diff -r c6acc34f98dc -r 1a7fe3bef514 lemon/circulation.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/circulation.h	Thu Nov 05 15:50:01 2009 +0100
@@ -0,0 +1,803 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2009
+ * 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_CIRCULATION_H
+#define LEMON_CIRCULATION_H
+
+#include <lemon/tolerance.h>
+#include <lemon/elevator.h>
+#include <limits>
+
+///\ingroup max_flow
+///\file
+///\brief Push-relabel algorithm for finding a feasible circulation.
+///
+namespace lemon {
+
+  /// \brief Default traits class of Circulation class.
+  ///
+  /// Default traits class of Circulation class.
+  ///
+  /// \tparam GR Type of the digraph the algorithm runs on.
+  /// \tparam LM The type of the lower bound map.
+  /// \tparam UM The type of the upper bound (capacity) map.
+  /// \tparam SM The type of the supply map.
+  template <typename GR, typename LM,
+            typename UM, typename SM>
+  struct CirculationDefaultTraits {
+
+    /// \brief The type of the digraph the algorithm runs on.
+    typedef GR Digraph;
+
+    /// \brief The type of the lower bound map.
+    ///
+    /// The type of the map that stores the lower bounds on the arcs.
+    /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
+    typedef LM LowerMap;
+
+    /// \brief The type of the upper bound (capacity) map.
+    ///
+    /// The type of the map that stores the upper bounds (capacities)
+    /// on the arcs.
+    /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
+    typedef UM UpperMap;
+
+    /// \brief The type of supply map.
+    ///
+    /// The type of the map that stores the signed supply values of the 
+    /// nodes. 
+    /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
+    typedef SM SupplyMap;
+
+    /// \brief The type of the flow and supply values.
+    typedef typename SupplyMap::Value Value;
+
+    /// \brief The type of the map that stores the flow values.
+    ///
+    /// The type of the map that stores the flow values.
+    /// It must conform to the \ref concepts::ReadWriteMap "ReadWriteMap"
+    /// concept.
+#ifdef DOXYGEN
+    typedef GR::ArcMap<Value> FlowMap;
+#else
+    typedef typename Digraph::template ArcMap<Value> FlowMap;
+#endif
+
+    /// \brief Instantiates a FlowMap.
+    ///
+    /// This function instantiates a \ref FlowMap.
+    /// \param digraph The digraph for which we would like to define
+    /// the flow map.
+    static FlowMap* createFlowMap(const Digraph& digraph) {
+      return new FlowMap(digraph);
+    }
+
+    /// \brief The elevator type used by the algorithm.
+    ///
+    /// The elevator type used by the algorithm.
+    ///
+    /// \sa Elevator, LinkedElevator
+#ifdef DOXYGEN
+    typedef lemon::Elevator<GR, GR::Node> Elevator;
+#else
+    typedef lemon::Elevator<Digraph, typename Digraph::Node> Elevator;
+#endif
+
+    /// \brief Instantiates an Elevator.
+    ///
+    /// This function instantiates an \ref Elevator.
+    /// \param digraph The digraph for which we would like to define
+    /// the elevator.
+    /// \param max_level The maximum level of the elevator.
+    static Elevator* createElevator(const Digraph& digraph, int max_level) {
+      return new Elevator(digraph, max_level);
+    }
+
+    /// \brief The tolerance used by the algorithm
+    ///
+    /// The tolerance used by the algorithm to handle inexact computation.
+    typedef lemon::Tolerance<Value> Tolerance;
+
+  };
+
+  /**
+     \brief Push-relabel algorithm for the network circulation problem.
+
+     \ingroup max_flow
+     This class implements a push-relabel algorithm for the \e network
+     \e circulation problem.
+     It is to find a feasible circulation when lower and upper bounds
+     are given for the flow values on the arcs and lower bounds are
+     given for the difference between the outgoing and incoming flow
+     at the nodes.
