Changeset 809:22bb98ca0101 in lemon-1.2

Timestamp:

11/12/09 23:30:45 (14 years ago)

Author:

Peter Kovacs <kpeter@…>

Branch:

default

Phase:

public

Rebase:

35333461653237666330353538396562623465656466303531646265343536366333386130366130

Message:

Entirely rework CostScaling? (#180)

• Use the new interface similarly to NetworkSimplex?.
• Rework the implementation using an efficient internal structure for handling the residual network. This improvement made the code much faster.
• Handle GEQ supply type (LEQ is not supported).
• Handle infinite upper bounds.
• Handle negative costs (for arcs of finite upper bound).
• Traits class + named parameter for the LargeCost? type used in internal computations.
• Extend the documentation.

File:

• lemon/cost_scaling.h (modified) (6 diffs)

lemon/cost_scaling.h

@@ -31 +31 @@
 #include <lemon/maps.h>
 #include <lemon/math.h>
-#include <lemon/adaptors.h>
+#include <lemon/static_graph.h>
 #include <lemon/circulation.h>
 #include <lemon/bellman_ford.h>
@@ -37 +37 @@
 namespace lemon {
 
+  /// \brief Default traits class of CostScaling algorithm.
+  ///
+  /// Default traits class of CostScaling algorithm.
+  /// \tparam GR Digraph type.
+  /// \tparam V The value type used for flow amounts, capacity bounds
+  /// and supply values. By default it is \c int.
+  /// \tparam C The value type used for costs and potentials.
+  /// By default it is the same as \c V.
+#ifdef DOXYGEN
+  template <typename GR, typename V = int, typename C = V>
+#else
+  template < typename GR, typename V = int, typename C = V,
+             bool integer = std::numeric_limits<C>::is_integer >
+#endif
+  struct CostScalingDefaultTraits
+  {
+    /// The type of the digraph
+    typedef GR Digraph;
+    /// The type of the flow amounts, capacity bounds and supply values
+    typedef V Value;
+    /// The type of the arc costs
+    typedef C Cost;
+
+    /// \brief The large cost type used for internal computations
+    ///
+    /// The large cost type used for internal computations.
+    /// It is \c long \c long if the \c Cost type is integer,
+    /// otherwise it is \c double.
+    /// \c Cost must be convertible to \c LargeCost.
+    typedef double LargeCost;
+  };
+
+  // Default traits class for integer cost types
+  template <typename GR, typename V, typename C>
+  struct CostScalingDefaultTraits<GR, V, C, true>
+  {
+    typedef GR Digraph;
+    typedef V Value;
+    typedef C Cost;
+#ifdef LEMON_HAVE_LONG_LONG
+    typedef long long LargeCost;
+#else
+    typedef long LargeCost;
+#endif
+  };
+
+
   /// \addtogroup min_cost_flow_algs
   /// @{
 
-  /// \brief Implementation of the cost scaling algorithm for finding a
-  /// minimum cost flow.
+  /// \brief Implementation of the Cost Scaling algorithm for
+  /// finding a \ref min_cost_flow "minimum cost flow".
   ///
-  /// \ref CostScaling implements the cost scaling algorithm performing
-  /// augment/push and relabel operations for finding a minimum cost
-  /// flow.
+  /// \ref CostScaling implements a cost scaling algorithm that performs
+  /// push/augment and relabel operations for finding a minimum cost
+  /// flow. It is an efficient primal-dual solution method, which
+  /// can be viewed as the generalization of the \ref Preflow
+  /// "preflow push-relabel" algorithm for the maximum flow problem.
   ///
-  /// \tparam Digraph The digraph type the algorithm runs on.
-  /// \tparam LowerMap The type of the lower bound map.
-  /// \tparam CapacityMap The type of the capacity (upper bound) map.
-  /// \tparam CostMap The type of the cost (length) map.
-  /// \tparam SupplyMap The type of the supply map.
+  /// Most of the parameters of the problem (except for the digraph)
+  /// can be given using separate functions, and the algorithm can be
+  /// executed using the \ref run() function. If some parameters are not
+  /// specified, then default values will be used.
   ///
-  /// \warning
-  /// - Arc capacities and costs should be \e non-negative \e integers.
-  /// - Supply values should be \e signed \e integers.
-  /// - The value types of the maps should be convertible to each other.
-  /// - \c CostMap::Value must be signed type.
+  /// \tparam GR The digraph type the algorithm runs on.
+  /// \tparam V The value type used for flow amounts, capacity bounds
+  /// and supply values in the algorithm. By default it is \c int.
+  /// \tparam C The value type used for costs and potentials in the
+  /// algorithm. By default it is the same as \c V.
   ///
-  /// \note Arc costs are multiplied with the number of nodes during
-  /// the algorithm so overflow problems may arise more easily than with
-  /// other minimum cost flow algorithms.
-  /// If it is available, <tt>long long int</tt> type is used instead of
-  /// <tt>long int</tt> in the inside computations.
-  ///
-  /// \author Peter Kovacs
-  template < typename Digraph,
-             typename LowerMap = typename Digraph::template ArcMap<int>,
-             typename CapacityMap = typename Digraph::template ArcMap<int>,
-             typename CostMap = typename Digraph::template ArcMap<int>,
-             typename SupplyMap = typename Digraph::template NodeMap<int> >
+  /// \warning Both value types must be signed and all input data must
+  /// be integer.
+  /// \warning This algorithm does not support negative costs for such
+  /// arcs that have infinite upper bound.
+#ifdef DOXYGEN
+  template <typename GR, typename V, typename C, typename TR>
+#else
+  template < typename GR, typename V = int, typename C = V,
+             typename TR = CostScalingDefaultTraits<GR, V, C> >
+#endif
   class CostScaling
   {
-    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
-
-    typedef typename CapacityMap::Value Capacity;
-    typedef typename CostMap::Value Cost;
-    typedef typename SupplyMap::Value Supply;
-    typedef typename Digraph::template ArcMap<Capacity> CapacityArcMap;
-    typedef typename Digraph::template NodeMap<Supply> SupplyNodeMap;
-
-    typedef ResidualDigraph< const Digraph,
-                             CapacityArcMap, CapacityArcMap > ResDigraph;
-    typedef typename ResDigraph::Arc ResArc;
-
-#if defined __GNUC__ && !defined __STRICT_ANSI__
-    typedef long long int LCost;
-#else
-    typedef long int LCost;
-#endif
-    typedef typename Digraph::template ArcMap<LCost> LargeCostMap;
-
   public:
 
