RhodeCode

      /// upper bound. It means that the objective function is unbounded

      /// on that arc, however, note that it could actually be bounded

      /// over the feasible flows, but this algroithm cannot handle

      /// these cases.

      UNBOUNDED

    };

  private:

    TEMPLATE_DIGRAPH_TYPEDEFS(GR);

    typedef std::vector<int> IntVector;

    typedef std::vector<char> BoolVector;

    typedef std::vector<Value> ValueVector;

    typedef std::vector<Cost> CostVector;

  private:

    // Data related to the underlying digraph

    const GR &_graph;

    int _node_num;

    int _arc_num;

    int _res_arc_num;

    int _root;

    // Parameters of the problem

    bool _have_lower;

    Value _sum_supply;

    // Data structures for storing the digraph

    IntNodeMap _node_id;

    IntArcMap _arc_idf;

    IntArcMap _arc_idb;

    IntVector _first_out;

    BoolVector _forward;

    IntVector _source;

    IntVector _target;

    IntVector _reverse;

    // Node and arc data

    ValueVector _lower;

    ValueVector _upper;

    CostVector _cost;

    ValueVector _supply;

    ValueVector _res_cap;

    CostVector _pi;

    ValueVector _excess;

    IntVector _excess_nodes;

    IntVector _deficit_nodes;

    Value _delta;

    int _factor;

    IntVector _pred;

  public:

    /// \brief Constant for infinite upper bounds (capacities).

    ///

    /// Constant for infinite upper bounds (capacities).

    /// It is \c std::numeric_limits<Value>::infinity() if available,

    /// \c std::numeric_limits<Value>::max() otherwise.

    const Value INF;

  private:

    // Special implementation of the Dijkstra algorithm for finding

    // shortest paths in the residual network of the digraph with

    // respect to the reduced arc costs and modifying the node

    // potentials according to the found distance labels.

    class ResidualDijkstra

    {

    private:

      int _node_num;

      bool _geq;

      const IntVector &_first_out;

      const IntVector &_target;

      const CostVector &_cost;

      const ValueVector &_res_cap;

      const ValueVector &_excess;

      CostVector &_pi;

      IntVector &_pred;

      IntVector _proc_nodes;

      CostVector _dist;

    public:

      ResidualDijkstra(CapacityScaling& cs) :

        _node_num(cs._node_num), _geq(cs._sum_supply < 0),

        _first_out(cs._first_out), _target(cs._target), _cost(cs._cost),

        _res_cap(cs._res_cap), _excess(cs._excess), _pi(cs._pi),

        _pred(cs._pred), _dist(cs._node_num)

      {}

      int run(int s, Value delta = 1) {

        RangeMap<int> heap_cross_ref(_node_num, Heap::PRE_HEAP);

        Heap heap(heap_cross_ref);

        heap.push(s, 0);

        _pred[s] = -1;

        _proc_nodes.clear();

        // Process nodes

        while (!heap.empty() && _excess[heap.top()] > -delta) {

          int u = heap.top(), v;

          Cost d = heap.prio() + _pi[u], dn;

          _dist[u] = heap.prio();

          _proc_nodes.push_back(u);

          heap.pop();

          // Traverse outgoing residual arcs

          int last_out = _geq ? _first_out[u+1] : _first_out[u+1] - 1;

          for (int a = _first_out[u]; a != last_out; ++a) {

            if (_res_cap[a] < delta) continue;

            v = _target[a];

            switch (heap.state(v)) {

              case Heap::PRE_HEAP:

                heap.push(v, d + _cost[a] - _pi[v]);

                _pred[v] = a;

                break;

              case Heap::IN_HEAP:

                dn = d + _cost[a] - _pi[v];

                if (dn < heap[v]) {

                  heap.decrease(v, dn);

                  _pred[v] = a;

                }

                break;

              case Heap::POST_HEAP:

                break;

            }

          }

        }

        if (heap.empty()) return -1;

        // Update potentials of processed nodes

        int t = heap.top();

        Cost dt = heap.prio();

        for (int i = 0; i < int(_proc_nodes.size()); ++i) {

          _pi[_proc_nodes[i]] += _dist[_proc_nodes[i]] - dt;

        }

        return t;

      }

    }; //class ResidualDijkstra

  public:

    /// \name Named Template Parameters

    /// @{

    template <typename T>

    struct SetHeapTraits : public Traits {

      typedef T Heap;

    };

    /// \brief \ref named-templ-param "Named parameter" for setting

    /// \c Heap type.