+
+     The exact formulation of this problem is the following.
+     Let \f$G=(V,A)\f$ be a digraph, \f$lower: A\rightarrow\mathbf{R}\f$
+     \f$upper: A\rightarrow\mathbf{R}\cup\{\infty\}\f$ denote the lower and
+     upper bounds on the arcs, for which \f$lower(uv) \leq upper(uv)\f$
+     holds for all \f$uv\in A\f$, and \f$sup: V\rightarrow\mathbf{R}\f$
+     denotes the signed supply values of the nodes.
+     If \f$sup(u)>0\f$, then \f$u\f$ is a supply node with \f$sup(u)\f$
+     supply, if \f$sup(u)<0\f$, then \f$u\f$ is a demand node with
+     \f$-sup(u)\f$ demand.
+     A feasible circulation is an \f$f: A\rightarrow\mathbf{R}\f$
+     solution of the following problem.
+
+     \f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu)
+     \geq sup(u) \quad \forall u\in V, \f]
+     \f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A. \f]
+     
+     The sum of the supply values, i.e. \f$\sum_{u\in V} sup(u)\f$ must be
+     zero or negative in order to have a feasible solution (since the sum
+     of the expressions on the left-hand side of the inequalities is zero).
+     It means that the total demand must be greater or equal to the total
+     supply and all the supplies have to be carried out from the supply nodes,
+     but there could be demands that are not satisfied.
+     If \f$\sum_{u\in V} sup(u)\f$ is zero, then all the supply/demand
+     constraints have to be satisfied with equality, i.e. all demands
+     have to be satisfied and all supplies have to be used.
+     
+     If you need the opposite inequalities in the supply/demand constraints
+     (i.e. the total demand is less than the total supply and all the demands
+     have to be satisfied while there could be supplies that are not used),
+     then you could easily transform the problem to the above form by reversing
+     the direction of the arcs and taking the negative of the supply values
+     (e.g. using \ref ReverseDigraph and \ref NegMap adaptors).
+
+     This algorithm either calculates a feasible circulation, or provides
+     a \ref barrier() "barrier", which prooves that a feasible soultion
+     cannot exist.
+
+     Note that this algorithm also provides a feasible solution for the
+     \ref min_cost_flow "minimum cost flow problem".
+
+     \tparam GR The type of the digraph the algorithm runs on.
+     \tparam LM The type of the lower bound map. The default
+     map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
+     \tparam UM The type of the upper bound (capacity) map.
+     The default map type is \c LM.
+     \tparam SM The type of the supply map. The default map type is
+     \ref concepts::Digraph::NodeMap "GR::NodeMap<UM::Value>".
+  */
+#ifdef DOXYGEN
+template< typename GR,
+          typename LM,
+          typename UM,
+          typename SM,
+          typename TR >
+#else
+template< typename GR,
+          typename LM = typename GR::template ArcMap<int>,
+          typename UM = LM,
+          typename SM = typename GR::template NodeMap<typename UM::Value>,
+          typename TR = CirculationDefaultTraits<GR, LM, UM, SM> >
+#endif
+  class Circulation {
+  public:
+
+    ///The \ref CirculationDefaultTraits "traits class" of the algorithm.
+    typedef TR Traits;
+    ///The type of the digraph the algorithm runs on.
+    typedef typename Traits::Digraph Digraph;
+    ///The type of the flow and supply values.
+    typedef typename Traits::Value Value;
+
+    ///The type of the lower bound map.
+    typedef typename Traits::LowerMap LowerMap;
+    ///The type of the upper bound (capacity) map.
+    typedef typename Traits::UpperMap UpperMap;
+    ///The type of the supply map.
+    typedef typename Traits::SupplyMap SupplyMap;
+    ///The type of the flow map.
+    typedef typename Traits::FlowMap FlowMap;
+
+    ///The type of the elevator.