-    /// The type of the flow map.
-    typedef typename Digraph::template ArcMap<Capacity> FlowMap;
-    /// The type of the potential map.
-    typedef typename Digraph::template NodeMap<LCost> PotentialMap;
+    /// The type of the digraph
+    typedef typename TR::Digraph Digraph;
+    /// The type of the flow amounts, capacity bounds and supply values
+    typedef typename TR::Value Value;
+    /// The type of the arc costs
+    typedef typename TR::Cost Cost;
+
+    /// \brief The large cost type
+    ///
+    /// The large cost type used for internal computations.
+    /// Using the \ref CostScalingDefaultTraits "default traits class",
+    /// it is \c long \c long if the \c Cost type is integer,
+    /// otherwise it is \c double.
+    typedef typename TR::LargeCost LargeCost;
+
+    /// 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
+    };
 
   private:
 
-    /// \brief Map adaptor class for handling residual arc costs.
-    ///
-    /// Map adaptor class for handling residual arc costs.
-    template <typename Map>
-    class ResidualCostMap : public MapBase<ResArc, typename Map::Value>
+    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 VectorMap {
+    public:
+      typedef KT Key;
+      typedef VT Value;
+      
+      VectorMap(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 VectorMap<StaticDigraph::Node, LargeCost> LargeCostNodeMap;
+    typedef VectorMap<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())
     {
-    private:
-
-      const Map &_cost_map;
-
-    public:
-
-      ///\e
-      ResidualCostMap(const Map &cost_map) :
-        _cost_map(cost_map) {}
-
-      ///\e
-      inline typename Map::Value operator[](const ResArc &e) const {
-        return ResDigraph::forward(e) ? _cost_map[e] : -_cost_map[e];
-      }
-
-    }; //class ResidualCostMap
-
-    /// \brief Map adaptor class for handling reduced arc costs.
-    ///
-    /// Map adaptor class for handling reduced arc costs.
-    class ReducedCostMap : public MapBase<Arc, LCost>
-    {
-    private:
-
-      const Digraph &_gr;
-      const LargeCostMap &_cost_map;
-      const PotentialMap &_pot_map;
-
-    public:
-
-      ///\e
-      ReducedCostMap( const Digraph &gr,
-                      const LargeCostMap &cost_map,
-                      const PotentialMap &pot_map ) :
-        _gr(gr), _cost_map(cost_map), _pot_map(pot_map) {}
-
-      ///\e
-      inline LCost operator[](const Arc &e) const {
-        return _cost_map[e] + _pot_map[_gr.source(e)]
-                            - _pot_map[_gr.target(e)];
-      }
-
-    }; //class ReducedCostMap
-
-  private:
-
-    // The digraph the algorithm runs on
-    const Digraph &_graph;
-    // The original lower bound map
-    const LowerMap *_lower;
-    // The modified capacity map
-    CapacityArcMap _capacity;
-    // The original cost map
-    const CostMap &_orig_cost;
-    // The scaled cost map
-    LargeCostMap _cost;
-    // The modified supply map
-    SupplyNodeMap _supply;
-    bool _valid_supply;
-
-    // Arc map of the current flow
-    FlowMap *_flow;
-    bool _local_flow;
-    // Node map of the current potentials
-    PotentialMap *_potential;
-    bool _local_potential;
-
-    // The residual cost map
-    ResidualCostMap<LargeCostMap> _res_cost;
-    // The residual digraph
-    ResDigraph *_res_graph;
-    // The reduced cost map
-    ReducedCostMap *_red_cost;
-    // The excess map
-    SupplyNodeMap _excess;
-    // The epsilon parameter used for cost scaling
-    LCost _epsilon;
-    // The scaling factor
-    int _alpha;
-
-  public:
-
-    /// \brief General constructor (with lower bounds).
-    ///
-    /// General constructor (with lower bounds).
-    ///
-    /// \param digraph The digraph the algorithm runs on.
-    /// \param lower The lower bounds of the arcs.
-    /// \param capacity The capacities (upper bounds) of the arcs.
-    /// \param cost The cost (length) values of the arcs.
-    /// \param supply The supply values of the nodes (signed).
-    CostScaling( const Digraph &digraph,
-                 const LowerMap &lower,
-                 const CapacityMap &capacity,
-                 const CostMap &cost,
-                 const SupplyMap &supply ) :
-      _graph(digraph), _lower(&lower), _capacity(digraph), _orig_cost(cost),
-      _cost(digraph), _supply(digraph), _flow(NULL), _local_flow(false),
-      _potential(NULL), _local_potential(false), _res_cost(_cost),
-      _res_graph(NULL), _red_cost(NULL), _excess(digraph, 0)
-    {
-      // Check the sum of supply values
-      Supply sum = 0;
-      for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n];
-      _valid_supply = sum == 0;
+      // Check the value 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");
+
+      // Resize vectors
+      _node_num = countNodes(_graph);
+      _arc_num = countArcs(_graph);
+      _res_node_num = _node_num + 1;
+      _res_arc_num = 2 * (_arc_num + _node_num);
+      _root = _node_num;
+
+      _first_out.resize(_res_node_num + 1);
+      _forward.resize(_res_arc_num);
+      _source.resize(_res_arc_num);
+      _target.resize(_res_arc_num);
+      _reverse.resize(_res_arc_num);
+
+      _lower.resize(_res_arc_num);
+      _upper.resize(_res_arc_num);
+      _scost.resize(_res_arc_num);
+      _supply.resize(_res_node_num);
       
