source: lemon-main/lemon/hao_orlin.h @ 409:b8ce15103485

/* -*- mode: C++; indent-tabs-mode: nil; -*-
 *
 * This file is a part of LEMON, a generic C++ optimization library.
 *
 * Copyright (C) 2003-2008
 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
 * (Egervary Research Group on Combinatorial Optimization, EGRES).
 *
 * Permission to use, modify and distribute this software is granted
 * provided that this copyright notice appears in all copies. For
 * precise terms see the accompanying LICENSE file.
 *
 * This software is provided "AS IS" with no warranty of any kind,
 * express or implied, and with no claim as to its suitability for any
 * purpose.
 *
 */

#ifndef LEMON_HAO_ORLIN_H
#define LEMON_HAO_ORLIN_H

#include <vector>
#include <list>
#include <limits>

#include <lemon/maps.h>
#include <lemon/core.h>
#include <lemon/tolerance.h>

/// \file
/// \ingroup min_cut
/// \brief Implementation of the Hao-Orlin algorithm.
///
/// Implementation of the Hao-Orlin algorithm class for testing network
/// reliability.

namespace lemon {

  /// \ingroup min_cut
  ///
  /// \brief %Hao-Orlin algorithm to find a minimum cut in directed graphs.
  ///
  /// Hao-Orlin calculates a minimum cut in a directed graph
  /// \f$D=(V,A)\f$. It takes a fixed node \f$ source \in V \f$ and
  /// consists of two phases: in the first phase it determines a
  /// minimum cut with \f$ source \f$ on the source-side (i.e. a set
  /// \f$ X\subsetneq V \f$ with \f$ source \in X \f$ and minimal
  /// out-degree) and in the second phase it determines a minimum cut
  /// with \f$ source \f$ on the sink-side (i.e. a set
  /// \f$ X\subsetneq V \f$ with \f$ source \notin X \f$ and minimal
  /// out-degree). Obviously, the smaller of these two cuts will be a
  /// minimum cut of \f$ D \f$. The algorithm is a modified
  /// push-relabel preflow algorithm and our implementation calculates
  /// the minimum cut in \f$ O(n^2\sqrt{m}) \f$ time (we use the
  /// highest-label rule), or in \f$O(nm)\f$ for unit capacities. The
  /// purpose of such algorithm is testing network reliability. For an
  /// undirected graph you can run just the first phase of the
  /// algorithm or you can use the algorithm of Nagamochi and Ibaraki
  /// which solves the undirected problem in
  /// \f$ O(nm + n^2 \log(n)) \f$ time: it is implemented in the
  /// NagamochiIbaraki algorithm class.
  ///
  /// \param _Digraph is the graph type of the algorithm.
  /// \param _CapacityMap is an edge map of capacities which should
  /// be any numreric type. The default type is _Digraph::ArcMap<int>.
  /// \param _Tolerance is the handler of the inexact computation. The
  /// default type for this is Tolerance<CapacityMap::Value>.
#ifdef DOXYGEN
  template <typename _Digraph, typename _CapacityMap, typename _Tolerance>
#else
  template <typename _Digraph,
            typename _CapacityMap = typename _Digraph::template ArcMap<int>,
            typename _Tolerance = Tolerance<typename _CapacityMap::Value> >
#endif
  class HaoOrlin {
  private:

    typedef _Digraph Digraph;
    typedef _CapacityMap CapacityMap;
    typedef _Tolerance Tolerance;

    typedef typename CapacityMap::Value Value;

    TEMPLATE_GRAPH_TYPEDEFS(Digraph);

    const Digraph& _graph;
    const CapacityMap* _capacity;

    typedef typename Digraph::template ArcMap<Value> FlowMap;
    FlowMap* _flow;

    Node _source;

    int _node_num;

    // Bucketing structure
    std::vector<Node> _first, _last;
    typename Digraph::template NodeMap<Node>* _next;
    typename Digraph::template NodeMap<Node>* _prev;
    typename Digraph::template NodeMap<bool>* _active;
    typename Digraph::template NodeMap<int>* _bucket;

    std::vector<bool> _dormant;

    std::list<std::list<int> > _sets;
    std::list<int>::iterator _highest;

    typedef typename Digraph::template NodeMap<Value> ExcessMap;
    ExcessMap* _excess;

    typedef typename Digraph::template NodeMap<bool> SourceSetMap;
    SourceSetMap* _source_set;