+    typedef typename Traits::Elevator Elevator;
+    ///The type of the tolerance.
+    typedef typename Traits::Tolerance Tolerance;
+
+  private:
+
+    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
+
+    const Digraph &_g;
+    int _node_num;
+
+    const LowerMap *_lo;
+    const UpperMap *_up;
+    const SupplyMap *_supply;
+
+    FlowMap *_flow;
+    bool _local_flow;
+
+    Elevator* _level;
+    bool _local_level;
+
+    typedef typename Digraph::template NodeMap<Value> ExcessMap;
+    ExcessMap* _excess;
+
+    Tolerance _tol;
+    int _el;
+
+  public:
+
+    typedef Circulation Create;
+
+    ///\name Named Template Parameters
+
+    ///@{
+
+    template <typename T>
+    struct SetFlowMapTraits : public Traits {
+      typedef T FlowMap;
+      static FlowMap *createFlowMap(const Digraph&) {
+        LEMON_ASSERT(false, "FlowMap is not initialized");
+        return 0; // ignore warnings
+      }
+    };
+
+    /// \brief \ref named-templ-param "Named parameter" for setting
+    /// FlowMap type
+    ///
+    /// \ref named-templ-param "Named parameter" for setting FlowMap
+    /// type.
+    template <typename T>
+    struct SetFlowMap
+      : public Circulation<Digraph, LowerMap, UpperMap, SupplyMap,
+                           SetFlowMapTraits<T> > {
+      typedef Circulation<Digraph, LowerMap, UpperMap, SupplyMap,
+                          SetFlowMapTraits<T> > Create;
+    };
+
+    template <typename T>
+    struct SetElevatorTraits : public Traits {
+      typedef T Elevator;
+      static Elevator *createElevator(const Digraph&, int) {
+        LEMON_ASSERT(false, "Elevator is not initialized");
+        return 0; // ignore warnings
+      }
+    };
+
+    /// \brief \ref named-templ-param "Named parameter" for setting
+    /// Elevator type
+    ///
+    /// \ref named-templ-param "Named parameter" for setting Elevator
+    /// type. If this named parameter is used, then an external
+    /// elevator object must be passed to the algorithm using the
+    /// \ref elevator(Elevator&) "elevator()" function before calling
+    /// \ref run() or \ref init().
+    /// \sa SetStandardElevator
+    template <typename T>
+    struct SetElevator
+      : public Circulation<Digraph, LowerMap, UpperMap, SupplyMap,
+                           SetElevatorTraits<T> > {
+      typedef Circulation<Digraph, LowerMap, UpperMap, SupplyMap,
+                          SetElevatorTraits<T> > Create;
+    };
+
+    template <typename T>
+    struct SetStandardElevatorTraits : public Traits {
+      typedef T Elevator;
+      static Elevator *createElevator(const Digraph& digraph, int max_level) {
+        return new Elevator(digraph, max_level);
+      }
+    };
+
+    /// \brief \ref named-templ-param "Named parameter" for setting
+    /// Elevator type with automatic allocation
+    ///
+    /// \ref named-templ-param "Named parameter" for setting Elevator
+    /// type with automatic allocation.
+    /// The Elevator should have standard constructor interface to be
+    /// able to automatically created by the algorithm (i.e. the
+    /// digraph and the maximum level should be passed to it).
+    /// However an external elevator object could also be passed to the
+    /// algorithm with the \ref elevator(Elevator&) "elevator()" function
+    /// before calling \ref run() or \ref init().
+    /// \sa SetElevator
+    template <typename T>
+    struct SetStandardElevator
+      : public Circulation<Digraph, LowerMap, UpperMap, SupplyMap,
+                       SetStandardElevatorTraits<T> > {
+      typedef Circulation<Digraph, LowerMap, UpperMap, SupplyMap,
+                      SetStandardElevatorTraits<T> > Create;
+    };
+
+    /// @}
+
+  protected:
+
+    Circulation() {}
+
+  public:
+
+    /// Constructor.
