COIN-OR::LEMON - Graph Library

source: lemon/lemon/hao_orlin.h

Last change on this file was 1270:dceba191c00d, checked in by Alpar Juttner <alpar@…>, 11 years ago

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[425]1/* -*- mode: C++; indent-tabs-mode: nil; -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library.
4 *
[1270]5 * Copyright (C) 2003-2013
[425]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///
[956]34/// Implementation of the Hao-Orlin algorithm for finding a minimum cut
[643]35/// in a digraph.
[425]36
37namespace lemon {
38
39  /// \ingroup min_cut
40  ///
[643]41  /// \brief Hao-Orlin algorithm for finding a minimum cut in a digraph.
[425]42  ///
[643]43  /// This class implements the Hao-Orlin algorithm for finding a minimum
[956]44  /// value cut in a directed graph \f$D=(V,A)\f$.
[643]45  /// It takes a fixed node \f$ source \in V \f$ and
[425]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
[643]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
[425]50  /// with \f$ source \f$ on the sink-side (i.e. a set
[643]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
[425]53  /// minimum cut of \f$ D \f$. The algorithm is a modified
[643]54  /// preflow push-relabel algorithm. Our implementation calculates
[425]55  /// the minimum cut in \f$ O(n^2\sqrt{m}) \f$ time (we use the
[1019]56  /// highest-label rule), or in \f$O(nm)\f$ for unit capacities. A notable
57  /// use of this algorithm is testing network reliability.
[425]58  ///
[643]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,
[956]61  /// which solves the undirected problem in \f$ O(nm + n^2 \log n) \f$
[643]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
[606]69  /// default tolerance type is \ref Tolerance "Tolerance<CAP::Value>".
[425]70#ifdef DOXYGEN
[606]71  template <typename GR, typename CAP, typename TOL>
[425]72#else
[606]73  template <typename GR,
74            typename CAP = typename GR::template ArcMap<int>,
75            typename TOL = Tolerance<typename CAP::Value> >
[425]76#endif
77  class HaoOrlin {
[643]78  public:
[956]79
[643]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
[425]87  private:
88
89    typedef typename CapacityMap::Value Value;
90
[643]91    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
[425]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
[934]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
[425]185  private:
186
187    void activate(const Node& i) {
[628]188      (*_active)[i] = true;
[425]189
190      int bucket = (*_bucket)[i];
191
192      if ((*_prev)[i] == INVALID || (*_active)[(*_prev)[i]]) return;
193      //unlace
[628]194      (*_next)[(*_prev)[i]] = (*_next)[i];
[425]195      if ((*_next)[i] != INVALID) {
[628]196        (*_prev)[(*_next)[i]] = (*_prev)[i];
[425]197      } else {
198        _last[bucket] = (*_prev)[i];
199      }
200      //lace
[628]201      (*_next)[i] = _first[bucket];
202      (*_prev)[_first[bucket]] = i;
203      (*_prev)[i] = INVALID;
[425]204      _first[bucket] = i;
205    }
206
207    void deactivate(const Node& i) {
[628]208      (*_active)[i] = false;
[425]209      int bucket = (*_bucket)[i];
210
211      if ((*_next)[i] == INVALID || !(*_active)[(*_next)[i]]) return;
212
213      //unlace
[628]214      (*_prev)[(*_next)[i]] = (*_prev)[i];
[425]215      if ((*_prev)[i] != INVALID) {
[628]216        (*_next)[(*_prev)[i]] = (*_next)[i];
[425]217      } else {
218        _first[bucket] = (*_next)[i];
219      }
220      //lace
[628]221      (*_prev)[i] = _last[bucket];
222      (*_next)[_last[bucket]] = i;
223      (*_next)[i] = INVALID;
[425]224      _last[bucket] = i;
225    }
226
227    void addItem(const Node& i, int bucket) {
228      (*_bucket)[i] = bucket;
229      if (_last[bucket] != INVALID) {
[628]230        (*_prev)[i] = _last[bucket];
231        (*_next)[_last[bucket]] = i;
232        (*_next)[i] = INVALID;
[425]233        _last[bucket] = i;
234      } else {
[628]235        (*_prev)[i] = INVALID;
[425]236        _first[bucket] = i;
[628]237        (*_next)[i] = INVALID;
[425]238        _last[bucket] = i;
239      }
240    }
241
242    void findMinCutOut() {
243
244      for (NodeIt n(_graph); n != INVALID; ++n) {
[628]245        (*_excess)[n] = 0;