    ///

    /// \ref named-templ-param "Named parameter" for setting \c Heap

    /// type, which is used for internal Dijkstra computations.

    /// It must conform to the \ref lemon::concepts::Heap "Heap" concept,

    /// its priority type must be \c Cost and its cross reference type

    /// must be \ref RangeMap "RangeMap<int>".

    template <typename T>

    struct SetHeap

      : public CapacityScaling<GR, V, C, SetHeapTraits<T> > {

      typedef  CapacityScaling<GR, V, C, SetHeapTraits<T> > Create;

    };

    /// @}

  public:

    /// \brief Constructor.

    ///

    /// The constructor of the class.

    ///

    /// \param graph The digraph the algorithm runs on.

    CapacityScaling(const GR& graph) :

      _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph),

      INF(std::numeric_limits<Value>::has_infinity ?

          std::numeric_limits<Value>::infinity() :

          std::numeric_limits<Value>::max())

    {

      // Check the number types

      LEMON_ASSERT(std::numeric_limits<Value>::is_signed,

        "The flow type of CapacityScaling must be signed");

      LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,

        "The cost type of CapacityScaling must be signed");

      reset();

    }

    /// \name Parameters

    /// The parameters of the algorithm can be specified using these

    /// functions.

    /// @{

    /// \brief Set the lower bounds on the arcs.

    ///

    /// This function sets the lower bounds on the arcs.

    /// If it is not used before calling \ref run(), the lower bounds

    /// will be set to zero on all arcs.

    ///

    /// \param map An arc map storing the lower bounds.

    /// Its \c Value type must be convertible to the \c Value type

    /// of the algorithm.

    ///

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

    template <typename LowerMap>

    CapacityScaling& lowerMap(const LowerMap& map) {

      _have_lower = true;

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

        _lower[_arc_idf[a]] = map[a];

        _lower[_arc_idb[a]] = map[a];

      }

      return *this;

    }

    /// \brief Set the upper bounds (capacities) on the arcs.

    ///

    /// This function sets the upper bounds (capacities) on the arcs.

    /// If it is not used before calling \ref run(), the upper bounds

    /// will be set to \ref INF on all arcs (i.e. the flow value will be

    /// unbounded from above).

    ///

    /// \param map An arc map storing the upper bounds.

    /// Its \c Value type must be convertible to the \c Value type

    /// of the algorithm.

    ///

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

    template<typename UpperMap>

    CapacityScaling& upperMap(const UpperMap& map) {

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

        _upper[_arc_idf[a]] = map[a];

      }

      return *this;

    }

    /// \brief Set the costs of the arcs.

    ///

    /// This function sets the costs of the arcs.

    /// If it is not used before calling \ref run(), the costs

    /// will be set to \c 1 on all arcs.

    ///

    /// \param map An arc map storing the costs.

    /// Its \c Value type must be convertible to the \c Cost type

    /// of the algorithm.

    ///

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

    template<typename CostMap>

    CapacityScaling& costMap(const CostMap& map) {

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

        _cost[_arc_idf[a]] =  map[a];

        _cost[_arc_idb[a]] = -map[a];

      }

      return *this;

    }

    /// \brief Set the supply values of the nodes.

    ///

    /// This function sets the supply values of the nodes.

    /// If neither this function nor \ref stSupply() is used before

    /// calling \ref run(), the supply of each node will be set to zero.

    ///

    /// \param map A node map storing the supply values.

    /// Its \c Value type must be convertible to the \c Value type

    /// of the algorithm.

    ///

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

    template<typename SupplyMap>

    CapacityScaling& supplyMap(const SupplyMap& map) {

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

        _supply[_node_id[n]] = map[n];

      }

      return *this;

    }

    /// \brief Set single source and target nodes and a supply value.

    ///

    /// This function sets a single source node and a single target node

    /// and the required flow value.

    /// If neither this function nor \ref supplyMap() is used before

    /// calling \ref run(), the supply of each node will be set to zero.