+
+    /// The constructor of the class.
+    ///
+    /// \param graph The digraph the algorithm runs on.
+    /// \param lower The lower bounds for the flow values on the arcs.
+    /// \param upper The upper bounds (capacities) for the flow values 
+    /// on the arcs.
+    /// \param supply The signed supply values of the nodes.
+    Circulation(const Digraph &graph, const LowerMap &lower,
+                const UpperMap &upper, const SupplyMap &supply)
+      : _g(graph), _lo(&lower), _up(&upper), _supply(&supply),
+        _flow(NULL), _local_flow(false), _level(NULL), _local_level(false),
+        _excess(NULL) {}
+
+    /// Destructor.
+    ~Circulation() {
+      destroyStructures();
+    }
+
+
+  private:
+
+    bool checkBoundMaps() {
+      for (ArcIt e(_g);e!=INVALID;++e) {
+        if (_tol.less((*_up)[e], (*_lo)[e])) return false;
+      }
+      return true;
+    }
+
+    void createStructures() {
+      _node_num = _el = countNodes(_g);
+
+      if (!_flow) {
+        _flow = Traits::createFlowMap(_g);
+        _local_flow = true;
+      }
+      if (!_level) {
+        _level = Traits::createElevator(_g, _node_num);
+        _local_level = true;
+      }
+      if (!_excess) {
+        _excess = new ExcessMap(_g);
+      }
+    }
+
+    void destroyStructures() {
+      if (_local_flow) {
+        delete _flow;
+      }
+      if (_local_level) {
+        delete _level;
+      }
+      if (_excess) {
+        delete _excess;
+      }
+    }
+
+  public:
+
+    /// Sets the lower bound map.
+
+    /// Sets the lower bound map.
+    /// \return <tt>(*this)</tt>
+    Circulation& lowerMap(const LowerMap& map) {
+      _lo = &map;
+      return *this;
+    }
+
+    /// Sets the upper bound (capacity) map.
+
+    /// Sets the upper bound (capacity) map.
+    /// \return <tt>(*this)</tt>
+    Circulation& upperMap(const UpperMap& map) {
+      _up = &map;
+      return *this;
+    }
+
+    /// Sets the supply map.
+
+    /// Sets the supply map.
+    /// \return <tt>(*this)</tt>
+    Circulation& supplyMap(const SupplyMap& map) {
+      _supply = &map;
+      return *this;
+    }
+
+    /// \brief Sets the flow map.
+    ///
+    /// Sets the flow map.
+    /// If you don't use this function before calling \ref run() or
+    /// \ref init(), an instance will be allocated automatically.
+    /// The destructor deallocates this automatically allocated map,
+    /// of course.
+    /// \return <tt>(*this)</tt>
+    Circulation& flowMap(FlowMap& map) {
+      if (_local_flow) {
+        delete _flow;
+        _local_flow = false;
+      }
+      _flow = &map;
+      return *this;
+    }
+
+    /// \brief Sets the elevator used by algorithm.
+    ///
+    /// Sets the elevator used by algorithm.
+    /// If you don't use this function before calling \ref run() or
+    /// \ref init(), an instance will be allocated automatically.
+    /// The destructor deallocates this automatically allocated elevator,
+    /// of course.
+    /// \return <tt>(*this)</tt>
+    Circulation& elevator(Elevator& elevator) {
+      if (_local_level) {
+        delete _level;
+        _local_level = false;
+      }
+      _level = &elevator;
+      return *this;
+    }
+
+    /// \brief Returns a const reference to the elevator.
+    ///
+    /// Returns a const reference to the elevator.
+    ///
+    /// \pre Either \ref run() or \ref init() must be called before
+    /// using this function.
+    const Elevator& elevator() const {
+      return *_level;
+    }
+
+    /// \brief Sets the tolerance used by the algorithm.
