RhodeCode

#include <lemon/tolerance.h>

#include <lemon/elevator.h>

///\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.

  template <typename GR, typename LM,

  struct CirculationDefaultTraits {

    /// \brief The type of the digraph the algorithm runs on.

    typedef GR Digraph;

    ///

    ///

    ///

    /// \brief The type of the flow values.

    /// \brief The type of the map that stores the flow values.

    ///

    /// The type of the map that stores the flow values.

    /// \brief Instantiates a FlowMap.

    ///

    /// This function instantiates a \ref FlowMap.

    /// 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

    /// \sa LinkedElevator

    typedef lemon::Elevator<Digraph, typename Digraph::Node> Elevator;

    /// \brief Instantiates an Elevator.

    ///

    /// This function instantiates an \ref Elevator.

    /// 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.

  };

  /**

     \brief Push-relabel algorithm for the network circulation problem.

     \ingroup max_flow

     It is to find a feasible circulation when lower and upper bounds

     The exact formulation of this problem is the following.

     Let \f$G=(V,A)\f$ be a digraph,

     \tparam GR The type of the digraph the algorithm runs on.

     map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".

     \ref concepts::Digraph::NodeMap "GR::NodeMap<UM::Value>".

  */

#ifdef DOXYGEN

template< typename GR,

          typename LM,

          typename UM,

          typename TR >

#else

template< typename GR,

          typename LM = typename GR::template ArcMap<int>,

          typename UM = LM,

#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 values.

    ///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;

    FlowMap *_flow;

    bool _local_flow;

    Elevator* _level;

    bool _local_level;

    ExcessMap* _excess;

    Tolerance _tol;

    int _el;

  public:

    typedef Circulation Create;

    ///\name Named Template Parameters

    ///@{

        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 _FlowMap>

    struct SetFlowMap

                           SetFlowMapTraits<_FlowMap> > {

                          SetFlowMapTraits<_FlowMap> > Create;

    };

    template <typename _Elevator>

    struct SetElevatorTraits : public Traits {

      typedef _Elevator 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 _Elevator>

    struct SetElevator

                           SetElevatorTraits<_Elevator> > {

                          SetElevatorTraits<_Elevator> > Create;

    };

    template <typename _Elevator>

    struct SetStandardElevatorTraits : public Traits {

      typedef _Elevator 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

    ///

    /// \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 _Elevator>

    struct SetStandardElevator

                       SetStandardElevatorTraits<_Elevator> > {

                      SetStandardElevatorTraits<_Elevator> > Create;

    };

    /// @}

  protected:

    Circulation() {}

  public:

    /// The constructor of the class.

    /// Destructor.

    ~Circulation() {

      destroyStructures();

    }

  private:

    void createStructures() {

      _node_num = _el = countNodes(_g);

        delete _flow;

      }

      if (_local_level) {

        delete _level;

      }

      if (_excess) {

        delete _excess;

      }

    }

  public:

    /// \return <tt>(*this)</tt>

      _lo = ↦

      return *this;

    }

    /// \return <tt>(*this)</tt>

      _up = ↦

      return *this;

    }

    /// \return <tt>(*this)</tt>

      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) {

    ///@{

    /// Initializes the internal data structures.

    /// Initializes the internal data structures and sets all flow values

    /// to the lower bound.

    void init()

    {

      createStructures();

      for(NodeIt n(_g);n!=INVALID;++n) {

      }

      for (ArcIt e(_g);e!=INVALID;++e) {

        _flow->set(e, (*_lo)[e]);

        _excess->set(_g.target(e), (*_excess)[_g.target(e)] + (*_flow)[e]);

        _excess->set(_g.source(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->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()

    {

      createStructures();

      for(NodeIt n(_g);n!=INVALID;++n) {

      }

      for (ArcIt e(_g);e!=INVALID;++e) {

        if (!_tol.positive((*_excess)[_g.target(e)] + (*_up)[e])) {

          _flow->set(e, (*_up)[e]);

          _excess->set(_g.target(e), (*_excess)[_g.target(e)] + (*_up)[e]);

          _excess->set(_g.source(e), (*_excess)[_g.source(e)] - (*_up)[e]);