    Value _min_cut;

    typedef typename Digraph::template NodeMap<bool> MinCutMap;
    MinCutMap* _min_cut_map;

    Tolerance _tolerance;

  public:

    /// \brief Constructor
    ///
    /// Constructor of the algorithm class.
    HaoOrlin(const Digraph& graph, const CapacityMap& capacity,
             const Tolerance& tolerance = Tolerance()) :
      _graph(graph), _capacity(&capacity), _flow(0), _source(),
      _node_num(), _first(), _last(), _next(0), _prev(0),
      _active(0), _bucket(0), _dormant(), _sets(), _highest(),
      _excess(0), _source_set(0), _min_cut(), _min_cut_map(0),
      _tolerance(tolerance) {}

    ~HaoOrlin() {
      if (_min_cut_map) {
        delete _min_cut_map;
      }
      if (_source_set) {
        delete _source_set;
      }
      if (_excess) {
        delete _excess;
      }
      if (_next) {
        delete _next;
      }
      if (_prev) {
        delete _prev;
      }
      if (_active) {
        delete _active;
      }
      if (_bucket) {
        delete _bucket;
      }
      if (_flow) {
        delete _flow;
      }
    }

  private:

    void activate(const Node& i) {
      _active->set(i, true);

      int bucket = (*_bucket)[i];

      if ((*_prev)[i] == INVALID || (*_active)[(*_prev)[i]]) return;
      //unlace
      _next->set((*_prev)[i], (*_next)[i]);
      if ((*_next)[i] != INVALID) {
        _prev->set((*_next)[i], (*_prev)[i]);
      } else {
        _last[bucket] = (*_prev)[i];
      }
      //lace
      _next->set(i, _first[bucket]);
      _prev->set(_first[bucket], i);
      _prev->set(i, INVALID);
      _first[bucket] = i;
    }

    void deactivate(const Node& i) {
      _active->set(i, false);
      int bucket = (*_bucket)[i];

      if ((*_next)[i] == INVALID || !(*_active)[(*_next)[i]]) return;

      //unlace
      _prev->set((*_next)[i], (*_prev)[i]);
      if ((*_prev)[i] != INVALID) {
        _next->set((*_prev)[i], (*_next)[i]);
      } else {
        _first[bucket] = (*_next)[i];
      }
      //lace
      _prev->set(i, _last[bucket]);
      _next->set(_last[bucket], i);
      _next->set(i, INVALID);
      _last[bucket] = i;
    }

    void addItem(const Node& i, int bucket) {
      (*_bucket)[i] = bucket;
      if (_last[bucket] != INVALID) {
        _prev->set(i, _last[bucket]);
        _next->set(_last[bucket], i);
        _next->set(i, INVALID);
        _last[bucket] = i;
      } else {
        _prev->set(i, INVALID);
        _first[bucket] = i;
        _next->set(i, INVALID);
        _last[bucket] = i;
      }
    }

    void findMinCutOut() {

      for (NodeIt n(_graph); n != INVALID; ++n) {
        _excess->set(n, 0);
      }

      for (ArcIt a(_graph); a != INVALID; ++a) {
        _flow->set(a, 0);
      }

      int bucket_num = 1;

      {
        typename Digraph::template NodeMap<bool> reached(_graph, false);

        reached.set(_source, true);

        bool first_set = true;

        for (NodeIt t(_graph); t != INVALID; ++t) {
          if (reached[t]) continue;
          _sets.push_front(std::list<int>());
          _sets.front().push_front(bucket_num);
          _dormant[bucket_num] = !first_set;

          _bucket->set(t, bucket_num);
          _first[bucket_num] = _last[bucket_num] = t;
          _next->set(t, INVALID);
          _prev->set(t, INVALID);

          ++bucket_num;

          std::vector<Node> queue;
          queue.push_back(t);
          reached.set(t, true);

          while (!queue.empty()) {
            _sets.front().push_front(bucket_num);
            _dormant[bucket_num] = !first_set;
            _first[bucket_num] = _last[bucket_num] = INVALID;

            std::vector<Node> nqueue;
            for (int i = 0; i < int(queue.size()); ++i) {
              Node n = queue[i];
              for (InArcIt a(_graph, n); a != INVALID; ++a) {
                Node u = _graph.source(a);
                if (!reached[u] && _tolerance.positive((*_capacity)[a])) {
                  reached.set(u, true);
                  addItem(u, bucket_num);
                  nqueue.push_back(u);
                }
              }
            }
            queue.swap(nqueue);
            ++bucket_num;
          }
          _sets.front().pop_front();
          --bucket_num;
          first_set = false;
        }

