }
   240     }
   241 
   242     void findMinCutOut() {
   243 
   244       for (NodeIt n(_graph); n != INVALID; ++n) {
   245         (*_excess)[n] = 0;
   246         (*_source_set)[n] = false;
   247       }
   248 
   249       for (ArcIt a(_graph); a != INVALID; ++a) {
   250         (*_flow)[a] = 0;
   251       }
   252 
   253       int bucket_num = 0;
   254       std::vector<Node> queue(_node_num);
   255       int qfirst = 0, qlast = 0, qsep = 0;
   256 
   257       {
   258         typename Digraph::template NodeMap<bool> reached(_graph, false);
   259 
   260         reached[_source] = true;
   261         bool first_set = true;
   262 
   263         for (NodeIt t(_graph); t != INVALID; ++t) {
   264           if (reached[t]) continue;
   265           _sets.push_front(std::list<int>());
   266 
   267           queue[qlast++] = t;
   268           reached[t] = true;
   269 
   270           while (qfirst != qlast) {
   271             if (qsep == qfirst) {
   272               ++bucket_num;
   273               _sets.front().push_front(bucket_num);
   274               _dormant[bucket_num] = !first_set;
   275               _first[bucket_num] = _last[bucket_num] = INVALID;
   276               qsep = qlast;
   277             }
   278 
   279             Node n = queue[qfirst++];
   280             addItem(n, bucket_num);
   281 
   282             for (InArcIt a(_graph, n); a != INVALID; ++a) {
   283               Node u = _graph.source(a);
   284               if (!reached[u] && _tolerance.positive((*_capacity)[a])) {
   285                 reached[u] = true;
   286                 queue[qlast++] = u;
   287               }
   288             }
   289           }
   290           first_set = false;
   291         }
   292 
   293         ++bucket_num;
   294         (*_bucket)[_source] = 0;
   295         _dormant[0] = true;
   296       }
   297       (*_source_set)[_source] = true;
   298 
   299       Node target = _last[_sets.back().back()];
   300       {
   301         for (OutArcIt a(_graph, _source); a != INVALID; ++a) {
   302           if (_tolerance.positive((*_capacity)[a])) {
   303             Node u = _graph.target(a);
   304             (*_flow)[a] = (*_capacity)[a];
   305             (*_excess)[u] += (*_capacity)[a];
   306             if (!(*_active)[u] && u != _source) {
   307               activate(u);
   308             }
   309           }
   310         }
   311 
   312         if ((*_active)[target]) {
   313           deactivate(target);
   314         }
   315 
   316         _highest = _sets.back().begin();
   317         while (_highest != _sets.back().end() &&
   318                !(*_active)[_first[*_highest]]) {
   319           ++_highest;
   320         }
   321       }
   322 
   323       while (true) {
   324         while (_highest != _sets.back().end()) {
   325           Node n = _first[*_highest];
   326           Value excess = (*_excess)[n];
   327           int next_bucket = _node_num;
   328 
   329           int under_bucket;
   330           if (++std::list<int>::iterator(_highest) == _sets.back().end()) {
   331             under_bucket = -1;
   332           } else {
   333             under_bucket = *(++std::list<int>::iterator(_highest));
   334           }
   335 
   336           for (OutArcIt a(_graph, n); a != INVALID; ++a) {
   337             Node v = _graph.target(a);
   338             if (_dormant[(*_bucket)[v]]) continue;
   339             Value rem = (*_capacity)[a] - (*_flow)[a];
   340             if (!_tolerance.positive(rem)) continue;
   341             if ((*_bucket)[v] == under_bucket) {
   342               if (!(*_active)[v] && v != target) {
   343                 activate(v);
   344               }
   345               if (!_tolerance.less(rem, excess)) {
   346                 (*_flow)[a] += excess;
   347                 (*_excess)[v] += excess;
   348                 excess = 0;
   349                 goto no_more_push;
   350               } else {
   351                 excess -= rem;
   352                 (*_excess)[v] += rem;
   353                 (*_flow)[a] = (*_capacity)[a];
   354               }
   355             } else if (next_bucket > (*_bucket)[v]) {
   356               next_bucket = (*_bucket)[v];
   357             }
   358           }