        } else if (_tol.positive((*_excess)[_g.target(e)] + (*_lo)[e])) {

          _flow->set(e, (*_lo)[e]);

          _excess->set(_g.target(e), (*_excess)[_g.target(e)] + (*_lo)[e]);

          _excess->set(_g.source(e), (*_excess)[_g.source(e)] - (*_lo)[e]);

        } else {

          _flow->set(e, fc);

          _excess->set(_g.target(e), 0);

          _excess->set(_g.source(e), (*_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]))

    ///

    ///\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;

        for(OutArcIt e(_g,act);e!=INVALID; ++e) {

          Node v = _g.target(e);

          if(!_tol.positive(fc)) continue;

          if((*_level)[v]<actlevel) {

            if(!_tol.less(fc, exc)) {

              _flow->set(e, (*_flow)[e] + exc);

              _excess->set(v, (*_excess)[v] + exc);

              if(!_level->active(v) && _tol.positive((*_excess)[v]))

                _level->activate(v);

              _excess->set(act,0);

              _level->deactivate(act);

              goto next_l;

            }

            else {

              _flow->set(e, (*_up)[e]);

              _excess->set(v, (*_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);

          if(!_tol.positive(fc)) continue;

          if((*_level)[v]<actlevel) {

            if(!_tol.less(fc, exc)) {

              _flow->set(e, (*_flow)[e] - exc);

              _excess->set(v, (*_excess)[v] + exc);

              if(!_level->active(v) && _tol.positive((*_excess)[v]))

                _level->activate(v);

              _excess->set(act,0);

              _level->deactivate(act);

              goto next_l;

            }

            else {

    /// these functions.\n

    /// Either \ref run() or \ref start() should be called before

    /// using them.

    ///@{

    /// \brief Returns the flow on the given arc.

    ///

    /// Returns the flow on the given arc.

    ///

    /// \pre Either \ref run() or \ref init() must be called before

    /// using this function.

      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

       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()

    ///@{

    ///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)

        {

          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

    {

      for(NodeIt n(_g);n!=INVALID;++n)

        if(barrier(n))

      for(ArcIt e(_g);e!=INVALID;++e)

        {

          Node s=_g.source(e);

          Node t=_g.target(e);

          if(barrier(s)&&!barrier(t)) delta+=(*_up)[e];

          else if(barrier(t)&&!barrier(s)) delta-=(*_lo)[e];

        }

      return _tol.negative(delta);

    }

    /// @}

  struct PreflowDefaultTraits {

    /// \brief The type of the digraph the algorithm runs on.

    typedef GR Digraph;

    /// \brief The type of the map that stores the arc capacities.

    ///

    /// The type of the map that stores the arc capacities.

    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.

    typedef CM CapacityMap;

    /// \brief The type of the flow values.

    /// \brief The type of the map that stores the flow values.

    ///

    /// The type of the map that stores the flow values.

    /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.

    /// \brief Instantiates a FlowMap.

    ///

    /// This function instantiates a \ref FlowMap.

    /// the flow map.

    static FlowMap* createFlowMap(const Digraph& digraph) {

      return new FlowMap(digraph);

    }

    /// \brief The elevator type used by Preflow algorithm.

    ///

    /// The elevator type used by Preflow algorithm.

    ///

    /// \sa Elevator

    /// \sa LinkedElevator

    typedef LinkedElevator<Digraph, typename Digraph::Node> Elevator;

    /// \brief Instantiates an Elevator.

    ///

    /// This function instantiates an \ref Elevator.

    /// 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.

  };

  /// \ingroup max_flow

  ///

  /// \brief %Preflow algorithm class.

  ///

  /// This class provides an implementation of Goldberg-Tarjan's \e preflow

  /// \e push-relabel algorithm producing a flow of maximum value in a

  /// digraph. The preflow algorithms are the fastest known maximum

  /// flow algorithms. The current implementation use a mixture of the

            typename TR = PreflowDefaultTraits<GR, CM> >

#endif

  class Preflow {

  public:

    ///The \ref PreflowDefaultTraits "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 capacity map.

    typedef typename Traits::CapacityMap CapacityMap;

    ///The type of the flow values.