    ///

    /// Using this function has the same effect as using \ref supplyMap()

    /// with such a map in which \c k is assigned to \c s, \c -k is

    /// assigned to \c t and all other nodes have zero supply value.

    ///

    /// \param s The source node.

    /// \param t The target node.

    /// \param k The required amount of flow from node \c s to node \c t

    /// (i.e. the supply of \c s and the demand of \c t).

    ///

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

    CapacityScaling& stSupply(const Node& s, const Node& t, Value k) {

      for (int i = 0; i != _node_num; ++i) {

        _supply[i] = 0;

      }

      _supply[_node_id[s]] =  k;

      _supply[_node_id[t]] = -k;

      return *this;

    }

    /// @}

    /// \name Execution control

    /// The algorithm can be executed using \ref run().

    /// @{

    /// \brief Run the algorithm.

    ///

    /// This function runs the algorithm.

    /// The paramters can be specified using functions \ref lowerMap(),

    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().

    /// For example,

    /// \code

    ///   CapacityScaling<ListDigraph> cs(graph);

    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)

    ///     .supplyMap(sup).run();

    /// \endcode

    ///

    ///

    /// \param factor The capacity scaling factor. It must be larger than

    /// one to use scaling. If it is less or equal to one, then scaling

    /// will be disabled.

    ///

    /// \return \c INFEASIBLE if no feasible flow exists,

    /// \n \c OPTIMAL if the problem has optimal solution

    /// (i.e. it is feasible and bounded), and the algorithm has found

    /// optimal flow and node potentials (primal and dual solutions),

    /// \n \c UNBOUNDED if the digraph contains an arc of negative cost

    /// and infinite upper bound. It means that the objective function

    /// is unbounded on that arc, however, note that it could actually be

    /// bounded over the feasible flows, but this algroithm cannot handle

    /// these cases.

    ///

    /// \see ProblemType

    ProblemType run(int factor = 4) {

      _factor = factor;

      ProblemType pt = init();

      if (pt != OPTIMAL) return pt;

      return start();

    }

    /// \brief Reset all the parameters that have been given before.

    ///

    /// This function resets all the paramaters that have been given

    /// before using functions \ref lowerMap(), \ref upperMap(),

    /// \ref costMap(), \ref supplyMap(), \ref stSupply().

    ///

    ///

    /// For example,

    /// \code

    ///   CapacityScaling<ListDigraph> cs(graph);

    ///

    ///   // First run

    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)

    ///     .supplyMap(sup).run();

    ///

    ///   // so only the cost map have to be set again)

    ///   cost[e] += 100;

    ///   cs.costMap(cost).run();

    ///

    ///   // (the lower bounds will be set to zero on all arcs)

    ///   cs.upperMap(capacity).costMap(cost)

    ///     .supplyMap(sup).run();

    /// \endcode

    ///

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

      for (int i = 0; i != _node_num; ++i) {

        _supply[i] = 0;

      }

      for (int j = 0; j != _res_arc_num; ++j) {

        _lower[j] = 0;

        _upper[j] = INF;

        _cost[j] = _forward[j] ? 1 : -1;

      }

      _have_lower = false;

      return *this;

    }

    /// @}

    /// \name Query Functions

    /// The results of the algorithm can be obtained using these

    /// functions.\n

    /// The \ref run() function must be called before using them.

    /// @{

    /// \brief Return the total cost of the found flow.

    ///

    /// This function returns the total cost of the found flow.

    /// Its complexity is O(e).

    ///

    /// \note The return type of the function can be specified as a

    /// template parameter. For example,

    /// \code

    ///   cs.totalCost<double>();

    /// \endcode

    /// It is useful if the total cost cannot be stored in the \c Cost

    /// type of the algorithm, which is the default return type of the

    /// function.

    ///

    /// \pre \ref run() must be called before using this function.

    template <typename Number>

    Number totalCost() const {

      Number c = 0;

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

        int i = _arc_idb[a];

        c += static_cast<Number>(_res_cap[i]) *

             (-static_cast<Number>(_cost[i]));

      }

      return c;

    }

#ifndef DOXYGEN

    Cost totalCost() const {

      return totalCost<Cost>();

    }

#endif

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

    ///

    /// This function returns the flow on the given arc.

    ///

    /// \pre \ref run() must be called before using this function.