[644]246        (*_source_set)[n] = false;
[425]247      }
248
249      for (ArcIt a(_graph); a != INVALID; ++a) {
[628]250        (*_flow)[a] = 0;
[425]251      }
252
[427]253      int bucket_num = 0;
254      std::vector<Node> queue(_node_num);
255      int qfirst = 0, qlast = 0, qsep = 0;
[425]256
257      {
258        typename Digraph::template NodeMap<bool> reached(_graph, false);
259
[628]260        reached[_source] = true;
[425]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>());
[463]266
[427]267          queue[qlast++] = t;
[628]268          reached[t] = true;
[425]269
[427]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            }
[425]278
[427]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])) {
[628]285                reached[u] = true;
[427]286                queue[qlast++] = u;
[425]287              }
288            }
289          }
290          first_set = false;
291        }
292
[427]293        ++bucket_num;
[628]294        (*_bucket)[_source] = 0;
[425]295        _dormant[0] = true;
296      }
[628]297      (*_source_set)[_source] = true;
[425]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);
[628]304            (*_flow)[a] = (*_capacity)[a];
305            (*_excess)[u] += (*_capacity)[a];
[425]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)) {
[628]346                (*_flow)[a] += excess;
347                (*_excess)[v] += excess;
[425]348                excess = 0;
349                goto no_more_push;
350              } else {
351                excess -= rem;
[628]352                (*_excess)[v] += rem;
353                (*_flow)[a] = (*_capacity)[a];
[425]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)) {
[628]370                (*_flow)[a] -= excess;
371                (*_excess)[v] += excess;
[425]372                excess = 0;
373                goto no_more_push;
374              } else {
375                excess -= rem;
[628]376                (*_excess)[v] += rem;
377                (*_flow)[a] = 0;
[425]378              }
379            } else if (next_bucket > (*_bucket)[v]) {
380              next_bucket = (*_bucket)[v];
381            }
382          }
383
384        no_more_push:
385
[628]386          (*_excess)[n] = excess;
[425]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];
[628]404              (*_prev)[(*_next)[n]] = INVALID;
[425]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);
[628]410              (*_bucket)[n] = bucket_num;
[425]411              _first[bucket_num] = _last[bucket_num] = n;
[628]412              (*_next)[n] = INVALID;
413              (*_prev)[n] = INVALID;
[425]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];
[628]423              (*_prev)[(*_next)[n]] = INVALID;
[425]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
[628]437              (*_bucket)[n] = *_highest;
438              (*_next)[n] = _first[*_highest];
[425]439              if (_first[*_highest] != INVALID) {
[628]440                (*_prev)[_first[*_highest]] = n;
[425]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) {
[628]462            (*_min_cut_map)[i] = true;
[425]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) {
[628]468              (*_min_cut_map)[n] = false;
[425]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 {
[628]481              (*_prev)[(*_next)[target]] = (*_prev)[target];
[425]482              new_target = (*_next)[target];
483            }
484            if ((*_prev)[target] == INVALID) {
485              _first[(*_bucket)[target]] = (*_next)[target];
486            } else {
[628]487              (*_next)[(*_prev)[target]] = (*_next)[target];
[425]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
[628]503          (*_bucket)[target] = 0;
[425]504
[628]505          (*_source_set)[target] = true;
[425]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            }
[628]513            (*_excess)[v] += rem;
514            (*_flow)[a] = (*_capacity)[a];
[425]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            }
[628]524            (*_excess)[v] += rem;
525            (*_flow)[a] = 0;
[425]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) {
[628]545        (*_excess)[n] = 0;
[644]546        (*_source_set)[n] = false;
[425]547      }
548