    ///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 CapacityMap* _capacity;

    int _node_num;

    Node _source, _target;

    FlowMap* _flow;

    bool _local_flow;

    Elevator* _level;

    bool _local_level;

    ExcessMap* _excess;

    Tolerance _tolerance;

    bool _phase;

    void createStructures() {

      _node_num = countNodes(_graph);

      if (!_flow) {

        _flow = Traits::createFlowMap(_graph);

    /// source node the incoming flow should greater or equal to the

    /// outgoing flow.

    /// \return \c false if the given \c flowMap is not a preflow.

    template <typename FlowMap>

    bool init(const FlowMap& flowMap) {

      createStructures();

      for (ArcIt e(_graph); e != INVALID; ++e) {

        _flow->set(e, flowMap[e]);

      }

      for (NodeIt n(_graph); n != INVALID; ++n) {

        for (InArcIt e(_graph, n); e != INVALID; ++e) {

          excess += (*_flow)[e];

        }

        for (OutArcIt e(_graph, n); e != INVALID; ++e) {

          excess -= (*_flow)[e];

        }

        if (excess < 0 && n != _source) return false;

        _excess->set(n, excess);

      }

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

            if (!reached[v] && _tolerance.positive((*_flow)[e])) {

              reached.set(v, true);

              _level->initAddItem(v);

              nqueue.push_back(v);

            }

          }

        }

        queue.swap(nqueue);

      }

      _level->initFinish();

      for (OutArcIt e(_graph, _source); e != INVALID; ++e) {

        if (_tolerance.positive(rem)) {

          Node u = _graph.target(e);

          if ((*_level)[u] == _level->maxLevel()) continue;

          _flow->set(e, (*_capacity)[e]);

          _excess->set(u, (*_excess)[u] + rem);

          if (u != _target && !_level->active(u)) {

            _level->activate(u);

          }

        }

      }

      for (InArcIt e(_graph, _source); e != INVALID; ++e) {

        if (_tolerance.positive(rem)) {

          Node v = _graph.source(e);

          if ((*_level)[v] == _level->maxLevel()) continue;

          _flow->set(e, 0);

          _excess->set(v, (*_excess)[v] + rem);

          if (v != _target && !_level->active(v)) {

            _level->activate(v);

          }

        }

      }

      return true;

    }

    /// minCut() returns a minimum cut.

    /// \pre One of the \ref init() functions must be called before

    /// using this function.

    void startFirstPhase() {

      _phase = true;

      Node n = _level->highestActive();

      int level = _level->highestActiveLevel();

      while (n != INVALID) {

        int num = _node_num;

        while (num > 0 && n != INVALID) {

          int new_level = _level->maxLevel();

          for (OutArcIt e(_graph, n); e != INVALID; ++e) {

            if (!_tolerance.positive(rem)) continue;

            Node v = _graph.target(e);

            if ((*_level)[v] < level) {

              if (!_level->active(v) && v != _target) {

                _level->activate(v);

              }

              if (!_tolerance.less(rem, excess)) {

                _flow->set(e, (*_flow)[e] + excess);

                _excess->set(v, (*_excess)[v] + excess);

                excess = 0;

                goto no_more_push_1;

              } else {

                excess -= rem;

                _excess->set(v, (*_excess)[v] + rem);

                _flow->set(e, (*_capacity)[e]);

              }

            } else if (new_level > (*_level)[v]) {

              new_level = (*_level)[v];

            }

          }

          for (InArcIt e(_graph, n); e != INVALID; ++e) {

            if (!_tolerance.positive(rem)) continue;

            Node v = _graph.source(e);

            if ((*_level)[v] < level) {

              if (!_level->active(v) && v != _target) {

                _level->activate(v);

              }

              if (!_tolerance.less(rem, excess)) {

                _flow->set(e, (*_flow)[e] - excess);

                _excess->set(v, (*_excess)[v] + excess);

                excess = 0;

                goto no_more_push_1;

              } else {

            }

          } else {

            _level->deactivate(n);

          }

          n = _level->highestActive();

          level = _level->highestActiveLevel();

          --num;