+    ///
+    /// Sets the tolerance object used by the algorithm.
+    /// \return <tt>(*this)</tt>
+    Circulation& tolerance(const Tolerance& tolerance) {
+      _tol = tolerance;
+      return *this;
+    }
+
+    /// \brief Returns a const reference to the tolerance.
+    ///
+    /// Returns a const reference to the tolerance object used by
+    /// the algorithm.
+    const Tolerance& tolerance() const {
+      return _tol;
+    }
+
+    /// \name Execution Control
+    /// The simplest way to execute the algorithm is to call \ref run().\n
+    /// If you need better control on the initial solution or the execution,
+    /// you have to call one of the \ref init() functions first, then
+    /// the \ref start() function.
+
+    ///@{
+
+    /// Initializes the internal data structures.
+
+    /// Initializes the internal data structures and sets all flow values
+    /// to the lower bound.
+    void init()
+    {
+      LEMON_DEBUG(checkBoundMaps(),
+        "Upper bounds must be greater or equal to the lower bounds");
+
+      createStructures();
+
+      for(NodeIt n(_g);n!=INVALID;++n) {
+        (*_excess)[n] = (*_supply)[n];
+      }
+
+      for (ArcIt e(_g);e!=INVALID;++e) {
+        _flow->set(e, (*_lo)[e]);
+        (*_excess)[_g.target(e)] += (*_flow)[e];
+        (*_excess)[_g.source(e)] -= (*_flow)[e];
+      }
+
+      // global relabeling tested, but in general case it provides
+      // worse performance for random digraphs
+      _level->initStart();
+      for(NodeIt n(_g);n!=INVALID;++n)
+        _level->initAddItem(n);
+      _level->initFinish();
+      for(NodeIt n(_g);n!=INVALID;++n)
+        if(_tol.positive((*_excess)[n]))
+          _level->activate(n);
+    }
+
+    /// Initializes the internal data structures using a greedy approach.
+
+    /// Initializes the internal data structures using a greedy approach
+    /// to construct the initial solution.
+    void greedyInit()
+    {
+      LEMON_DEBUG(checkBoundMaps(),
+        "Upper bounds must be greater or equal to the lower bounds");
+
+      createStructures();
+
+      for(NodeIt n(_g);n!=INVALID;++n) {
+        (*_excess)[n] = (*_supply)[n];
+      }
+
+      for (ArcIt e(_g);e!=INVALID;++e) {
+        if (!_tol.less(-(*_excess)[_g.target(e)], (*_up)[e])) {
+          _flow->set(e, (*_up)[e]);
+          (*_excess)[_g.target(e)] += (*_up)[e];
+          (*_excess)[_g.source(e)] -= (*_up)[e];
+        } else if (_tol.less(-(*_excess)[_g.target(e)], (*_lo)[e])) {
+          _flow->set(e, (*_lo)[e]);
+          (*_excess)[_g.target(e)] += (*_lo)[e];
+          (*_excess)[_g.source(e)] -= (*_lo)[e];
+        } else {
+          Value fc = -(*_excess)[_g.target(e)];
+          _flow->set(e, fc);
+          (*_excess)[_g.target(e)] = 0;
+          (*_excess)[_g.source(e)] -= fc;
+        }
+      }
+
+      _level->initStart();
+      for(NodeIt n(_g);n!=INVALID;++n)
+        _level->initAddItem(n);
+      _level->initFinish();
+      for(NodeIt n(_g);n!=INVALID;++n)
+        if(_tol.positive((*_excess)[n]))
+          _level->activate(n);
+    }
+
+    ///Executes the algorithm
+
+    ///This function executes the algorithm.
+    ///
+    ///\return \c true if a feasible circulation is found.