        _bucket->set(_source, 0);
        _dormant[0] = true;
      }
      _source_set->set(_source, true);

      Node target = _last[_sets.back().back()];
      {
        for (OutArcIt a(_graph, _source); a != INVALID; ++a) {
          if (_tolerance.positive((*_capacity)[a])) {
            Node u = _graph.target(a);
            _flow->set(a, (*_capacity)[a]);
            _excess->set(u, (*_excess)[u] + (*_capacity)[a]);
            if (!(*_active)[u] && u != _source) {
              activate(u);
            }
          }
        }

        if ((*_active)[target]) {
          deactivate(target);
        }

        _highest = _sets.back().begin();
        while (_highest != _sets.back().end() &&
               !(*_active)[_first[*_highest]]) {
          ++_highest;
        }
      }

      while (true) {
        while (_highest != _sets.back().end()) {
          Node n = _first[*_highest];
          Value excess = (*_excess)[n];
          int next_bucket = _node_num;

          int under_bucket;
          if (++std::list<int>::iterator(_highest) == _sets.back().end()) {
            under_bucket = -1;
          } else {
            under_bucket = *(++std::list<int>::iterator(_highest));
          }

          for (OutArcIt a(_graph, n); a != INVALID; ++a) {
            Node v = _graph.target(a);
            if (_dormant[(*_bucket)[v]]) continue;
            Value rem = (*_capacity)[a] - (*_flow)[a];
            if (!_tolerance.positive(rem)) continue;
            if ((*_bucket)[v] == under_bucket) {
              if (!(*_active)[v] && v != target) {
                activate(v);
              }
              if (!_tolerance.less(rem, excess)) {
                _flow->set(a, (*_flow)[a] + excess);
                _excess->set(v, (*_excess)[v] + excess);
                excess = 0;
                goto no_more_push;
              } else {
                excess -= rem;
                _excess->set(v, (*_excess)[v] + rem);
                _flow->set(a, (*_capacity)[a]);
              }
            } else if (next_bucket > (*_bucket)[v]) {
              next_bucket = (*_bucket)[v];
            }
          }

          for (InArcIt a(_graph, n); a != INVALID; ++a) {
            Node v = _graph.source(a);
            if (_dormant[(*_bucket)[v]]) continue;
            Value rem = (*_flow)[a];
            if (!_tolerance.positive(rem)) continue;
            if ((*_bucket)[v] == under_bucket) {
              if (!(*_active)[v] && v != target) {
                activate(v);
              }
              if (!_tolerance.less(rem, excess)) {
                _flow->set(a, (*_flow)[a] - excess);
                _excess->set(v, (*_excess)[v] + excess);
                excess = 0;
                goto no_more_push;
              } else {
                excess -= rem;
                _excess->set(v, (*_excess)[v] + rem);
                _flow->set(a, 0);
              }
            } else if (next_bucket > (*_bucket)[v]) {
              next_bucket = (*_bucket)[v];
            }
          }

        no_more_push:

          _excess->set(n, excess);

          if (excess != 0) {
            if ((*_next)[n] == INVALID) {
              typename std::list<std::list<int> >::iterator new_set =
                _sets.insert(--_sets.end(), std::list<int>());
              new_set->splice(new_set->end(), _sets.back(),
                              _sets.back().begin(), ++_highest);
              for (std::list<int>::iterator it = new_set->begin();
                   it != new_set->end(); ++it) {
                _dormant[*it] = true;
              }
              while (_highest != _sets.back().end() &&
                     !(*_active)[_first[*_highest]]) {
                ++_highest;
              }
            } else if (next_bucket == _node_num) {
              _first[(*_bucket)[n]] = (*_next)[n];
              _prev->set((*_next)[n], INVALID);

              std::list<std::list<int> >::iterator new_set =
                _sets.insert(--_sets.end(), std::list<int>());

              new_set->push_front(bucket_num);
              _bucket->set(n, bucket_num);
              _first[bucket_num] = _last[bucket_num] = n;
              _next->set(n, INVALID);
              _prev->set(n, INVALID);
              _dormant[bucket_num] = true;
              ++bucket_num;

              while (_highest != _sets.back().end() &&
                     !(*_active)[_first[*_highest]]) {
                ++_highest;
              }
            } else {
              _first[*_highest] = (*_next)[n];
              _prev->set((*_next)[n], INVALID);

              while (next_bucket != *_highest) {
                --_highest;
              }

              if (_highest == _sets.back().begin()) {
                _sets.back().push_front(bucket_num);
                _dormant[bucket_num] = false;
                _first[bucket_num] = _last[bucket_num] = INVALID;
                ++bucket_num;
              }
              --_highest;