        }

        num = _node_num * 20;

        while (num > 0 && n != INVALID) {

          int new_level = _level->maxLevel();

          for (OutArcIt e(_graph, n); e != INVALID; ++e) {

            if (!_tolerance.positive(rem)) continue;

            Node v = _graph.target(e);

            if ((*_level)[v] < level) {

              if (!_level->active(v) && v != _target) {

                _level->activate(v);

              }

              if (!_tolerance.less(rem, excess)) {

                _flow->set(e, (*_flow)[e] + excess);

                _excess->set(v, (*_excess)[v] + excess);

                excess = 0;

                goto no_more_push_2;

              } else {

                excess -= rem;

                _excess->set(v, (*_excess)[v] + rem);

                _flow->set(e, (*_capacity)[e]);

              }

            } else if (new_level > (*_level)[v]) {

              new_level = (*_level)[v];

            }

          }

          for (InArcIt e(_graph, n); e != INVALID; ++e) {

            if (!_tolerance.positive(rem)) continue;

            Node v = _graph.source(e);

            if ((*_level)[v] < level) {

              if (!_level->active(v) && v != _target) {

                _level->activate(v);

              }

              if (!_tolerance.less(rem, excess)) {

                _flow->set(e, (*_flow)[e] - excess);

                _excess->set(v, (*_excess)[v] + excess);

                excess = 0;

                goto no_more_push_2;

              } else {

      _level->initFinish();

      for (NodeIt n(_graph); n != INVALID; ++n) {

        if (!reached[n]) {

          _level->dirtyTopButOne(n);

        } else if ((*_excess)[n] > 0 && _target != n) {

          _level->activate(n);

        }

      }

      Node n;

      while ((n = _level->highestActive()) != INVALID) {

        int level = _level->highestActiveLevel();

        int new_level = _level->maxLevel();

        for (OutArcIt e(_graph, n); e != INVALID; ++e) {

          if (!_tolerance.positive(rem)) continue;

          Node v = _graph.target(e);

          if ((*_level)[v] < level) {

            if (!_level->active(v) && v != _source) {

              _level->activate(v);

            }

            if (!_tolerance.less(rem, excess)) {

              _flow->set(e, (*_flow)[e] + excess);

              _excess->set(v, (*_excess)[v] + excess);

              excess = 0;

              goto no_more_push;

            } else {

              excess -= rem;

              _excess->set(v, (*_excess)[v] + rem);

              _flow->set(e, (*_capacity)[e]);

            }

          } else if (new_level > (*_level)[v]) {

            new_level = (*_level)[v];

          }

        }

        for (InArcIt e(_graph, n); e != INVALID; ++e) {

          if (!_tolerance.positive(rem)) continue;

          Node v = _graph.source(e);

          if ((*_level)[v] < level) {

            if (!_level->active(v) && v != _source) {

              _level->activate(v);

            }

            if (!_tolerance.less(rem, excess)) {

              _flow->set(e, (*_flow)[e] - excess);

              _excess->set(v, (*_excess)[v] + excess);

              excess = 0;

              goto no_more_push;

            } else {

    /// before using them.

    ///@{

    /// \brief Returns the value of the maximum flow.

    ///

    /// Returns the value of the maximum flow by returning the excess

    /// of the target node. This value equals to the value of

    /// the maximum flow already after the first phase of the algorithm.

    ///

    /// \pre Either \ref run() or \ref init() must be called before

    /// using this function.

      return (*_excess)[_target];

    }

    /// \brief Returns the flow on the given arc.

    ///

    /// Returns the flow on the given arc. This method can

    /// be called after the second phase of the algorithm.

    ///

    /// \pre Either \ref run() or \ref init() must be called before

    /// using this function.

      return (*_flow)[arc];

    }

    /// \brief Returns a const reference to the flow map.

    ///

    /// Returns a const reference to the arc map storing the found flow.

    /// This method can be called after the second phase of the algorithm.

    ///

    /// \pre Either \ref run() or \ref init() must be called before

    /// using this function.

    const FlowMap& flowMap() const {

      return *_flow;

  "@attributes\n"

  "source 0\n"

  "sink   5\n";