549      for (ArcIt a(_graph); a != INVALID; ++a) {
[628]550        (*_flow)[a] = 0;
[425]551      }
552
[427]553      int bucket_num = 0;
554      std::vector<Node> queue(_node_num);
555      int qfirst = 0, qlast = 0, qsep = 0;
[425]556
557      {
558        typename Digraph::template NodeMap<bool> reached(_graph, false);
559
[628]560        reached[_source] = true;
[425]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>());
[463]567
[427]568          queue[qlast++] = t;
[628]569          reached[t] = true;
[425]570
[427]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            }
[425]579
[427]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])) {
[628]586                reached[u] = true;
[427]587                queue[qlast++] = u;
[425]588              }
589            }
590          }
591          first_set = false;
592        }
593
[427]594        ++bucket_num;
[628]595        (*_bucket)[_source] = 0;
[425]596        _dormant[0] = true;
597      }
[628]598      (*_source_set)[_source] = true;
[425]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);
[628]605            (*_flow)[a] = (*_capacity)[a];
606            (*_excess)[u] += (*_capacity)[a];
[425]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)) {
[628]647                (*_flow)[a] += excess;
648                (*_excess)[v] += excess;
[425]649                excess = 0;
650                goto no_more_push;
651              } else {
652                excess -= rem;
[628]653                (*_excess)[v] += rem;
654                (*_flow)[a] = (*_capacity)[a];
[425]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)) {
[628]671                (*_flow)[a] -= excess;
672                (*_excess)[v] += excess;
[425]673                excess = 0;
674                goto no_more_push;
675              } else {
676                excess -= rem;
[628]677                (*_excess)[v] += rem;
678                (*_flow)[a] = 0;
[425]679              }
680            } else if (next_bucket > (*_bucket)[v]) {
681              next_bucket = (*_bucket)[v];
682            }
683          }
684
685        no_more_push:
686
[628]687          (*_excess)[n] = excess;
[425]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];
[628]705              (*_prev)[(*_next)[n]] = INVALID;
[425]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);
[628]711              (*_bucket)[n] = bucket_num;
[425]712              _first[bucket_num] = _last[bucket_num] = n;
[628]713              (*_next)[n] = INVALID;
714              (*_prev)[n] = INVALID;
[425]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];
[628]724              (*_prev)[(*_next)[n]] = INVALID;
[425]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
[628]737              (*_bucket)[n] = *_highest;
738              (*_next)[n] = _first[*_highest];
[425]739              if (_first[*_highest] != INVALID) {
[628]740                (*_prev)[_first[*_highest]] = n;
[425]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) {
[628]762            (*_min_cut_map)[i] = false;
[425]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) {
[628]768              (*_min_cut_map)[n] = true;
[425]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 {
[628]781              (*_prev)[(*_next)[target]] = (*_prev)[target];
[425]782              new_target = (*_next)[target];
783            }
784            if ((*_prev)[target] == INVALID) {
785              _first[(*_bucket)[target]] = (*_next)[target];
786            } else {
[628]787              (*_next)[(*_prev)[target]] = (*_next)[target];
[425]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
[628]803          (*_bucket)[target] = 0;
[425]804
[628]805          (*_source_set)[target] = true;
[425]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            }
[628]813            (*_excess)[v] += rem;
814            (*_flow)[a] = (*_capacity)[a];
[425]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            }
[628]824            (*_excess)[v] += rem;
825            (*_flow)[a] = 0;
[425]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
[643]844    /// \name Execution Control
[425]845    /// The simplest way to execute the algorithm is to use
[606]846    /// one of the member functions called \ref run().