    Value flow(const Arc& a) const {

      return _res_cap[_arc_idb[a]];

    }

    /// \brief Return the flow map (the primal solution).

    ///

    /// This function copies the flow value on each arc into the given

    /// map. The \c Value type of the algorithm must be convertible to

    /// the \c Value type of the map.

    ///

    /// \pre \ref run() must be called before using this function.

    template <typename FlowMap>

    void flowMap(FlowMap &map) const {

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

        map.set(a, _res_cap[_arc_idb[a]]);

      }

    }

    /// \brief Return the potential (dual value) of the given node.

    ///

    /// This function returns the potential (dual value) of the

    /// given node.

    ///

    /// \pre \ref run() must be called before using this function.

    Cost potential(const Node& n) const {

      return _pi[_node_id[n]];

    }

    /// \brief Return the potential map (the dual solution).

    ///

    /// This function copies the potential (dual value) of each node

    /// into the given map.

    /// The \c Cost type of the algorithm must be convertible to the

    /// \c Value type of the map.

    ///

    /// \pre \ref run() must be called before using this function.

    template <typename PotentialMap>

    void potentialMap(PotentialMap &map) const {

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

        map.set(n, _pi[_node_id[n]]);

      }

    }

    /// @}

  private:

    // Initialize the algorithm

    ProblemType init() {

      if (_node_num <= 1) return INFEASIBLE;

      // Check the sum of supply values

      _sum_supply = 0;

      for (int i = 0; i != _root; ++i) {

        _sum_supply += _supply[i];

      }

      if (_sum_supply > 0) return INFEASIBLE;

      // Initialize vectors

      for (int i = 0; i != _root; ++i) {

        _pi[i] = 0;

        _excess[i] = _supply[i];

      }

      // Remove non-zero lower bounds

      const Value MAX = std::numeric_limits<Value>::max();

      int last_out;

      if (_have_lower) {

        for (int i = 0; i != _root; ++i) {

          last_out = _first_out[i+1];

          for (int j = _first_out[i]; j != last_out; ++j) {

            if (_forward[j]) {

              Value c = _lower[j];

              if (c >= 0) {

                _res_cap[j] = _upper[j] < MAX ? _upper[j] - c : INF;

              } else {

                _res_cap[j] = _upper[j] < MAX + c ? _upper[j] - c : INF;

              }

              _excess[i] -= c;

              _excess[_target[j]] += c;

            } else {

              _res_cap[j] = 0;

            }

          }

        }

      } else {

        for (int j = 0; j != _res_arc_num; ++j) {

          _res_cap[j] = _forward[j] ? _upper[j] : 0;

        }

      }

      // Handle negative costs

      for (int i = 0; i != _root; ++i) {

        last_out = _first_out[i+1] - 1;

        for (int j = _first_out[i]; j != last_out; ++j) {

          Value rc = _res_cap[j];

          if (_cost[j] < 0 && rc > 0) {

            if (rc >= MAX) return UNBOUNDED;

            _excess[i] -= rc;

            _excess[_target[j]] += rc;

            _res_cap[j] = 0;

            _res_cap[_reverse[j]] += rc;

          }

        }

      }

      // Handle GEQ supply type

      if (_sum_supply < 0) {

        _pi[_root] = 0;

        _excess[_root] = -_sum_supply;

        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {

          int ra = _reverse[a];

          _res_cap[a] = -_sum_supply + 1;

          _res_cap[ra] = 0;

          _cost[a] = 0;

          _cost[ra] = 0;

        }

      } else {

        _pi[_root] = 0;

        _excess[_root] = 0;

        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {

          int ra = _reverse[a];

          _res_cap[a] = 1;

          _res_cap[ra] = 0;

          _cost[a] = 0;

          _cost[ra] = 0;

        }

      }

      // Initialize delta value

      if (_factor > 1) {

        // With scaling

        Value max_sup = 0, max_dem = 0;

        for (int i = 0; i != _node_num; ++i) {

          Value ex = _excess[i];

          if ( ex > max_sup) max_sup =  ex;

          if (-ex > max_dem) max_dem = -ex;

        }

        Value max_cap = 0;

        for (int j = 0; j != _res_arc_num; ++j) {

          if (_res_cap[j] > max_cap) max_cap = _res_cap[j];

        }

        max_sup = std::min(std::min(max_sup, max_dem), max_cap);

        for (_delta = 1; 2 * _delta <= max_sup; _delta *= 2) ;

      } else {

        // Without scaling

    /// The \ref CostScalingDefaultTraits "traits class" of the algorithm

    typedef TR Traits;

  public:

    /// \brief Problem type constants for the \c run() function.