   359 
   360           for (InArcIt a(_graph, n); a != INVALID; ++a) {
   361             Node v = _graph.source(a);
   362             if (_dormant[(*_bucket)[v]]) continue;
   363             Value rem = (*_flow)[a];
   364             if (!_tolerance.positive(rem)) continue;
   365             if ((*_bucket)[v] == under_bucket) {
   366               if (!(*_active)[v] && v != target) {
   367                 activate(v);
   368               }
   369               if (!_tolerance.less(rem, excess)) {
   370                 (*_flow)[a] -= excess;
   371                 (*_excess)[v] += excess;
   372                 excess = 0;
   373                 goto no_more_push;
   374               } else {
   375                 excess -= rem;
   376                 (*_excess)[v] += rem;
   377                 (*_flow)[a] = 0;
   378               }
   379             } else if (next_bucket > (*_bucket)[v]) {
   380               next_bucket = (*_bucket)[v];
   381             }
   382           }
   383 
   384         no_more_push:
   385 
   386           (*_excess)[n] = excess;
   387 
   388           if (excess != 0) {
   389             if ((*_next)[n] == INVALID) {
   390               typename std::list<std::list<int> >::iterator new_set =
   391                 _sets.insert(--_sets.end(), std::list<int>());
   392               new_set->splice(new_set->end(), _sets.back(),
   393                               _sets.back().begin(), ++_highest);
   394               for (std::list<int>::iterator it = new_set->begin();
   395                    it != new_set->end(); ++it) {
   396                 _dormant[*it] = true;
   397               }
   398               while (_highest != _sets.back().end() &&
   399                      !(*_active)[_first[*_highest]]) {
   400                 ++_highest;
   401               }
   402             } else if (next_bucket == _node_num) {
   403               _first[(*_bucket)[n]] = (*_next)[n];
   404               (*_prev)[(*_next)[n]] = INVALID;
   405 
   406               std::list<std::list<int> >::iterator new_set =
   407                 _sets.insert(--_sets.end(), std::list<int>());
   408 
   409               new_set->push_front(bucket_num);
   410               (*_bucket)[n] = bucket_num;
   411               _first[bucket_num] = _last[bucket_num] = n;
   412               (*_next)[n] = INVALID;
   413               (*_prev)[n] = INVALID;
   414               _dormant[bucket_num] = true;
   415               ++bucket_num;
   416 
   417               while (_highest != _sets.back().end() &&
   418                      !(*_active)[_first[*_highest]]) {
   419                 ++_highest;
   420               }
   421             } else {
   422               _first[*_highest] = (*_next)[n];
   423               (*_prev)[(*_next)[n]] = INVALID;
   424 
   425               while (next_bucket != *_highest) {
   426                 --_highest;
   427               }
   428 
   429               if (_highest == _sets.back().begin()) {
   430                 _sets.back().push_front(bucket_num);
   431                 _dormant[bucket_num] = false;
   432                 _first[bucket_num] = _last[bucket_num] = INVALID;
   433                 ++bucket_num;
   434               }
   435               --_highest;
   436 
   437               (*_bucket)[n] = *_highest;
   438               (*_next)[n] = _first[*_highest];
   439               if (_first[*_highest] != INVALID) {
   440                 (*_prev)[_first[*_highest]] = n;
   441               } else {
   442                 _last[*_highest] = n;
   443               }
   444               _first[*_highest] = n;
   445             }
   446           } else {
   447 
   448             deactivate(n);
   449             if (!(*_active)[_first[*_highest]]) {
   450               ++_highest;
   451               if (_highest != _sets.back().end() &&
   452                   !(*_active)[_first[*_highest]]) {
   453                 _highest = _sets.back().end();
   454               }
   455             }
   456           }
   457         }
   458 
   459         if ((*_excess)[target] < _min_cut) {
   460           _min_cut = (*_excess)[target];
   461           for (NodeIt i(_graph); i != INVALID; ++i) {
   462             (*_min_cut_map)[i] = true;