-      for (ArcIt e(_graph); e != INVALID; ++e) _capacity[e] = capacity[e];
-      for (NodeIt n(_graph); n != INVALID; ++n) _supply[n] = supply[n];
-
-      // Remove non-zero lower bounds
-      for (ArcIt e(_graph); e != INVALID; ++e) {
-        if (lower[e] != 0) {
-          _capacity[e] -= lower[e];
-          _supply[_graph.source(e)] -= lower[e];
-          _supply[_graph.target(e)] += lower[e];
-        }
-      }
-    }
-/*
-    /// \brief General constructor (without lower bounds).
-    ///
-    /// General constructor (without lower bounds).
-    ///
-    /// \param digraph The digraph the algorithm runs on.
-    /// \param capacity The capacities (upper bounds) of the arcs.
-    /// \param cost The cost (length) values of the arcs.
-    /// \param supply The supply values of the nodes (signed).
-    CostScaling( const Digraph &digraph,
-                 const CapacityMap &capacity,
-                 const CostMap &cost,
-                 const SupplyMap &supply ) :
-      _graph(digraph), _lower(NULL), _capacity(capacity), _orig_cost(cost),
-      _cost(digraph), _supply(supply), _flow(NULL), _local_flow(false),
-      _potential(NULL), _local_potential(false), _res_cost(_cost),
-      _res_graph(NULL), _red_cost(NULL), _excess(digraph, 0)
-    {
-      // Check the sum of supply values
-      Supply sum = 0;
-      for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n];
-      _valid_supply = sum == 0;
-    }
-
-    /// \brief Simple constructor (with lower bounds).
-    ///
-    /// Simple constructor (with lower bounds).
-    ///
-    /// \param digraph The digraph the algorithm runs on.
-    /// \param lower The lower bounds of the arcs.
-    /// \param capacity The capacities (upper bounds) of the arcs.
-    /// \param cost The cost (length) values of the arcs.
+      _res_cap.resize(_res_arc_num);
+      _cost.resize(_res_arc_num);
+      _pi.resize(_res_node_num);
+      _excess.resize(_res_node_num);
+      _next_out.resize(_res_node_num);
+
+      _arc_vec.reserve(_res_arc_num);
+      _cost_vec.reserve(_res_arc_num);
+
+      // Copy the graph
+      int i = 0, j = 0, k = 2 * _arc_num + _node_num;
+      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
+        _node_id[n] = i;
+      }
+      i = 0;
+      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
+        _first_out[i] = j;
+        for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) {
+          _arc_idf[a] = j;
+          _forward[j] = true;
+          _source[j] = i;
+          _target[j] = _node_id[_graph.runningNode(a)];
+        }
+        for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) {
+          _arc_idb[a] = j;
+          _forward[j] = false;
+          _source[j] = i;
+          _target[j] = _node_id[_graph.runningNode(a)];
+        }
+        _forward[j] = false;
+        _source[j] = i;
+        _target[j] = _root;
+        _reverse[j] = k;
+        _forward[k] = true;
+        _source[k] = _root;
+        _target[k] = i;
+        _reverse[k] = j;
+        ++j; ++k;
+      }
+      _first_out[i] = j;
+      _first_out[_res_node_num] = k;
+      for (ArcIt a(_graph); a != INVALID; ++a) {
+        int fi = _arc_idf[a];
+        int bi = _arc_idb[a];
+        _reverse[fi] = bi;
+        _reverse[bi] = fi;
+      }
+      
+      // Reset parameters
+      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 on each arc).
+    ///
+    /// \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>
+    CostScaling& 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 flow_value 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).
-    CostScaling( const Digraph &digraph,
-                 const LowerMap &lower,
-                 const CapacityMap &capacity,
-                 const CostMap &cost,
-                 Node s, Node t,
-                 Supply flow_value ) :
-      _graph(digraph), _lower(&lower), _capacity(capacity), _orig_cost(cost),
-      _cost(digraph), _supply(digraph, 0), _flow(NULL), _local_flow(false),
-      _potential(NULL), _local_potential(false), _res_cost(_cost),
-      _res_graph(NULL), _red_cost(NULL), _excess(digraph, 0)
-    {
-      // Remove non-zero lower bounds
-      _supply[s] =  flow_value;
-      _supply[t] = -flow_value;
-      for (ArcIt e(_graph); e != INVALID; ++e) {
-        if (lower[e] != 0) {
-          _capacity[e] -= lower[e];
-          _supply[_graph.source(e)] -= lower[e];
-          _supply[_graph.target(e)] += lower[e];
-        }
-      }
-      _valid_supply = true;
-    }
-
-    /// \brief Simple constructor (without lower bounds).
-    ///
-    /// Simple constructor (without lower bounds).
-    ///
-    /// \param digraph The digraph the algorithm runs on.
-    /// \param capacity The capacities (upper bounds) of the arcs.
-    /// \param cost The cost (length) values of the arcs.
-    /// \param s The source node.
-    /// \param t The target node.
-    /// \param flow_value 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).
-    CostScaling( const Digraph &digraph,
-                 const CapacityMap &capacity,
-                 const CostMap &cost,
-                 Node s, Node t,
-                 Supply flow_value ) :
-      _graph(digraph), _lower(NULL), _capacity(capacity), _orig_cost(cost),
-      _cost(digraph), _supply(digraph, 0), _flow(NULL), _local_flow(false),
-      _potential(NULL), _local_potential(false), _res_cost(_cost),
-      _res_graph(NULL), _red_cost(NULL), _excess(digraph, 0)
-    {
-      _supply[s] =  flow_value;
-      _supply[t] = -flow_value;
-      _valid_supply = true;
-    }
-*/
-    /// Destructor.
-    ~CostScaling() {
-      if (_local_flow) delete _flow;
-      if (_local_potential) delete _potential;
-      delete _res_graph;
-      delete _red_cost;
-    }
-
-    /// \brief Set the flow map.
-    ///
-    /// Set the flow map.
-    ///
-    /// \return \c (*this)
-    CostScaling& flowMap(FlowMap &map) {
-      if (_local_flow) {
-        delete _flow;
-        _local_flow = false;
-      }
-      _flow = &map;
+    /// \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>
+    CostScaling& stSupply(const Node& s, const Node& t, Value k) {
+      for (int i = 0; i != _res_node_num; ++i) {
+        _supply[i] = 0;
+      }
+      _supply[_node_id[s]] =  k;
+      _supply[_node_id[t]] = -k;
       return *this;
     }
-
-    /// \brief Set the potential map.
-    ///
-    /// Set the potential map.
-    ///
-    /// \return \c (*this)
-    CostScaling& potentialMap(PotentialMap &map) {
-      if (_local_potential) {
-        delete _potential;
-        _local_potential = false;
-      }
-      _potential = &map;
-      return *this;
-    }
+    
+    /// @}
 
     /// \name Execution control
+    /// The algorithm can be executed using \ref run().
 