    ///

    /// Enum type containing the problem type constants that can be

    /// returned by the \ref run() function of the algorithm.

    enum ProblemType {

      /// The problem has no feasible solution (flow).

      INFEASIBLE,

      /// The problem has optimal solution (i.e. it is feasible and

      /// bounded), and the algorithm has found optimal flow and node

      /// potentials (primal and dual solutions).

      OPTIMAL,

      /// The digraph contains an arc of negative cost and infinite

      /// upper bound. It means that the objective function is unbounded

      /// on that arc, however, note that it could actually be bounded

      /// over the feasible flows, but this algroithm cannot handle

      /// these cases.

      UNBOUNDED

    };

    /// \brief Constants for selecting the internal method.

    ///

    /// Enum type containing constants for selecting the internal method

    /// for the \ref run() function.

    ///

    /// \ref CostScaling provides three internal methods that differ mainly

    /// in their base operations, which are used in conjunction with the

    /// relabel operation.

    /// By default, the so called \ref PARTIAL_AUGMENT

    /// "Partial Augment-Relabel" method is used, which proved to be

    /// the most efficient and the most robust on various test inputs.

    /// However, the other methods can be selected using the \ref run()

    /// function with the proper parameter.

    enum Method {

      /// Local push operations are used, i.e. flow is moved only on one

      /// admissible arc at once.

      PUSH,

      /// Augment operations are used, i.e. flow is moved on admissible

      /// paths from a node with excess to a node with deficit.

      AUGMENT,

      /// Partial augment operations are used, i.e. flow is moved on 

      /// admissible paths started from a node with excess, but the

      /// lengths of these paths are limited. This method can be viewed

      /// as a combined version of the previous two operations.

      PARTIAL_AUGMENT

    };

  private:

    TEMPLATE_DIGRAPH_TYPEDEFS(GR);

    typedef std::vector<int> IntVector;

    typedef std::vector<char> BoolVector;

    typedef std::vector<Value> ValueVector;

    typedef std::vector<Cost> CostVector;

    typedef std::vector<LargeCost> LargeCostVector;

  private:

    template <typename KT, typename VT>

    class StaticVectorMap {

    public:

      typedef KT Key;

      typedef VT Value;

      StaticVectorMap(std::vector<Value>& v) : _v(v) {}

      const Value& operator[](const Key& key) const {

        return _v[StaticDigraph::id(key)];

      }

      Value& operator[](const Key& key) {

        return _v[StaticDigraph::id(key)];

      }

      void set(const Key& key, const Value& val) {

        _v[StaticDigraph::id(key)] = val;

      }

    private:

      std::vector<Value>& _v;

    };

    typedef StaticVectorMap<StaticDigraph::Node, LargeCost> LargeCostNodeMap;

    typedef StaticVectorMap<StaticDigraph::Arc, LargeCost> LargeCostArcMap;

  private:

    // Data related to the underlying digraph

    const GR &_graph;

    int _node_num;

    int _arc_num;

    int _res_node_num;

    int _res_arc_num;

    int _root;

    // Parameters of the problem

    bool _have_lower;

    Value _sum_supply;

    // Data structures for storing the digraph

    IntNodeMap _node_id;

    IntArcMap _arc_idf;

    IntArcMap _arc_idb;

    IntVector _first_out;

    BoolVector _forward;

    IntVector _source;

    IntVector _target;

    IntVector _reverse;

    // Node and arc data

    ValueVector _lower;

    ValueVector _upper;

    CostVector _scost;

    ValueVector _supply;

    ValueVector _res_cap;

    LargeCostVector _cost;

    LargeCostVector _pi;

    ValueVector _excess;

    IntVector _next_out;

    std::deque<int> _active_nodes;

    // Data for scaling

    LargeCost _epsilon;

    int _alpha;

    // Data for a StaticDigraph structure

    typedef std::pair<int, int> IntPair;

    StaticDigraph _sgr;

    std::vector<IntPair> _arc_vec;

    std::vector<LargeCost> _cost_vec;

    LargeCostArcMap _cost_map;

    LargeCostNodeMap _pi_map;

  public:

    /// \brief Constant for infinite upper bounds (capacities).