+    ///
+    ///\sa barrier()
+    ///\sa barrierMap()
+    bool start()
+    {
+
+      Node act;
+      Node bact=INVALID;
+      Node last_activated=INVALID;
+      while((act=_level->highestActive())!=INVALID) {
+        int actlevel=(*_level)[act];
+        int mlevel=_node_num;
+        Value exc=(*_excess)[act];
+
+        for(OutArcIt e(_g,act);e!=INVALID; ++e) {
+          Node v = _g.target(e);
+          Value fc=(*_up)[e]-(*_flow)[e];
+          if(!_tol.positive(fc)) continue;
+          if((*_level)[v]<actlevel) {
+            if(!_tol.less(fc, exc)) {
+              _flow->set(e, (*_flow)[e] + exc);
+              (*_excess)[v] += exc;
+              if(!_level->active(v) && _tol.positive((*_excess)[v]))
+                _level->activate(v);
+              (*_excess)[act] = 0;
+              _level->deactivate(act);
+              goto next_l;
+            }
+            else {
+              _flow->set(e, (*_up)[e]);
+              (*_excess)[v] += fc;
+              if(!_level->active(v) && _tol.positive((*_excess)[v]))
+                _level->activate(v);
+              exc-=fc;
+            }
+          }
+          else if((*_level)[v]<mlevel) mlevel=(*_level)[v];
+        }
+        for(InArcIt e(_g,act);e!=INVALID; ++e) {
+          Node v = _g.source(e);
+          Value fc=(*_flow)[e]-(*_lo)[e];
+          if(!_tol.positive(fc)) continue;
+          if((*_level)[v]<actlevel) {
+            if(!_tol.less(fc, exc)) {
+              _flow->set(e, (*_flow)[e] - exc);
+              (*_excess)[v] += exc;
+              if(!_level->active(v) && _tol.positive((*_excess)[v]))
+                _level->activate(v);
+              (*_excess)[act] = 0;
+              _level->deactivate(act);
+              goto next_l;
+            }
+            else {
+              _flow->set(e, (*_lo)[e]);
+              (*_excess)[v] += fc;
+              if(!_level->active(v) && _tol.positive((*_excess)[v]))
+                _level->activate(v);
+              exc-=fc;
+            }
+          }
+          else if((*_level)[v]<mlevel) mlevel=(*_level)[v];
+        }
+
+        (*_excess)[act] = exc;
+        if(!_tol.positive(exc)) _level->deactivate(act);
+        else if(mlevel==_node_num) {
+          _level->liftHighestActiveToTop();
+          _el = _node_num;
+          return false;
+        }
+        else {
+          _level->liftHighestActive(mlevel+1);
+          if(_level->onLevel(actlevel)==0) {
+            _el = actlevel;
+            return false;
+          }
+        }
+      next_l:
+        ;
+      }
+      return true;
+    }
+
+    /// Runs the algorithm.
+
+    /// This function runs the algorithm.
+    ///
+    /// \return \c true if a feasible circulation is found.
+    ///
+    /// \note Apart from the return value, c.run() is just a shortcut of
+    /// the following code.
+    /// \code
+    ///   c.greedyInit();
+    ///   c.start();
+    /// \endcode
+    bool run() {
+      greedyInit();
+      return start();
+    }
+
+    /// @}
+
+    /// \name Query Functions
+    /// The results of the circulation algorithm can be obtained using
+    /// these functions.\n
+    /// Either \ref run() or \ref start() should be called before
+    /// using them.
+
+    ///@{
+
+    /// \brief Returns the flow value on the given arc.
+    ///
+    /// Returns the flow value on the given arc.
+    ///
+    /// \pre Either \ref run() or \ref init() must be called before
+    /// using this function.
+    Value flow(const Arc& arc) const {
+      return (*_flow)[arc];
+    }
+
+    /// \brief Returns a const reference to the flow map.
+    ///
+    /// Returns a const reference to the arc map storing the found flow.
+    ///
+    /// \pre Either \ref run() or \ref init() must be called before
+    /// using this function.