   463           }
   464           for (std::list<int>::iterator it = _sets.back().begin();
   465                it != _sets.back().end(); ++it) {
   466             Node n = _first[*it];
   467             while (n != INVALID) {
   468               (*_min_cut_map)[n] = false;
   469               n = (*_next)[n];
   470             }
   471           }
   472         }
   473 
   474         {
   475           Node new_target;
   476           if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) {
   477             if ((*_next)[target] == INVALID) {
   478               _last[(*_bucket)[target]] = (*_prev)[target];
   479               new_target = (*_prev)[target];
   480             } else {
   481               (*_prev)[(*_next)[target]] = (*_prev)[target];
   482               new_target = (*_next)[target];
   483             }
   484             if ((*_prev)[target] == INVALID) {
   485               _first[(*_bucket)[target]] = (*_next)[target];
   486             } else {
   487               (*_next)[(*_prev)[target]] = (*_next)[target];
   488             }
   489           } else {
   490             _sets.back().pop_back();
   491             if (_sets.back().empty()) {
   492               _sets.pop_back();
   493               if (_sets.empty())
   494                 break;
   495               for (std::list<int>::iterator it = _sets.back().begin();
   496                    it != _sets.back().end(); ++it) {
   497                 _dormant[*it] = false;
   498               }
   499             }
   500             new_target = _last[_sets.back().back()];
   501           }
   502 
   503           (*_bucket)[target] = 0;
   504 
   505           (*_source_set)[target] = true;
   506           for (OutArcIt a(_graph, target); a != INVALID; ++a) {
   507             Value rem = (*_capacity)[a] - (*_flow)[a];
   508             if (!_tolerance.positive(rem)) continue;
   509             Node v = _graph.target(a);
   510             if (!(*_active)[v] && !(*_source_set)[v]) {
   511               activate(v);
   512             }
   513             (*_excess)[v] += rem;
   514             (*_flow)[a] = (*_capacity)[a];
   515           }
   516 
   517           for (InArcIt a(_graph, target); a != INVALID; ++a) {
   518             Value rem = (*_flow)[a];
   519             if (!_tolerance.positive(rem)) continue;
   520             Node v = _graph.source(a);
   521             if (!(*_active)[v] && !(*_source_set)[v]) {
   522               activate(v);
   523             }
   524             (*_excess)[v] += rem;
   525             (*_flow)[a] = 0;
   526           }
   527 
   528           target = new_target;
   529           if ((*_active)[target]) {
   530             deactivate(target);
   531           }
   532 
   533           _highest = _sets.back().begin();
   534           while (_highest != _sets.back().end() &&
   535                  !(*_active)[_first[*_highest]]) {
   536             ++_highest;
   537           }
   538         }
   539       }
   540     }
   541 
   542     void findMinCutIn() {
   543 
   544       for (NodeIt n(_graph); n != INVALID; ++n) {
   545         (*_excess)[n] = 0;
   546         (*_source_set)[n] = false;
   547       }
   548 
   549       for (ArcIt a(_graph); a != INVALID; ++a) {
   550         (*_flow)[a] = 0;
   551       }
   552 
   553       int bucket_num = 0;
   554       std::vector<Node> queue(_node_num);
   555       int qfirst = 0, qlast = 0, qsep = 0;
   556 
   557       {
   558         typename Digraph::template NodeMap<bool> reached(_graph, false);
   559 
   560         reached[_source] = true;
   561 
   562         bool first_set = true;
   563 
   564         for (NodeIt t(_graph); t != INVALID; ++t) {
   565           if (reached[t]) continue;
   566           _sets.push_front(std::list<int>());
   567 
   568           queue[qlast++] = t;
   569           reached[t] = true;
   570 
   571           while (qfirst != qlast) {
   572             if (qsep == qfirst) {
   573               ++bucket_num;
   574               _sets.front().push_front(bucket_num);
   575               _dormant[bucket_num] = !first_set;
   576               _first[bucket_num] = _last[bucket_num] = INVALID;
   577               qsep = qlast;
   578             }