    ///

    /// Constant for infinite upper bounds (capacities).

    /// It is \c std::numeric_limits<Value>::infinity() if available,

    /// \c std::numeric_limits<Value>::max() otherwise.

    const Value INF;

  public:

    /// \name Named Template Parameters

    /// @{

    template <typename T>

    struct SetLargeCostTraits : public Traits {

      typedef T LargeCost;

    };

    /// \brief \ref named-templ-param "Named parameter" for setting

    /// \c LargeCost type.

    ///

    /// \ref named-templ-param "Named parameter" for setting \c LargeCost

    /// type, which is used for internal computations in the algorithm.

    /// \c Cost must be convertible to \c LargeCost.

    template <typename T>

    struct SetLargeCost

      : public CostScaling<GR, V, C, SetLargeCostTraits<T> > {

      typedef  CostScaling<GR, V, C, SetLargeCostTraits<T> > Create;

    };

    /// @}

  public:

    /// \brief Constructor.

    ///

    /// The constructor of the class.

    ///

    /// \param graph The digraph the algorithm runs on.

    CostScaling(const GR& graph) :

      _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph),

      _cost_map(_cost_vec), _pi_map(_pi),

      INF(std::numeric_limits<Value>::has_infinity ?

          std::numeric_limits<Value>::infinity() :

          std::numeric_limits<Value>::max())

    {

      // Check the number types

      LEMON_ASSERT(std::numeric_limits<Value>::is_signed,

        "The flow type of CostScaling must be signed");

      LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,

        "The cost type of CostScaling must be signed");

      reset();

    }

    /// \name Parameters

    /// The parameters of the algorithm can be specified using these

    /// functions.

    /// @{

    /// \brief Set the lower bounds on the arcs.

    ///

    /// This function sets the lower bounds on the arcs.

    /// If it is not used before calling \ref run(), the lower bounds

    /// will be set to zero on all arcs.

    ///

    /// \param map An arc map storing the lower bounds.

    /// Its \c Value type must be convertible to the \c Value type

    /// of the algorithm.

    ///

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

    template <typename LowerMap>

    CostScaling& lowerMap(const LowerMap& map) {

      _have_lower = true;

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

        _lower[_arc_idf[a]] = map[a];

        _lower[_arc_idb[a]] = map[a];

      }

      return *this;

    }

    /// \brief Set the upper bounds (capacities) on the arcs.

    ///

    /// This function sets the upper bounds (capacities) on the arcs.

    /// If it is not used before calling \ref run(), the upper bounds

    /// will be set to \ref INF on all arcs (i.e. the flow value will be

    /// unbounded from above).

    ///

    /// \param map An arc map storing the upper bounds.

    /// Its \c Value type must be convertible to the \c Value type

    /// of the algorithm.

    ///

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

    template<typename UpperMap>

    CostScaling& upperMap(const UpperMap& map) {

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

        _upper[_arc_idf[a]] = map[a];

      }

      return *this;

    }

    /// \brief Set the costs of the arcs.

    ///

    /// This function sets the costs of the arcs.

    /// If it is not used before calling \ref run(), the costs

    /// will be set to \c 1 on all arcs.

    ///

    /// \param map An arc map storing the costs.

    /// Its \c Value type must be convertible to the \c Cost type

    /// of the algorithm.

    ///

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

    template<typename CostMap>

    CostScaling& costMap(const CostMap& map) {

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

        _scost[_arc_idf[a]] =  map[a];

        _scost[_arc_idb[a]] = -map[a];

      }

      return *this;

    }

    /// \brief Set the supply values of the nodes.

    ///

    /// This function sets the supply values of the nodes.

    /// If neither this function nor \ref stSupply() is used before

    /// calling \ref run(), the supply of each node will be set to zero.

    ///

    /// \param map A node map storing the supply values.

    /// Its \c Value type must be convertible to the \c Value type

    /// of the algorithm.

    ///

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

    template<typename SupplyMap>