              _bucket->set(n, *_highest);
              _next->set(n, _first[*_highest]);
              if (_first[*_highest] != INVALID) {
                _prev->set(_first[*_highest], n);
              } else {
                _last[*_highest] = n;
              }
              _first[*_highest] = n;
            }
          } else {

            deactivate(n);
            if (!(*_active)[_first[*_highest]]) {
              ++_highest;
              if (_highest != _sets.back().end() &&
                  !(*_active)[_first[*_highest]]) {
                _highest = _sets.back().end();
              }
            }
          }
        }

        if ((*_excess)[target] < _min_cut) {
          _min_cut = (*_excess)[target];
          for (NodeIt i(_graph); i != INVALID; ++i) {
            _min_cut_map->set(i, true);
          }
          for (std::list<int>::iterator it = _sets.back().begin();
               it != _sets.back().end(); ++it) {
            Node n = _first[*it];
            while (n != INVALID) {
              _min_cut_map->set(n, false);
              n = (*_next)[n];
            }
          }
        }

        {
          Node new_target;
          if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) {
            if ((*_next)[target] == INVALID) {
              _last[(*_bucket)[target]] = (*_prev)[target];
              new_target = (*_prev)[target];
            } else {
              _prev->set((*_next)[target], (*_prev)[target]);
              new_target = (*_next)[target];
            }
            if ((*_prev)[target] == INVALID) {
              _first[(*_bucket)[target]] = (*_next)[target];
            } else {
              _next->set((*_prev)[target], (*_next)[target]);
            }
          } else {
            _sets.back().pop_back();
            if (_sets.back().empty()) {
              _sets.pop_back();
              if (_sets.empty())
                break;
              for (std::list<int>::iterator it = _sets.back().begin();
                   it != _sets.back().end(); ++it) {
                _dormant[*it] = false;
              }
            }
            new_target = _last[_sets.back().back()];
          }

          _bucket->set(target, 0);

          _source_set->set(target, true);
          for (OutArcIt a(_graph, target); a != INVALID; ++a) {
            Value rem = (*_capacity)[a] - (*_flow)[a];
            if (!_tolerance.positive(rem)) continue;
            Node v = _graph.target(a);
            if (!(*_active)[v] && !(*_source_set)[v]) {
              activate(v);
            }
            _excess->set(v, (*_excess)[v] + rem);
            _flow->set(a, (*_capacity)[a]);
          }

          for (InArcIt a(_graph, target); a != INVALID; ++a) {
            Value rem = (*_flow)[a];
            if (!_tolerance.positive(rem)) continue;
            Node v = _graph.source(a);
            if (!(*_active)[v] && !(*_source_set)[v]) {
              activate(v);
            }
            _excess->set(v, (*_excess)[v] + rem);
            _flow->set(a, 0);
          }

          target = new_target;
          if ((*_active)[target]) {
            deactivate(target);
          }

          _highest = _sets.back().begin();
          while (_highest != _sets.back().end() &&
                 !(*_active)[_first[*_highest]]) {
            ++_highest;
          }
        }
      }
    }

    void findMinCutIn() {

      for (NodeIt n(_graph); n != INVALID; ++n) {
        _excess->set(n, 0);
      }

      for (ArcIt a(_graph); a != INVALID; ++a) {
        _flow->set(a, 0);
      }

      int bucket_num = 1;

      {
        typename Digraph::template NodeMap<bool> reached(_graph, false);

        reached.set(_source, true);

        bool first_set = true;

        for (NodeIt t(_graph); t != INVALID; ++t) {
          if (reached[t]) continue;
          _sets.push_front(std::list<int>());
          _sets.front().push_front(bucket_num);
          _dormant[bucket_num] = !first_set;