     /// @{
@@ -353 +492 @@
     /// \brief Run the algorithm.
     ///
-    /// 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
+    ///   CostScaling<ListDigraph> cs(graph);
+    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
+    ///     .supplyMap(sup).run();
+    /// \endcode
+    ///
+    /// This function can be called more than once. All the parameters
+    /// that have been given are kept for the next call, unless
+    /// \ref reset() is called, thus only the modified parameters
+    /// have to be set again. See \ref reset() for examples.
+    /// However the underlying digraph must not be modified after this
+    /// class have been constructed, since it copies the digraph.
     ///
     /// \param partial_augment By default the algorithm performs
@@ -360 +514 @@
     /// relabel operations instead.
     ///
-    /// \return \c true if a feasible flow can be found.
-    bool run(bool partial_augment = true) {
+    /// \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(bool partial_augment = true) {
+      ProblemType pt = init();
+      if (pt != OPTIMAL) return pt;
+      start(partial_augment);
+      return OPTIMAL;
+    }
+
+    /// \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().
+    ///
+    /// It is useful for multiple run() calls. If this function is not
+    /// used, all the parameters given before are kept for the next
+    /// \ref run() call.
+    /// However the underlying digraph must not be modified after this
+    /// class have been constructed, since it copies and extends the graph.
+    ///
+    /// For example,
+    /// \code
+    ///   CostScaling<ListDigraph> cs(graph);
+    ///
+    ///   // First run
+    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
+    ///     .supplyMap(sup).run();
+    ///
+    ///   // Run again with modified cost map (reset() is not called,
+    ///   // so only the cost map have to be set again)
+    ///   cost[e] += 100;
+    ///   cs.costMap(cost).run();
+    ///
+    ///   // Run again from scratch using reset()
+    ///   // (the lower bounds will be set to zero on all arcs)
+    ///   cs.reset();
+    ///   cs.upperMap(capacity).costMap(cost)
+    ///     .supplyMap(sup).run();
+    /// \endcode
+    ///
+    /// \return <tt>(*this)</tt>
+    CostScaling& reset() {
+      for (int i = 0; i != _res_node_num; ++i) {
+        _supply[i] = 0;
+      }
+      int limit = _first_out[_root];
+      for (int j = 0; j != limit; ++j) {
+        _lower[j] = 0;
+        _upper[j] = INF;
+        _scost[j] = _forward[j] ? 1 : -1;
+      }
+      for (int j = limit; j != _res_arc_num; ++j) {
+        _lower[j] = 0;
+        _upper[j] = INF;
+        _scost[j] = 0;
+        _scost[_reverse[j]] = 0;
+      }      
+      _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>(_scost[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 static_cast<Cost>(_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, static_cast<Cost>(_pi[_node_id[n]]));
+      }
+    }
+
+    /// @}
+
+  private:
+
+    // Initialize the algorithm
+    ProblemType init() {
+      if (_res_node_num == 0) return INFEASIBLE;
+
+      // Scaling factor
+      _alpha = 8;
+
+      // 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 != _res_node_num; ++i) {
+        _pi[i] = 0;
+        _excess[i] = _supply[i];
+      }
+      
+      // Remove infinite upper bounds and check negative arcs
+      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 = _scost[j] < 0 ? _upper[j] : _lower[j];
+              if (c >= MAX) return UNBOUNDED;
+              _excess[i] -= c;
+              _excess[_target[j]] += c;
+            }
+          }
+        }
+      } else {
+        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] && _scost[j] < 0) {
+              Value c = _upper[j];
+              if (c >= MAX) return UNBOUNDED;
+              _excess[i] -= c;
+              _excess[_target[j]] += c;
+            }
+          }
+        }
+      }
+      Value ex, max_cap = 0;
+      for (int i = 0; i != _res_node_num; ++i) {
+        ex = _excess[i];
+        _excess[i] = 0;
+        if (ex < 0) max_cap -= ex;
+      }
+      for (int j = 0; j != _res_arc_num; ++j) {
+        if (_upper[j] >= MAX) _upper[j] = max_cap;
+      }
+
+      // Initialize the large cost vector and the epsilon parameter
+      _epsilon = 0;
+      LargeCost lc;
+      for (int i = 0; i != _root; ++i) {
+        last_out = _first_out[i+1];
+        for (int j = _first_out[i]; j != last_out; ++j) {
+          lc = static_cast<LargeCost>(_scost[j]) * _res_node_num * _alpha;
+          _cost[j] = lc;
+          if (lc > _epsilon) _epsilon = lc;
+        }
+      }
+      _epsilon /= _alpha;
+
+      // Initialize maps for Circulation and remove non-zero lower bounds
+      ConstMap<Arc, Value> low(0);
+      typedef typename Digraph::template ArcMap<Value> ValueArcMap;
+      typedef typename Digraph::template NodeMap<Value> ValueNodeMap;
+      ValueArcMap cap(_graph), flow(_graph);
+      ValueNodeMap sup(_graph);
+      for (NodeIt n(_graph); n != INVALID; ++n) {
+        sup[n] = _supply[_node_id[n]];
+      }
+      if (_have_lower) {
+        for (ArcIt a(_graph); a != INVALID; ++a) {
+          int j = _arc_idf[a];
+          Value c = _lower[j];
+          cap[a] = _upper[j] - c;
+          sup[_graph.source(a)] -= c;
+          sup[_graph.target(a)] += c;
+        }
+      } else {
+        for (ArcIt a(_graph); a != INVALID; ++a) {
+          cap[a] = _upper[_arc_idf[a]];
+        }
+      }
+
+      // Find a feasible flow using Circulation