   579 
   580             Node n = queue[qfirst++];
   581             addItem(n, bucket_num);
   582 
   583             for (OutArcIt a(_graph, n); a != INVALID; ++a) {
   584               Node u = _graph.target(a);
   585               if (!reached[u] && _tolerance.positive((*_capacity)[a])) {
   586                 reached[u] = true;
   587                 queue[qlast++] = u;
   588               }
   589             }
   590           }
   591           first_set = false;
   592         }
   593 
   594         ++bucket_num;
   595         (*_bucket)[_source] = 0;
   596         _dormant[0] = true;
   597       }
   598       (*_source_set)[_source] = true;
   599 
   600       Node target = _last[_sets.back().back()];
   601       {
   602         for (InArcIt a(_graph, _source); a != INVALID; ++a) {
   603           if (_tolerance.positive((*_capacity)[a])) {
   604             Node u = _graph.source(a);
   605             (*_flow)[a] = (*_capacity)[a];
   606             (*_excess)[u] += (*_capacity)[a];
   607             if (!(*_active)[u] && u != _source) {
   608               activate(u);
   609             }
   610           }
   611         }
   612         if ((*_active)[target]) {
   613           deactivate(target);
   614         }
   615 
   616         _highest = _sets.back().begin();
   617         while (_highest != _sets.back().end() &&
   618                !(*_active)[_first[*_highest]]) {
   619           ++_highest;
   620         }
   621       }
   622 
   623 
   624       while (true) {
   625         while (_highest != _sets.back().end()) {
   626           Node n = _first[*_highest];
   627           Value excess = (*_excess)[n];
   628           int next_bucket = _node_num;
   629 
   630           int under_bucket;
   631           if (++std::list<int>::iterator(_highest) == _sets.back().end()) {
   632             under_bucket = -1;
   633           } else {
   634             under_bucket = *(++std::list<int>::iterator(_highest));
   635           }
   636 
   637           for (InArcIt a(_graph, n); a != INVALID; ++a) {
   638             Node v = _graph.source(a);
   639             if (_dormant[(*_bucket)[v]]) continue;
   640             Value rem = (*_capacity)[a] - (*_flow)[a];
   641             if (!_tolerance.positive(rem)) continue;
   642             if ((*_bucket)[v] == under_bucket) {
   643               if (!(*_active)[v] && v != target) {
   644                 activate(v);
   645               }
   646               if (!_tolerance.less(rem, excess)) {
   647                 (*_flow)[a] += excess;
   648                 (*_excess)[v] += excess;
   649                 excess = 0;
   650                 goto no_more_push;
   651               } else {
   652                 excess -= rem;
   653                 (*_excess)[v] += rem;
   654                 (*_flow)[a] = (*_capacity)[a];
   655               }
   656             } else if (next_bucket > (*_bucket)[v]) {
   657               next_bucket = (*_bucket)[v];
   658             }
   659           }
   660 
   661           for (OutArcIt a(_graph, n); a != INVALID; ++a) {
   662             Node v = _graph.target(a);
   663             if (_dormant[(*_bucket)[v]]) continue;
   664             Value rem = (*_flow)[a];
   665             if (!_tolerance.positive(rem)) continue;
   666             if ((*_bucket)[v] == under_bucket) {
   667               if (!(*_active)[v] && v != target) {
   668                 activate(v);
   669               }
   670               if (!_tolerance.less(rem, excess)) {
   671                 (*_flow)[a] -= excess;
   672                 (*_excess)[v] += excess;
   673                 excess = 0;
   674                 goto no_more_push;
   675               } else {
   676                 excess -= rem;
   677                 (*_excess)[v] += rem;
   678                 (*_flow)[a] = 0;
   679               }
   680             } else if (next_bucket > (*_bucket)[v]) {
   681               next_bucket = (*_bucket)[v];
   682             }
   683           }
   684 
   685         no_more_push:
   686 
   687           (*_excess)[n] = excess;
   688 
   689           if (excess != 0) {
   690             if ((*_next)[n] == INVALID) {
   691               typename std::list<std::list<int> >::iterator new_set =