          _bucket->set(t, bucket_num);
          _first[bucket_num] = _last[bucket_num] = t;
          _next->set(t, INVALID);
          _prev->set(t, INVALID);

          ++bucket_num;

          std::vector<Node> queue;
          queue.push_back(t);
          reached.set(t, true);

          while (!queue.empty()) {
            _sets.front().push_front(bucket_num);
            _dormant[bucket_num] = !first_set;
            _first[bucket_num] = _last[bucket_num] = INVALID;

            std::vector<Node> nqueue;
            for (int i = 0; i < int(queue.size()); ++i) {
              Node n = queue[i];
              for (OutArcIt a(_graph, n); a != INVALID; ++a) {
                Node u = _graph.target(a);
                if (!reached[u] && _tolerance.positive((*_capacity)[a])) {
                  reached.set(u, true);
                  addItem(u, bucket_num);
                  nqueue.push_back(u);
                }
              }
            }
            queue.swap(nqueue);
            ++bucket_num;
          }
          _sets.front().pop_front();
          --bucket_num;
          first_set = false;
        }

        _bucket->set(_source, 0);
        _dormant[0] = true;
      }
      _source_set->set(_source, true);

      Node target = _last[_sets.back().back()];
      {
        for (InArcIt a(_graph, _source); a != INVALID; ++a) {
          if (_tolerance.positive((*_capacity)[a])) {
            Node u = _graph.source(a);
            _flow->set(a, (*_capacity)[a]);
            _excess->set(u, (*_excess)[u] + (*_capacity)[a]);
            if (!(*_active)[u] && u != _source) {
              activate(u);
            }
          }
        }
        if ((*_active)[target]) {
          deactivate(target);
        }

        _highest = _sets.back().begin();
        while (_highest != _sets.back().end() &&
               !(*_active)[_first[*_highest]]) {
          ++_highest;
        }
      }


      while (true) {
        while (_highest != _sets.back().end()) {
          Node n = _first[*_highest];
          Value excess = (*_excess)[n];
          int next_bucket = _node_num;

          int under_bucket;
          if (++std::list<int>::iterator(_highest) == _sets.back().end()) {
            under_bucket = -1;
          } else {
            under_bucket = *(++std::list<int>::iterator(_highest));
          }

          for (InArcIt a(_graph, n); a != INVALID; ++a) {
            Node v = _graph.source(a);
            if (_dormant[(*_bucket)[v]]) continue;
            Value rem = (*_capacity)[a] - (*_flow)[a];
            if (!_tolerance.positive(rem)) continue;
            if ((*_bucket)[v] == under_bucket) {
              if (!(*_active)[v] && v != target) {
                activate(v);
              }
              if (!_tolerance.less(rem, excess)) {
                _flow->set(a, (*_flow)[a] + excess);
                _excess->set(v, (*_excess)[v] + excess);
                excess = 0;
                goto no_more_push;
              } else {
                excess -= rem;
                _excess->set(v, (*_excess)[v] + rem);
                _flow->set(a, (*_capacity)[a]);
              }
            } else if (next_bucket > (*_bucket)[v]) {
              next_bucket = (*_bucket)[v];
            }
          }

          for (OutArcIt a(_graph, n); a != INVALID; ++a) {
            Node v = _graph.target(a);
            if (_dormant[(*_bucket)[v]]) continue;
            Value rem = (*_flow)[a];
            if (!_tolerance.positive(rem)) continue;
            if ((*_bucket)[v] == under_bucket) {
              if (!(*_active)[v] && v != target) {
                activate(v);
              }
              if (!_tolerance.less(rem, excess)) {
                _flow->set(a, (*_flow)[a] - excess);
                _excess->set(v, (*_excess)[v] + excess);
                excess = 0;
                goto no_more_push;
              } else {
                excess -= rem;
                _excess->set(v, (*_excess)[v] + rem);
                _flow->set(a, 0);
              }
            } else if (next_bucket > (*_bucket)[v]) {
              next_bucket = (*_bucket)[v];
            }
          }

        no_more_push:

          _excess->set(n, excess);

          if (excess != 0) {
            if ((*_next)[n] == INVALID) {
              typename std::list<std::list<int> >::iterator new_set =
                _sets.insert(--_sets.end(), std::list<int>());
              new_set->splice(new_set->end(), _sets.back(),
                              _sets.back().begin(), ++_highest);
              for (std::list<int>::iterator it = new_set->begin();
                   it != new_set->end(); ++it) {
                _dormant[*it] = true;
              }
              while (_highest != _sets.back().end() &&
                     !(*_active)[_first[*_highest]]) {
                ++_highest;
              }
            } else if (next_bucket == _node_num) {
              _first[(*_bucket)[n]] = (*_next)[n];
              _prev->set((*_next)[n], INVALID);

              std::list<std::list<int> >::iterator new_set =
                _sets.insert(--_sets.end(), std::list<int>());

              new_set->push_front(bucket_num);
              _bucket->set(n, bucket_num);
              _first[bucket_num] = _last[bucket_num] = n;
              _next->set(n, INVALID);
              _prev->set(n, INVALID);
              _dormant[bucket_num] = true;
              ++bucket_num;

              while (_highest != _sets.back().end() &&
                     !(*_active)[_first[*_highest]]) {
                ++_highest;
              }
            } else {
              _first[*_highest] = (*_next)[n];
              _prev->set((*_next)[n], INVALID);

              while (next_bucket != *_highest) {
                --_highest;
              }
              if (_highest == _sets.back().begin()) {
                _sets.back().push_front(bucket_num);
                _dormant[bucket_num] = false;
                _first[bucket_num] = _last[bucket_num] = INVALID;
                ++bucket_num;
              }
              --_highest;

              _bucket->set(n, *_highest);
              _next->set(n, _first[*_highest]);
              if (_first[*_highest] != INVALID) {
                _prev->set(_first[*_highest], n);
              } else {
                _last[*_highest] = n;
              }
              _first[*_highest] = n;
            }
          } else {

            deactivate(n);
            if (!(*_active)[_first[*_highest]]) {
              ++_highest;
              if (_highest != _sets.back().end() &&
                  !(*_active)[_first[*_highest]]) {
                _highest = _sets.back().end();
              }
            }
          }
        }

        if ((*_excess)[target] < _min_cut) {
          _min_cut = (*_excess)[target];
          for (NodeIt i(_graph); i != INVALID; ++i) {
            _min_cut_map->set(i, false);
          }
          for (std::list<int>::iterator it = _sets.back().begin();
               it != _sets.back().end(); ++it) {
            Node n = _first[*it];
            while (n != INVALID) {
              _min_cut_map->set(n, true);
              n = (*_next)[n];
            }
          }
        }

        {
          Node new_target;
          if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) {
            if ((*_next)[target] == INVALID) {
              _last[(*_bucket)[target]] = (*_prev)[target];
              new_target = (*_prev)[target];
            } else {
              _prev->set((*_next)[target], (*_prev)[target]);
              new_target = (*_next)[target];
            }
            if ((*_prev)[target] == INVALID) {
              _first[(*_bucket)[target]] = (*_next)[target];
            } else {
              _next->set((*_prev)[target], (*_next)[target]);
            }
          } else {
            _sets.back().pop_back();
            if (_sets.back().empty()) {
              _sets.pop_back();
              if (_sets.empty())
                break;
              for (std::list<int>::iterator it = _sets.back().begin();
                   it != _sets.back().end(); ++it) {
                _dormant[*it] = false;
              }
            }
            new_target = _last[_sets.back().back()];
          }

          _bucket->set(target, 0);

          _source_set->set(target, true);
          for (InArcIt a(_graph, target); a != INVALID; ++a) {
            Value rem = (*_capacity)[a] - (*_flow)[a];
            if (!_tolerance.positive(rem)) continue;
            Node v = _graph.source(a);
            if (!(*_active)[v] && !(*_source_set)[v]) {
              activate(v);
            }
            _excess->set(v, (*_excess)[v] + rem);
            _flow->set(a, (*_capacity)[a]);
          }

          for (OutArcIt a(_graph, target); a != INVALID; ++a) {
            Value rem = (*_flow)[a];
            if (!_tolerance.positive(rem)) continue;
            Node v = _graph.target(a);
            if (!(*_active)[v] && !(*_source_set)[v]) {
              activate(v);
            }
            _excess->set(v, (*_excess)[v] + rem);
            _flow->set(a, 0);
          }

          target = new_target;
          if ((*_active)[target]) {
            deactivate(target);
          }

          _highest = _sets.back().begin();
          while (_highest != _sets.back().end() &&
                 !(*_active)[_first[*_highest]]) {
            ++_highest;
          }
        }
      }
    }

  public:

    /// \name Execution control
    /// The simplest way to execute the algorithm is to use
    /// one of the member functions called \c run(...).
    /// \n
    /// If you need more control on the execution,
    /// first you must call \ref init(), then the \ref calculateIn() or
    /// \ref calculateIn() functions.