+      Circulation<Digraph, ConstMap<Arc, Value>, ValueArcMap, ValueNodeMap>
+        circ(_graph, low, cap, sup);
+      if (!circ.flowMap(flow).run()) return INFEASIBLE;
+
+      // Set residual capacities and handle GEQ supply type
+      if (_sum_supply < 0) {
+        for (ArcIt a(_graph); a != INVALID; ++a) {
+          Value fa = flow[a];
+          _res_cap[_arc_idf[a]] = cap[a] - fa;
+          _res_cap[_arc_idb[a]] = fa;
+          sup[_graph.source(a)] -= fa;
+          sup[_graph.target(a)] += fa;
+        }
+        for (NodeIt n(_graph); n != INVALID; ++n) {
+          _excess[_node_id[n]] = sup[n];
+        }
+        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
+          int u = _target[a];
+          int ra = _reverse[a];
+          _res_cap[a] = -_sum_supply + 1;
+          _res_cap[ra] = -_excess[u];
+          _cost[a] = 0;
+          _cost[ra] = 0;
+          _excess[u] = 0;
+        }
+      } else {
+        for (ArcIt a(_graph); a != INVALID; ++a) {
+          Value fa = flow[a];
+          _res_cap[_arc_idf[a]] = cap[a] - fa;
+          _res_cap[_arc_idb[a]] = fa;
+        }
+        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;
+        }
+      }
+      
+      return OPTIMAL;
+    }
+
+    // Execute the algorithm and transform the results
+    void start(bool partial_augment) {
+      // Execute the algorithm
       if (partial_augment) {
-        return init() && startPartialAugment();
+        startPartialAugment();
       } else {
-        return init() && startPushRelabel();
-      }
-    }
-
-    /// @}
-
-    /// \name Query Functions
-    /// The result of the algorithm can be obtained using these
-    /// functions.\n
-    /// \ref lemon::CostScaling::run() "run()" must be called before
-    /// using them.
-
-    /// @{
-
-    /// \brief Return a const reference to the arc map storing the
-    /// found flow.
-    ///
-    /// Return a const reference to the arc map storing the found flow.
-    ///
-    /// \pre \ref run() must be called before using this function.
-    const FlowMap& flowMap() const {
-      return *_flow;
-    }
-
-    /// \brief Return a const reference to the node map storing the
-    /// found potentials (the dual solution).
-    ///
-    /// Return a const reference to the node map storing the found
-    /// potentials (the dual solution).
-    ///
-    /// \pre \ref run() must be called before using this function.
-    const PotentialMap& potentialMap() const {
-      return *_potential;
-    }
-
-    /// \brief Return the flow on the given arc.
-    ///
-    /// Return the flow on the given arc.
-    ///
-    /// \pre \ref run() must be called before using this function.
-    Capacity flow(const Arc& arc) const {
-      return (*_flow)[arc];
-    }
-
-    /// \brief Return the potential of the given node.
-    ///
-    /// Return the potential of the given node.
-    ///
-    /// \pre \ref run() must be called before using this function.
-    Cost potential(const Node& node) const {
-      return (*_potential)[node];
-    }
-
-    /// \brief Return the total cost of the found flow.
-    ///
-    /// Return the total cost of the found flow. The complexity of the
-    /// function is \f$ O(e) \f$.
-    ///
-    /// \pre \ref run() must be called before using this function.
-    Cost totalCost() const {
-      Cost c = 0;
-      for (ArcIt e(_graph); e != INVALID; ++e)
-        c += (*_flow)[e] * _orig_cost[e];
-      return c;
-    }
-
-    /// @}
-
-  private:
-
-    /// Initialize the algorithm.
-    bool init() {
-      if (!_valid_supply) return false;
-      // The scaling factor
-      _alpha = 8;
-
-      // Initialize flow and potential maps
-      if (!_flow) {
-        _flow = new FlowMap(_graph);
-        _local_flow = true;
-      }
-      if (!_potential) {
-        _potential = new PotentialMap(_graph);
-        _local_potential = true;
-      }
-
-      _red_cost = new ReducedCostMap(_graph, _cost, *_potential);
-      _res_graph = new ResDigraph(_graph, _capacity, *_flow);
-
-      // Initialize the scaled cost map and the epsilon parameter
-      Cost max_cost = 0;
-      int node_num = countNodes(_graph);
-      for (ArcIt e(_graph); e != INVALID; ++e) {
-        _cost[e] = LCost(_orig_cost[e]) * node_num * _alpha;
-        if (_orig_cost[e] > max_cost) max_cost = _orig_cost[e];
-      }
-      _epsilon = max_cost * node_num;
-
-      // Find a feasible flow using Circulation
-      Circulation< Digraph, ConstMap<Arc, Capacity>, CapacityArcMap,
-                   SupplyMap >
-        circulation( _graph, constMap<Arc>(Capacity(0)), _capacity,
-                     _supply );
-      return circulation.flowMap(*_flow).run();
+        startPushRelabel();
+      }
+
+      // Compute node potentials for the original costs
+      _arc_vec.clear();
+      _cost_vec.clear();
+      for (int j = 0; j != _res_arc_num; ++j) {
+        if (_res_cap[j] > 0) {
+          _arc_vec.push_back(IntPair(_source[j], _target[j]));
+          _cost_vec.push_back(_scost[j]);
+        }
+      }
+      _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end());
+
+      typename BellmanFord<StaticDigraph, LargeCostArcMap>
+        ::template SetDistMap<LargeCostNodeMap>::Create bf(_sgr, _cost_map);
+      bf.distMap(_pi_map);
+      bf.init(0);
+      bf.start();
+
+      // Handle non-zero lower bounds
+      if (_have_lower) {
+        int limit = _first_out[_root];
+        for (int j = 0; j != limit; ++j) {
+          if (!_forward[j]) _res_cap[j] += _lower[j];
+        }
+      }
     }
 