   692                 _sets.insert(--_sets.end(), std::list<int>());
   693               new_set->splice(new_set->end(), _sets.back(),
   694                               _sets.back().begin(), ++_highest);
   695               for (std::list<int>::iterator it = new_set->begin();
   696                    it != new_set->end(); ++it) {
   697                 _dormant[*it] = true;
   698               }
   699               while (_highest != _sets.back().end() &&
   700                      !(*_active)[_first[*_highest]]) {
   701                 ++_highest;
   702               }
   703             } else if (next_bucket == _node_num) {
   704               _first[(*_bucket)[n]] = (*_next)[n];
   705               (*_prev)[(*_next)[n]] = INVALID;
   706 
   707               std::list<std::list<int> >::iterator new_set =
   708                 _sets.insert(--_sets.end(), std::list<int>());
   709 
   710               new_set->push_front(bucket_num);
   711               (*_bucket)[n] = bucket_num;
   712               _first[bucket_num] = _last[bucket_num] = n;
   713               (*_next)[n] = INVALID;
   714               (*_prev)[n] = INVALID;
   715               _dormant[bucket_num] = true;
   716               ++bucket_num;
   717 
   718               while (_highest != _sets.back().end() &&
   719                      !(*_active)[_first[*_highest]]) {
   720                 ++_highest;
   721               }
   722             } else {
   723               _first[*_highest] = (*_next)[n];
   724               (*_prev)[(*_next)[n]] = INVALID;
   725 
   726               while (next_bucket != *_highest) {
   727                 --_highest;
   728               }
   729               if (_highest == _sets.back().begin()) {
   730                 _sets.back().push_front(bucket_num);
   731                 _dormant[bucket_num] = false;
   732                 _first[bucket_num] = _last[bucket_num] = INVALID;
   733                 ++bucket_num;
   734               }
   735               --_highest;
   736 
   737               (*_bucket)[n] = *_highest;
   738               (*_next)[n] = _first[*_highest];
   739               if (_first[*_highest] != INVALID) {
   740                 (*_prev)[_first[*_highest]] = n;
   741               } else {
   742                 _last[*_highest] = n;
   743               }
   744               _first[*_highest] = n;
   745             }
   746           } else {
   747 
   748             deactivate(n);
   749             if (!(*_active)[_first[*_highest]]) {
   750               ++_highest;
   751               if (_highest != _sets.back().end() &&
   752                   !(*_active)[_first[*_highest]]) {
   753                 _highest = _sets.back().end();
   754               }
   755             }
   756           }
   757         }
   758 
   759         if ((*_excess)[target] < _min_cut) {
   760           _min_cut = (*_excess)[target];
   761           for (NodeIt i(_graph); i != INVALID; ++i) {
   762             (*_min_cut_map)[i] = false;
   763           }
   764           for (std::list<int>::iterator it = _sets.back().begin();
   765                it != _sets.back().end(); ++it) {
   766             Node n = _first[*it];
   767             while (n != INVALID) {
   768               (*_min_cut_map)[n] = true;
   769               n = (*_next)[n];
   770             }
   771           }
   772         }
   773 
   774         {
   775           Node new_target;
   776           if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) {
   777             if ((*_next)[target] == INVALID) {
   778               _last[(*_bucket)[target]] = (*_prev)[target];
   779               new_target = (*_prev)[target];
   780             } else {
   781               (*_prev)[(*_next)[target]] = (*_prev)[target];
   782               new_target = (*_next)[target];
   783             }
   784             if ((*_prev)[target] == INVALID) {
   785               _first[(*_bucket)[target]] = (*_next)[target];
   786             } else {
   787               (*_next)[(*_prev)[target]] = (*_next)[target];
   788             }
   789           } else {
   790             _sets.back().pop_back();
   791             if (_sets.back().empty()) {
   792               _sets.pop_back();