+    const FlowMap& flowMap() const {
+      return *_flow;
+    }
+
+    /**
+       \brief Returns \c true if the given node is in a barrier.
+
+       Barrier is a set \e B of nodes for which
+
+       \f[ \sum_{uv\in A: u\in B} upper(uv) -
+           \sum_{uv\in A: v\in B} lower(uv) < \sum_{v\in B} sup(v) \f]
+
+       holds. The existence of a set with this property prooves that a
+       feasible circualtion cannot exist.
+
+       This function returns \c true if the given node is in the found
+       barrier. If a feasible circulation is found, the function
+       gives back \c false for every node.
+
+       \pre Either \ref run() or \ref init() must be called before
+       using this function.
+
+       \sa barrierMap()
+       \sa checkBarrier()
+    */
+    bool barrier(const Node& node) const
+    {
+      return (*_level)[node] >= _el;
+    }
+
+    /// \brief Gives back a barrier.
+    ///
+    /// This function sets \c bar to the characteristic vector of the
+    /// found barrier. \c bar should be a \ref concepts::WriteMap "writable"
+    /// node map with \c bool (or convertible) value type.
+    ///
+    /// If a feasible circulation is found, the function gives back an
+    /// empty set, so \c bar[v] will be \c false for all nodes \c v.
+    ///
+    /// \note This function calls \ref barrier() for each node,
+    /// so it runs in O(n) time.
+    ///
+    /// \pre Either \ref run() or \ref init() must be called before
+    /// using this function.
+    ///
+    /// \sa barrier()
+    /// \sa checkBarrier()
+    template<class BarrierMap>
+    void barrierMap(BarrierMap &bar) const
+    {
+      for(NodeIt n(_g);n!=INVALID;++n)
+        bar.set(n, (*_level)[n] >= _el);
+    }
+
+    /// @}
+
+    /// \name Checker Functions
+    /// The feasibility of the results can be checked using
+    /// these functions.\n
+    /// Either \ref run() or \ref start() should be called before
+    /// using them.
+
+    ///@{
+
+    ///Check if the found flow is a feasible circulation
+
+    ///Check if the found flow is a feasible circulation,
+    ///
+    bool checkFlow() const {
+      for(ArcIt e(_g);e!=INVALID;++e)
+        if((*_flow)[e]<(*_lo)[e]||(*_flow)[e]>(*_up)[e]) return false;
+      for(NodeIt n(_g);n!=INVALID;++n)
+        {
+          Value dif=-(*_supply)[n];
+          for(InArcIt e(_g,n);e!=INVALID;++e) dif-=(*_flow)[e];
+          for(OutArcIt e(_g,n);e!=INVALID;++e) dif+=(*_flow)[e];
+          if(_tol.negative(dif)) return false;
+        }
+      return true;
+    }
+
+    ///Check whether or not the last execution provides a barrier
+
+    ///Check whether or not the last execution provides a barrier.
+    ///\sa barrier()
+    ///\sa barrierMap()
+    bool checkBarrier() const
+    {
+      Value delta=0;
+      Value inf_cap = std::numeric_limits<Value>::has_infinity ?
+        std::numeric_limits<Value>::infinity() :
+        std::numeric_limits<Value>::max();
+      for(NodeIt n(_g);n!=INVALID;++n)
+        if(barrier(n))
+          delta-=(*_supply)[n];
+      for(ArcIt e(_g);e!=INVALID;++e)
+        {
+          Node s=_g.source(e);
+          Node t=_g.target(e);
+          if(barrier(s)&&!barrier(t)) {
+            if (_tol.less(inf_cap - (*_up)[e], delta)) return false;
+            delta+=(*_up)[e];
+          }
+          else if(barrier(t)&&!barrier(s)) delta-=(*_lo)[e];
+        }
+      return _tol.negative(delta);
+    }
+
+    /// @}
+
+  };
+
+}
+
+#endif