     /// Execute the algorithm performing partial augmentation and
-    /// relabel operations.
-    bool startPartialAugment() {
+    /// relabel operations
+    void startPartialAugment() {
       // Paramters for heuristics
-//      const int BF_HEURISTIC_EPSILON_BOUND = 1000;
-//      const int BF_HEURISTIC_BOUND_FACTOR  = 3;
+      const int BF_HEURISTIC_EPSILON_BOUND = 1000;
+      const int BF_HEURISTIC_BOUND_FACTOR  = 3;
       // Maximum augment path length
       const int MAX_PATH_LENGTH = 4;
 
-      // Variables
-      typename Digraph::template NodeMap<Arc> pred_arc(_graph);
-      typename Digraph::template NodeMap<bool> forward(_graph);
-      typename Digraph::template NodeMap<OutArcIt> next_out(_graph);
-      typename Digraph::template NodeMap<InArcIt> next_in(_graph);
-      typename Digraph::template NodeMap<bool> next_dir(_graph);
-      std::deque<Node> active_nodes;
-      std::vector<Node> path_nodes;
-
-//      int node_num = countNodes(_graph);
+      // Perform cost scaling phases
+      IntVector pred_arc(_res_node_num);
+      std::vector<int> path_nodes;
       for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
                                         1 : _epsilon / _alpha )
       {
-/*
         // "Early Termination" heuristic: use Bellman-Ford algorithm
         // to check if the current flow is optimal
         if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) {
-          typedef ShiftMap< ResidualCostMap<LargeCostMap> > ShiftCostMap;
-          ShiftCostMap shift_cost(_res_cost, 1);
-          BellmanFord<ResDigraph, ShiftCostMap> bf(*_res_graph, shift_cost);
+          _arc_vec.clear();
+          _cost_vec.clear();
+          for (int j = 0; j != _res_arc_num; ++j) {
+            if (_res_cap[j] > 0) {
+              _arc_vec.push_back(IntPair(_source[j], _target[j]));
+              _cost_vec.push_back(_cost[j] + 1);
+            }
+          }
+          _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end());
+
+          BellmanFord<StaticDigraph, LargeCostArcMap> bf(_sgr, _cost_map);
           bf.init(0);
           bool done = false;
-          int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(node_num));
+          int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(_res_node_num));
           for (int i = 0; i < K && !done; ++i)
             done = bf.processNextWeakRound();
           if (done) break;
         }
-*/
+
         // Saturate arcs not satisfying the optimality condition
-        Capacity delta;
-        for (ArcIt e(_graph); e != INVALID; ++e) {
-          if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) {
-            delta = _capacity[e] - (*_flow)[e];
-            _excess[_graph.source(e)] -= delta;
-            _excess[_graph.target(e)] += delta;
-            (*_flow)[e] = _capacity[e];
+        for (int a = 0; a != _res_arc_num; ++a) {
+          if (_res_cap[a] > 0 &&
+              _cost[a] + _pi[_source[a]] - _pi[_target[a]] < 0) {
+            Value delta = _res_cap[a];
+            _excess[_source[a]] -= delta;
+            _excess[_target[a]] += delta;
+            _res_cap[a] = 0;
+            _res_cap[_reverse[a]] += delta;
           }
-          if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) {
-            _excess[_graph.target(e)] -= (*_flow)[e];
-            _excess[_graph.source(e)] += (*_flow)[e];
-            (*_flow)[e] = 0;
+        }
+        
+        // Find active nodes (i.e. nodes with positive excess)
+        for (int u = 0; u != _res_node_num; ++u) {
+          if (_excess[u] > 0) _active_nodes.push_back(u);
+        }
+
+        // Initialize the next arcs
+        for (int u = 0; u != _res_node_num; ++u) {
+          _next_out[u] = _first_out[u];
+        }
+
+        // Perform partial augment and relabel operations
+        while (true) {
+          // Select an active node (FIFO selection)
+          while (_active_nodes.size() > 0 &&
+                 _excess[_active_nodes.front()] <= 0) {
+            _active_nodes.pop_front();
           }
-        }
-
-        // Find active nodes (i.e. nodes with positive excess)
-        for (NodeIt n(_graph); n != INVALID; ++n) {
-          if (_excess[n] > 0) active_nodes.push_back(n);
-        }
-
-        // Initialize the next arc maps
-        for (NodeIt n(_graph); n != INVALID; ++n) {
-          next_out[n] = OutArcIt(_graph, n);
-          next_in[n] = InArcIt(_graph, n);
-          next_dir[n] = true;
-        }
-
-        // Perform partial augment and relabel operations
-        while (active_nodes.size() > 0) {
-          // Select an active node (FIFO selection)
-          if (_excess[active_nodes[0]] <= 0) {
-            active_nodes.pop_front();
-            continue;
-          }
-          Node start = active_nodes[0];
+          if (_active_nodes.size() == 0) break;
+          int start = _active_nodes.front();
           path_nodes.clear();
           path_nodes.push_back(start);
 
           // Find an augmenting path from the start node
-          Node u, tip = start;
-          LCost min_red_cost;
-          while ( _excess[tip] >= 0 &&
-                  int(path_nodes.size()) <= MAX_PATH_LENGTH )
-          {
-            if (next_dir[tip]) {
-              for (OutArcIt e = next_out[tip]; e != INVALID; ++e) {
-                if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) {
-                  u = _graph.target(e);
-                  pred_arc[u] = e;
-                  forward[u] = true;
-                  next_out[tip] = e;
-                  tip = u;
-                  path_nodes.push_back(tip);
-                  goto next_step;
-                }
-              }
-              next_dir[tip] = false;
-            }
-            for (InArcIt e = next_in[tip]; e != INVALID; ++e) {
-              if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) {
-                u = _graph.source(e);
-                pred_arc[u] = e;
-                forward[u] = false;
-                next_in[tip] = e;
+          int tip = start;
+          while (_excess[tip] >= 0 &&
+                 int(path_nodes.size()) <= MAX_PATH_LENGTH) {
+            int u;
+            LargeCost min_red_cost, rc;
+            int last_out = _sum_supply < 0 ?
+              _first_out[tip+1] : _first_out[tip+1] - 1;
+            for (int a = _next_out[tip]; a != last_out; ++a) {
+              if (_res_cap[a] > 0 &&
+                  _cost[a] + _pi[_source[a]] - _pi[_target[a]] < 0) {
+                u = _target[a];
+                pred_arc[u] = a;
+                _next_out[tip] = a;
                 tip = u;
                 path_nodes.push_back(tip);
@@ -580 +944 @@
 
             // Relabel tip node
-            min_red_cost = std::numeric_limits<LCost>::max() / 2;
-            for (OutArcIt oe(_graph, tip); oe != INVALID; ++oe) {
-              if ( _capacity[oe] - (*_flow)[oe] > 0 &&
-                   (*_red_cost)[oe] < min_red_cost )
-                min_red_cost = (*_red_cost)[oe];
+            min_red_cost = std::numeric_limits<LargeCost>::max() / 2;
+            for (int a = _first_out[tip]; a != last_out; ++a) {
+              rc = _cost[a] + _pi[_source[a]] - _pi[_target[a]];
+              if (_res_cap[a] > 0 && rc < min_red_cost) {
+                min_red_cost = rc;
+              }
             }
-            for (InArcIt ie(_graph, tip); ie != INVALID; ++ie) {
-              if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < min_red_cost)
-                min_red_cost = -(*_red_cost)[ie];
-            }
-            (*_potential)[tip] -= min_red_cost + _epsilon;
-
-            // Reset the next arc maps
-            next_out[tip] = OutArcIt(_graph, tip);
-            next_in[tip] = InArcIt(_graph, tip);
-            next_dir[tip] = true;
+            _pi[tip] -= min_red_cost + _epsilon;
+
+            // Reset the next arc of tip
+            _next_out[tip] = _first_out[tip];
 
             // Step back
             if (tip != start) {
               path_nodes.pop_back();
-              tip = path_nodes[path_nodes.size()-1];
+              tip = path_nodes.back();
             }
 
-          next_step:
-            continue;
+          next_step: ;
           }
 