    /// @{

    /// \brief Initializes the internal data structures.
    ///
    /// Initializes the internal data structures. It creates
    /// the maps, residual graph adaptors and some bucket structures
    /// for the algorithm.
    void init() {
      init(NodeIt(_graph));
    }

    /// \brief Initializes the internal data structures.
    ///
    /// Initializes the internal data structures. It creates
    /// the maps, residual graph adaptor and some bucket structures
    /// for the algorithm. Node \c source  is used as the push-relabel
    /// algorithm's source.
    void init(const Node& source) {
      _source = source;

      _node_num = countNodes(_graph);

      _first.resize(_node_num + 1);
      _last.resize(_node_num + 1);

      _dormant.resize(_node_num + 1);

      if (!_flow) {
        _flow = new FlowMap(_graph);
      }
      if (!_next) {
        _next = new typename Digraph::template NodeMap<Node>(_graph);
      }
      if (!_prev) {
        _prev = new typename Digraph::template NodeMap<Node>(_graph);
      }
      if (!_active) {
        _active = new typename Digraph::template NodeMap<bool>(_graph);
      }
      if (!_bucket) {
        _bucket = new typename Digraph::template NodeMap<int>(_graph);
      }
      if (!_excess) {
        _excess = new ExcessMap(_graph);
      }
      if (!_source_set) {
        _source_set = new SourceSetMap(_graph);
      }
      if (!_min_cut_map) {
        _min_cut_map = new MinCutMap(_graph);
      }

      _min_cut = std::numeric_limits<Value>::max();
    }


    /// \brief Calculates a minimum cut with \f$ source \f$ on the
    /// source-side.
    ///
    /// Calculates a minimum cut with \f$ source \f$ on the
    /// source-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source
    /// \in X \f$ and minimal out-degree).
    void calculateOut() {
      findMinCutOut();
    }

    /// \brief Calculates a minimum cut with \f$ source \f$ on the
    /// target-side.
    ///
    /// Calculates a minimum cut with \f$ source \f$ on the
    /// target-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source
    /// \in X \f$ and minimal out-degree).
    void calculateIn() {
      findMinCutIn();
    }


    /// \brief Runs the algorithm.
    ///
    /// Runs the algorithm. It finds nodes \c source and \c target
    /// arbitrarily and then calls \ref init(), \ref calculateOut()
    /// and \ref calculateIn().
    void run() {
      init();
      calculateOut();
      calculateIn();
    }

    /// \brief Runs the algorithm.
    ///
    /// Runs the algorithm. It uses the given \c source node, finds a
    /// proper \c target and then calls the \ref init(), \ref
    /// calculateOut() and \ref calculateIn().
    void run(const Node& s) {
      init(s);
      calculateOut();
      calculateIn();
    }

    /// @}

    /// \name Query Functions
    /// The result of the %HaoOrlin algorithm
    /// can be obtained using these functions.
    /// \n
    /// Before using these functions, either \ref run(), \ref
    /// calculateOut() or \ref calculateIn() must be called.

    /// @{

    /// \brief Returns the value of the minimum value cut.
    ///
    /// Returns the value of the minimum value cut.
    Value minCutValue() const {
      return _min_cut;
    }


    /// \brief Returns a minimum cut.
    ///
    /// Sets \c nodeMap to the characteristic vector of a minimum
    /// value cut: it will give a nonempty set \f$ X\subsetneq V \f$
    /// with minimal out-degree (i.e. \c nodeMap will be true exactly
    /// for the nodes of \f$ X \f$).  \pre nodeMap should be a
    /// bool-valued node-map.
    template <typename NodeMap>
    Value minCutMap(NodeMap& nodeMap) const {
      for (NodeIt it(_graph); it != INVALID; ++it) {
        nodeMap.set(it, (*_min_cut_map)[it]);
      }
      return _min_cut;
    }

    /// @}

  }; //class HaoOrlin


} //namespace lemon

#endif //LEMON_HAO_ORLIN_H