   793               if (_sets.empty())
   794                 break;
   795               for (std::list<int>::iterator it = _sets.back().begin();
   796                    it != _sets.back().end(); ++it) {
   797                 _dormant[*it] = false;
   798               }
   799             }
   800             new_target = _last[_sets.back().back()];
   801           }
   802 
   803           (*_bucket)[target] = 0;
   804 
   805           (*_source_set)[target] = true;
   806           for (InArcIt a(_graph, target); a != INVALID; ++a) {
   807             Value rem = (*_capacity)[a] - (*_flow)[a];
   808             if (!_tolerance.positive(rem)) continue;
   809             Node v = _graph.source(a);
   810             if (!(*_active)[v] && !(*_source_set)[v]) {
   811               activate(v);
   812             }
   813             (*_excess)[v] += rem;
   814             (*_flow)[a] = (*_capacity)[a];
   815           }
   816 
   817           for (OutArcIt a(_graph, target); a != INVALID; ++a) {
   818             Value rem = (*_flow)[a];
   819             if (!_tolerance.positive(rem)) continue;
   820             Node v = _graph.target(a);
   821             if (!(*_active)[v] && !(*_source_set)[v]) {
   822               activate(v);
   823             }
   824             (*_excess)[v] += rem;
   825             (*_flow)[a] = 0;
   826           }
   827 
   828           target = new_target;
   829           if ((*_active)[target]) {
   830             deactivate(target);
   831           }
   832 
   833           _highest = _sets.back().begin();
   834           while (_highest != _sets.back().end() &&
   835                  !(*_active)[_first[*_highest]]) {
   836             ++_highest;
   837           }
   838         }
   839       }
   840     }
   841 
   842   public:
   843 
   844     /// \name Execution Control
   845     /// The simplest way to execute the algorithm is to use
   846     /// one of the member functions called \ref run().
   847     /// \n
   848     /// If you need better control on the execution,
   849     /// you have to call one of the \ref init() functions first, then
   850     /// \ref calculateOut() and/or \ref calculateIn().
   851 
   852     /// @{
   853 
   854     /// \brief Initialize the internal data structures.
   855     ///
   856     /// This function initializes the internal data structures. It creates
   857     /// the maps and some bucket structures for the algorithm.
   858     /// The first node is used as the source node for the push-relabel
   859     /// algorithm.
   860     void init() {
   861       init(NodeIt(_graph));
   862     }
   863 
   864     /// \brief Initialize the internal data structures.
   865     ///
   866     /// This function initializes the internal data structures. It creates
   867     /// the maps and some bucket structures for the algorithm.
   868     /// The given node is used as the source node for the push-relabel
   869     /// algorithm.
   870     void init(const Node& source) {
   871       _source = source;
   872 
   873       _node_num = countNodes(_graph);
   874 
   875       _first.resize(_node_num);
   876       _last.resize(_node_num);
   877 
   878       _dormant.resize(_node_num);
   879 
   880       if (!_flow) {
   881         _flow = new FlowMap(_graph);
   882       }
   883       if (!_next) {
   884         _next = new typename Digraph::template NodeMap<Node>(_graph);
   885       }
   886       if (!_prev) {
   887         _prev = new typename Digraph::template NodeMap<Node>(_graph);
   888       }
   889       if (!_active) {
   890         _active = new typename Digraph::template NodeMap<bool>(_graph);
   891       }
   892       if (!_bucket) {
   893         _bucket = new typename Digraph::template NodeMap<int>(_graph);
   894       }
   895       if (!_excess) {
   896         _excess = new ExcessMap(_graph);
   897       }
   898       if (!_source_set) {
   899         _source_set = new SourceSetMap(_graph);
   900       }
   901       if (!_min_cut_map) {
   902         _min_cut_map = new MinCutMap(_graph);
   903       }
   904 
   905       _min_cut = std::numeric_limits<Value>::max();
   906     }
   907 
   908 
   909     /// \brief Calculate a minimum cut with \f$ source \f$ on the
   910     /// source-side.