           // Augment along the found path (as much flow as possible)
-          Capacity delta;
+          Value delta;
+          int u, v = path_nodes.front(), pa;
           for (int i = 1; i < int(path_nodes.size()); ++i) {
-            u = path_nodes[i];
-            delta = forward[u] ?
-              _capacity[pred_arc[u]] - (*_flow)[pred_arc[u]] :
-              (*_flow)[pred_arc[u]];
-            delta = std::min(delta, _excess[path_nodes[i-1]]);
-            (*_flow)[pred_arc[u]] += forward[u] ? delta : -delta;
-            _excess[path_nodes[i-1]] -= delta;
-            _excess[u] += delta;
-            if (_excess[u] > 0 && _excess[u] <= delta) active_nodes.push_back(u);
+            u = v;
+            v = path_nodes[i];
+            pa = pred_arc[v];
+            delta = std::min(_res_cap[pa], _excess[u]);
+            _res_cap[pa] -= delta;
+            _res_cap[_reverse[pa]] += delta;
+            _excess[u] -= delta;
+            _excess[v] += delta;
+            if (_excess[v] > 0 && _excess[v] <= delta)
+              _active_nodes.push_back(v);
           }
         }
       }
-
-      // Compute node potentials for the original costs
-      ResidualCostMap<CostMap> res_cost(_orig_cost);
-      BellmanFord< ResDigraph, ResidualCostMap<CostMap> >
-        bf(*_res_graph, res_cost);
-      bf.init(0); bf.start();
-      for (NodeIt n(_graph); n != INVALID; ++n)
-        (*_potential)[n] = bf.dist(n);
-
-      // Handle non-zero lower bounds
-      if (_lower) {
-        for (ArcIt e(_graph); e != INVALID; ++e)
-          (*_flow)[e] += (*_lower)[e];
-      }
-      return true;
-    }
-
-    /// Execute the algorithm performing push and relabel operations.
-    bool startPushRelabel() {
+    }
+
+    /// Execute the algorithm performing push and relabel operations
+    void startPushRelabel() {
       // Paramters for heuristics
-//      const int BF_HEURISTIC_EPSILON_BOUND = 1000;
-//      const int BF_HEURISTIC_BOUND_FACTOR  = 3;
-
-      typename Digraph::template NodeMap<bool> hyper(_graph, false);
-      typename Digraph::template NodeMap<Arc> pred_arc(_graph);
-      typename Digraph::template NodeMap<bool> forward(_graph);
-      typename Digraph::template NodeMap<OutArcIt> next_out(_graph);
-      typename Digraph::template NodeMap<InArcIt> next_in(_graph);
-      typename Digraph::template NodeMap<bool> next_dir(_graph);
-      std::deque<Node> active_nodes;
-
-//      int node_num = countNodes(_graph);
+      const int BF_HEURISTIC_EPSILON_BOUND = 1000;
+      const int BF_HEURISTIC_BOUND_FACTOR  = 3;
+
+      // Perform cost scaling phases
+      BoolVector hyper(_res_node_num, false);
       for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
                                         1 : _epsilon / _alpha )
       {
-/*
         // "Early Termination" heuristic: use Bellman-Ford algorithm
         // to check if the current flow is optimal
         if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) {
-          typedef ShiftMap< ResidualCostMap<LargeCostMap> > ShiftCostMap;
-          ShiftCostMap shift_cost(_res_cost, 1);
-          BellmanFord<ResDigraph, ShiftCostMap> bf(*_res_graph, shift_cost);
+          _arc_vec.clear();
+          _cost_vec.clear();
+          for (int j = 0; j != _res_arc_num; ++j) {
+            if (_res_cap[j] > 0) {
+              _arc_vec.push_back(IntPair(_source[j], _target[j]));
+              _cost_vec.push_back(_cost[j] + 1);
+            }
+          }
+          _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end());
+
+          BellmanFord<StaticDigraph, LargeCostArcMap> bf(_sgr, _cost_map);
           bf.init(0);
           bool done = false;
-          int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(node_num));
+          int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(_res_node_num));
           for (int i = 0; i < K && !done; ++i)
             done = bf.processNextWeakRound();
           if (done) break;
         }
-*/
 
         // Saturate arcs not satisfying the optimality condition
-        Capacity delta;
-        for (ArcIt e(_graph); e != INVALID; ++e) {
-          if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) {
-            delta = _capacity[e] - (*_flow)[e];
-            _excess[_graph.source(e)] -= delta;
-            _excess[_graph.target(e)] += delta;
-            (*_flow)[e] = _capacity[e];
+        for (int a = 0; a != _res_arc_num; ++a) {
+          if (_res_cap[a] > 0 &&
+              _cost[a] + _pi[_source[a]] - _pi[_target[a]] < 0) {
+            Value delta = _res_cap[a];
+            _excess[_source[a]] -= delta;
+            _excess[_target[a]] += delta;
+            _res_cap[a] = 0;
+            _res_cap[_reverse[a]] += delta;
           }
-          if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) {
-            _excess[_graph.target(e)] -= (*_flow)[e];
-            _excess[_graph.source(e)] += (*_flow)[e];
-            (*_flow)[e] = 0;
-          }
         }
 
         // Find active nodes (i.e. nodes with positive excess)
-        for (NodeIt n(_graph); n != INVALID; ++n) {
-          if (_excess[n] > 0) active_nodes.push_back(n);
-        }
-
-        // Initialize the next arc maps
-        for (NodeIt n(_graph); n != INVALID; ++n) {
-          next_out[n] = OutArcIt(_graph, n);
-          next_in[n] = InArcIt(_graph, n);
-          next_dir[n] = true;
+        for (int u = 0; u != _res_node_num; ++u) {
+          if (_excess[u] > 0) _active_nodes.push_back(u);
+        }
+
+        // Initialize the next arcs
+        for (int u = 0; u != _res_node_num; ++u) {
+          _next_out[u] = _first_out[u];
         }
 
         // Perform push and relabel operations
-        while (active_nodes.size() > 0) {
+        while (_active_nodes.size() > 0) {
+          LargeCost min_red_cost, rc;
+          Value delta;
+          int n, t, a, last_out = _res_arc_num;
+
           // Select an active node (FIFO selection)
-          Node n = active_nodes[0], t;
-          bool relabel_enabled = true;
+        next_node:
+          n = _active_nodes.front();
+          last_out = _sum_supply < 0 ?
+            _first_out[n+1] : _first_out[n+1] - 1;
 
           // Perform push operations if there are admissible arcs
-          if (_excess[n] > 0 && next_dir[n]) {
-            OutArcIt e = next_out[n];
-            for ( ; e != INVALID; ++e) {
-              if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) {
-                delta = std::min(_capacity[e] - (*_flow)[e], _excess[n]);
-                t = _graph.target(e);
+          if (_excess[n] > 0) {
+            for (a = _next_out[n]; a != last_out; ++a) {
+              if (_res_cap[a] > 0 &&
+                  _cost[a] + _pi[_source[a]] - _pi[_target[a]] < 0) {
+                delta = std::min(_res_cap[a], _excess[n]);
+                t = _target[a];
 