[425]847    /// \n
[643]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().
[425]851
852    /// @{
853
[643]854    /// \brief Initialize the internal data structures.
[425]855    ///
[643]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.
[425]860    void init() {
861      init(NodeIt(_graph));
862    }
863
[643]864    /// \brief Initialize the internal data structures.
[425]865    ///
[643]866    /// This function initializes the internal data structures. It creates
[956]867    /// the maps and some bucket structures for the algorithm.
[643]868    /// The given node is used as the source node for the push-relabel
869    /// algorithm.
[425]870    void init(const Node& source) {
871      _source = source;
872
873      _node_num = countNodes(_graph);
874
[427]875      _first.resize(_node_num);
876      _last.resize(_node_num);
[425]877
[427]878      _dormant.resize(_node_num);
[425]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
[643]909    /// \brief Calculate a minimum cut with \f$ source \f$ on the
[425]910    /// source-side.
911    ///
[643]912    /// This function calculates a minimum cut with \f$ source \f$ on the
[428]913    /// source-side (i.e. a set \f$ X\subsetneq V \f$ with
[643]914    /// \f$ source \in X \f$ and minimal outgoing capacity).
[1019]915    /// It updates the stored cut if (and only if) the newly found one
916    /// is better.
[643]917    ///
918    /// \pre \ref init() must be called before using this function.
[425]919    void calculateOut() {
920      findMinCutOut();
921    }
922
[643]923    /// \brief Calculate a minimum cut with \f$ source \f$ on the
924    /// sink-side.
[425]925    ///
[643]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).
[1019]929    /// It updates the stored cut if (and only if) the newly found one
930    /// is better.
[643]931    ///
932    /// \pre \ref init() must be called before using this function.
[425]933    void calculateIn() {
934      findMinCutIn();
935    }
936
937
[643]938    /// \brief Run the algorithm.
[425]939    ///
[1019]940    /// This function runs the algorithm. It chooses source node,
941    /// then calls \ref init(), \ref calculateOut()
[425]942    /// and \ref calculateIn().
943    void run() {
944      init();
945      calculateOut();
946      calculateIn();
947    }
948
[643]949    /// \brief Run the algorithm.
[425]950    ///
[1019]951    /// This function runs the algorithm. It calls \ref init(),
952    /// \ref calculateOut() and \ref calculateIn() with the given
953    /// source node.
[425]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
[643]964    /// can be obtained using these functions.\n
[956]965    /// \ref run(), \ref calculateOut() or \ref calculateIn()
[643]966    /// should be called before using them.
[425]967
968    /// @{
969
[643]970    /// \brief Return the value of the minimum cut.
[425]971    ///
[1019]972    /// This function returns the value of the best cut found by the
973    /// previously called \ref run(), \ref calculateOut() or \ref
974    /// calculateIn().
[643]975    ///
[956]976    /// \pre \ref run(), \ref calculateOut() or \ref calculateIn()
[643]977    /// must be called before using this function.
[425]978    Value minCutValue() const {
979      return _min_cut;
980    }
981
982
[643]983    /// \brief Return a minimum cut.
[425]984    ///
[1019]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
[643]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    ///
[956]999    /// \pre \ref run(), \ref calculateOut() or \ref calculateIn()
[643]1000    /// must be called before using this function.
1001    template <typename CutMap>
1002    Value minCutMap(CutMap& cutMap) const {
[425]1003      for (NodeIt it(_graph); it != INVALID; ++it) {
[643]1004        cutMap.set(it, (*_min_cut_map)[it]);
[425]1005      }
1006      return _min_cut;
1007    }
1008
1009    /// @}
1010
1011  }; //class HaoOrlin
1012
1013} //namespace lemon
1014
1015#endif //LEMON_HAO_ORLIN_H
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