   911     ///
   912     /// This function calculates a minimum cut with \f$ source \f$ on the
   913     /// source-side (i.e. a set \f$ X\subsetneq V \f$ with
   914     /// \f$ source \in X \f$ and minimal outgoing capacity).
   915     /// It updates the stored cut if (and only if) the newly found one
   916     /// is better.
   917     ///
   918     /// \pre \ref init() must be called before using this function.
   919     void calculateOut() {
   920       findMinCutOut();
   921     }
   922 
   923     /// \brief Calculate a minimum cut with \f$ source \f$ on the
   924     /// sink-side.
   925     ///
   926     /// This function calculates a minimum cut with \f$ source \f$ on the
   927     /// sink-side (i.e. a set \f$ X\subsetneq V \f$ with
   928     /// \f$ source \notin X \f$ and minimal outgoing capacity).
   929     /// It updates the stored cut if (and only if) the newly found one
   930     /// is better.
   931     ///
   932     /// \pre \ref init() must be called before using this function.
   933     void calculateIn() {
   934       findMinCutIn();
   935     }
   936 
   937 
   938     /// \brief Run the algorithm.
   939     ///
   940     /// This function runs the algorithm. It chooses source node,
   941     /// then calls \ref init(), \ref calculateOut()
   942     /// and \ref calculateIn().
   943     void run() {
   944       init();
   945       calculateOut();
   946       calculateIn();
   947     }
   948 
   949     /// \brief Run the algorithm.
   950     ///
   951     /// This function runs the algorithm. It calls \ref init(),
   952     /// \ref calculateOut() and \ref calculateIn() with the given
   953     /// source node.
   954     void run(const Node& s) {
   955       init(s);
   956       calculateOut();
   957       calculateIn();
   958     }
   959 
   960     /// @}
   961 
   962     /// \name Query Functions
   963     /// The result of the %HaoOrlin algorithm
   964     /// can be obtained using these functions.\n
   965     /// \ref run(), \ref calculateOut() or \ref calculateIn()
   966     /// should be called before using them.
   967 
   968     /// @{
   969 
   970     /// \brief Return the value of the minimum cut.
   971     ///
   972     /// This function returns the value of the best cut found by the
   973     /// previously called \ref run(), \ref calculateOut() or \ref
   974     /// calculateIn().
   975     ///
   976     /// \pre \ref run(), \ref calculateOut() or \ref calculateIn()
   977     /// must be called before using this function.
   978     Value minCutValue() const {
   979       return _min_cut;
   980     }
   981 
   982 
   983     /// \brief Return a minimum cut.
   984     ///
   985     /// This function gives the best cut found by the
   986     /// previously called \ref run(), \ref calculateOut() or \ref
   987     /// calculateIn().
   988     ///
   989     /// It sets \c cutMap to the characteristic vector of the found
   990     /// minimum value cut - a non-empty set \f$ X\subsetneq V \f$
   991     /// of minimum outgoing capacity (i.e. \c cutMap will be \c true exactly
   992     /// for the nodes of \f$ X \f$).
   993     ///
   994     /// \param cutMap A \ref concepts::WriteMap "writable" node map with
   995     /// \c bool (or convertible) value type.
   996     ///
   997     /// \return The value of the minimum cut.
   998     ///
   999     /// \pre \ref run(), \ref calculateOut() or \ref calculateIn()
  1000     /// must be called before using this function.
  1001     template <typename CutMap>
  1002     Value minCutMap(CutMap& cutMap) const {
  1003       for (NodeIt it(_graph); it != INVALID; ++it) {
  1004         cutMap.set(it, (*_min_cut_map)[it]);
  1005       }
  1006       return _min_cut;
  1007     }
  1008 
  1009     /// @}
  1010 
  1011   }; //class HaoOrlin
  1012 
  1013 } //namespace lemon
  1014 
  1015 #endif //LEMON_HAO_ORLIN_H