                 // Push-look-ahead heuristic
-                Capacity ahead = -_excess[t];
-                for (OutArcIt oe(_graph, t); oe != INVALID; ++oe) {
-                  if (_capacity[oe] - (*_flow)[oe] > 0 && (*_red_cost)[oe] < 0)
-                    ahead += _capacity[oe] - (*_flow)[oe];
-                }
-                for (InArcIt ie(_graph, t); ie != INVALID; ++ie) {
-                  if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < 0)
-                    ahead += (*_flow)[ie];
+                Value ahead = -_excess[t];
+                int last_out_t = _sum_supply < 0 ?
+                  _first_out[t+1] : _first_out[t+1] - 1;
+                for (int ta = _next_out[t]; ta != last_out_t; ++ta) {
+                  if (_res_cap[ta] > 0 && 
+                      _cost[ta] + _pi[_source[ta]] - _pi[_target[ta]] < 0)
+                    ahead += _res_cap[ta];
+                  if (ahead >= delta) break;
                 }
                 if (ahead < 0) ahead = 0;
@@ -729 +1073 @@
                 // Push flow along the arc
                 if (ahead < delta) {
-                  (*_flow)[e] += ahead;
+                  _res_cap[a] -= ahead;
+                  _res_cap[_reverse[a]] += ahead;
                   _excess[n] -= ahead;
                   _excess[t] += ahead;
-                  active_nodes.push_front(t);
+                  _active_nodes.push_front(t);
                   hyper[t] = true;
-                  relabel_enabled = false;
-                  break;
+                  _next_out[n] = a;
+                  goto next_node;
                 } else {
-                  (*_flow)[e] += delta;
+                  _res_cap[a] -= delta;
+                  _res_cap[_reverse[a]] += delta;
                   _excess[n] -= delta;
                   _excess[t] += delta;
                   if (_excess[t] > 0 && _excess[t] <= delta)
-                    active_nodes.push_back(t);
+                    _active_nodes.push_back(t);
                 }
 
-                if (_excess[n] == 0) break;
+                if (_excess[n] == 0) {
+                  _next_out[n] = a;
+                  goto remove_nodes;
+                }
               }
             }
-            if (e != INVALID) {
-              next_out[n] = e;
-            } else {
-              next_dir[n] = false;
-            }
+            _next_out[n] = a;
           }
 
-          if (_excess[n] > 0 && !next_dir[n]) {
-            InArcIt e = next_in[n];
-            for ( ; e != INVALID; ++e) {
-              if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) {
-                delta = std::min((*_flow)[e], _excess[n]);
-                t = _graph.source(e);
-
-                // Push-look-ahead heuristic
-                Capacity ahead = -_excess[t];
-                for (OutArcIt oe(_graph, t); oe != INVALID; ++oe) {
-                  if (_capacity[oe] - (*_flow)[oe] > 0 && (*_red_cost)[oe] < 0)
-                    ahead += _capacity[oe] - (*_flow)[oe];
-                }
-                for (InArcIt ie(_graph, t); ie != INVALID; ++ie) {
-                  if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < 0)
-                    ahead += (*_flow)[ie];
-                }
-                if (ahead < 0) ahead = 0;
-
-                // Push flow along the arc
-                if (ahead < delta) {
-                  (*_flow)[e] -= ahead;
-                  _excess[n] -= ahead;
-                  _excess[t] += ahead;
-                  active_nodes.push_front(t);
-                  hyper[t] = true;
-                  relabel_enabled = false;
-                  break;
-                } else {
-                  (*_flow)[e] -= delta;
-                  _excess[n] -= delta;
-                  _excess[t] += delta;
-                  if (_excess[t] > 0 && _excess[t] <= delta)
-                    active_nodes.push_back(t);
-                }
-
-                if (_excess[n] == 0) break;
+          // Relabel the node if it is still active (or hyper)
+          if (_excess[n] > 0 || hyper[n]) {
+            min_red_cost = std::numeric_limits<LargeCost>::max() / 2;
+            for (int a = _first_out[n]; a != last_out; ++a) {
+              rc = _cost[a] + _pi[_source[a]] - _pi[_target[a]];
+              if (_res_cap[a] > 0 && rc < min_red_cost) {
+                min_red_cost = rc;
               }
             }
-            next_in[n] = e;
+            _pi[n] -= min_red_cost + _epsilon;
+            hyper[n] = false;
+
+            // Reset the next arc
+            _next_out[n] = _first_out[n];
           }
-
-          // Relabel the node if it is still active (or hyper)
-          if (relabel_enabled && (_excess[n] > 0 || hyper[n])) {
-            LCost min_red_cost = std::numeric_limits<LCost>::max() / 2;
-            for (OutArcIt oe(_graph, n); oe != INVALID; ++oe) {
-              if ( _capacity[oe] - (*_flow)[oe] > 0 &&
-                   (*_red_cost)[oe] < min_red_cost )
-                min_red_cost = (*_red_cost)[oe];
-            }
-            for (InArcIt ie(_graph, n); ie != INVALID; ++ie) {
-              if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < min_red_cost)
-                min_red_cost = -(*_red_cost)[ie];
-            }
-            (*_potential)[n] -= min_red_cost + _epsilon;
-            hyper[n] = false;
-
-            // Reset the next arc maps
-            next_out[n] = OutArcIt(_graph, n);
-            next_in[n] = InArcIt(_graph, n);
-            next_dir[n] = true;
+        
+          // Remove nodes that are not active nor hyper
+        remove_nodes:
+          while ( _active_nodes.size() > 0 &&
+                  _excess[_active_nodes.front()] <= 0 &&
+                  !hyper[_active_nodes.front()] ) {
+            _active_nodes.pop_front();
           }
-
-          // Remove nodes that are not active nor hyper
-          while ( active_nodes.size() > 0 &&
-                  _excess[active_nodes[0]] <= 0 &&
-                  !hyper[active_nodes[0]] ) {
-            active_nodes.pop_front();
-          }
-        }
-      }
-
-      // Compute node potentials for the original costs
-      ResidualCostMap<CostMap> res_cost(_orig_cost);
-      BellmanFord< ResDigraph, ResidualCostMap<CostMap> >
-        bf(*_res_graph, res_cost);
-      bf.init(0); bf.start();
-      for (NodeIt n(_graph); n != INVALID; ++n)
-        (*_potential)[n] = bf.dist(n);
-
-      // Handle non-zero lower bounds
-      if (_lower) {
-        for (ArcIt e(_graph); e != INVALID; ++e)
-          (*_flow)[e] += (*_lower)[e];
-      }
-      return true;
+        }
+      }
     }