alpar@877: /* -*- mode: C++; indent-tabs-mode: nil; -*-
kpeter@808:  *
alpar@877:  * This file is a part of LEMON, a generic C++ optimization library.
kpeter@808:  *
alpar@877:  * Copyright (C) 2003-2010
kpeter@808:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
kpeter@808:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
kpeter@808:  *
kpeter@808:  * Permission to use, modify and distribute this software is granted
kpeter@808:  * provided that this copyright notice appears in all copies. For
kpeter@808:  * precise terms see the accompanying LICENSE file.
kpeter@808:  *
kpeter@808:  * This software is provided "AS IS" with no warranty of any kind,
kpeter@808:  * express or implied, and with no claim as to its suitability for any
kpeter@808:  * purpose.
kpeter@808:  *
kpeter@808:  */
kpeter@808: 
kpeter@808: #ifndef LEMON_COST_SCALING_H
kpeter@808: #define LEMON_COST_SCALING_H
kpeter@808: 
kpeter@808: /// \ingroup min_cost_flow_algs
kpeter@808: /// \file
kpeter@808: /// \brief Cost scaling algorithm for finding a minimum cost flow.
kpeter@808: 
kpeter@808: #include <vector>
kpeter@808: #include <deque>
kpeter@808: #include <limits>
kpeter@808: 
kpeter@808: #include <lemon/core.h>
kpeter@808: #include <lemon/maps.h>
kpeter@808: #include <lemon/math.h>
kpeter@809: #include <lemon/static_graph.h>
kpeter@808: #include <lemon/circulation.h>
kpeter@808: #include <lemon/bellman_ford.h>
kpeter@808: 
kpeter@808: namespace lemon {
kpeter@808: 
kpeter@809:   /// \brief Default traits class of CostScaling algorithm.
kpeter@809:   ///
kpeter@809:   /// Default traits class of CostScaling algorithm.
kpeter@809:   /// \tparam GR Digraph type.
kpeter@812:   /// \tparam V The number type used for flow amounts, capacity bounds
kpeter@809:   /// and supply values. By default it is \c int.
kpeter@812:   /// \tparam C The number type used for costs and potentials.
kpeter@809:   /// By default it is the same as \c V.
kpeter@809: #ifdef DOXYGEN
kpeter@809:   template <typename GR, typename V = int, typename C = V>
kpeter@809: #else
kpeter@809:   template < typename GR, typename V = int, typename C = V,
kpeter@809:              bool integer = std::numeric_limits<C>::is_integer >
kpeter@809: #endif
kpeter@809:   struct CostScalingDefaultTraits
kpeter@809:   {
kpeter@809:     /// The type of the digraph
kpeter@809:     typedef GR Digraph;
kpeter@809:     /// The type of the flow amounts, capacity bounds and supply values
kpeter@809:     typedef V Value;
kpeter@809:     /// The type of the arc costs
kpeter@809:     typedef C Cost;
kpeter@809: 
kpeter@809:     /// \brief The large cost type used for internal computations
kpeter@809:     ///
kpeter@809:     /// The large cost type used for internal computations.
kpeter@809:     /// It is \c long \c long if the \c Cost type is integer,
kpeter@809:     /// otherwise it is \c double.
kpeter@809:     /// \c Cost must be convertible to \c LargeCost.
kpeter@809:     typedef double LargeCost;
kpeter@809:   };
kpeter@809: 
kpeter@809:   // Default traits class for integer cost types
kpeter@809:   template <typename GR, typename V, typename C>
kpeter@809:   struct CostScalingDefaultTraits<GR, V, C, true>
kpeter@809:   {
kpeter@809:     typedef GR Digraph;
kpeter@809:     typedef V Value;
kpeter@809:     typedef C Cost;
kpeter@809: #ifdef LEMON_HAVE_LONG_LONG
kpeter@809:     typedef long long LargeCost;
kpeter@809: #else
kpeter@809:     typedef long LargeCost;
kpeter@809: #endif
kpeter@809:   };
kpeter@809: 
kpeter@809: 
kpeter@808:   /// \addtogroup min_cost_flow_algs
kpeter@808:   /// @{
kpeter@808: 
kpeter@809:   /// \brief Implementation of the Cost Scaling algorithm for
kpeter@809:   /// finding a \ref min_cost_flow "minimum cost flow".
kpeter@808:   ///
kpeter@809:   /// \ref CostScaling implements a cost scaling algorithm that performs
kpeter@813:   /// push/augment and relabel operations for finding a \ref min_cost_flow
alpar@1053:   /// "minimum cost flow" \cite amo93networkflows, \cite goldberg90approximation,
alpar@1053:   /// \cite goldberg97efficient, \cite bunnagel98efficient.
kpeter@813:   /// It is a highly efficient primal-dual solution method, which
kpeter@809:   /// can be viewed as the generalization of the \ref Preflow
kpeter@809:   /// "preflow push-relabel" algorithm for the maximum flow problem.
kpeter@1049:   /// It is a polynomial algorithm, its running time complexity is
kpeter@1080:   /// \f$O(n^2m\log(nK))\f$, where <i>K</i> denotes the maximum arc cost.
kpeter@808:   ///
kpeter@919:   /// In general, \ref NetworkSimplex and \ref CostScaling are the fastest
kpeter@1003:   /// implementations available in LEMON for solving this problem.
kpeter@1003:   /// (For more information, see \ref min_cost_flow_algs "the module page".)
kpeter@919:   ///
kpeter@809:   /// Most of the parameters of the problem (except for the digraph)
kpeter@809:   /// can be given using separate functions, and the algorithm can be
kpeter@809:   /// executed using the \ref run() function. If some parameters are not
kpeter@809:   /// specified, then default values will be used.
kpeter@808:   ///
kpeter@809:   /// \tparam GR The digraph type the algorithm runs on.
kpeter@812:   /// \tparam V The number type used for flow amounts, capacity bounds
kpeter@825:   /// and supply values in the algorithm. By default, it is \c int.
kpeter@812:   /// \tparam C The number type used for costs and potentials in the
kpeter@825:   /// algorithm. By default, it is the same as \c V.
kpeter@825:   /// \tparam TR The traits class that defines various types used by the
kpeter@825:   /// algorithm. By default, it is \ref CostScalingDefaultTraits
kpeter@825:   /// "CostScalingDefaultTraits<GR, V, C>".
kpeter@825:   /// In most cases, this parameter should not be set directly,
kpeter@825:   /// consider to use the named template parameters instead.
kpeter@808:   ///
kpeter@921:   /// \warning Both \c V and \c C must be signed number types.
kpeter@921:   /// \warning All input data (capacities, supply values, and costs) must
kpeter@809:   /// be integer.
kpeter@919:   /// \warning This algorithm does not support negative costs for
kpeter@919:   /// arcs having infinite upper bound.
kpeter@810:   ///
kpeter@810:   /// \note %CostScaling provides three different internal methods,
kpeter@810:   /// from which the most efficient one is used by default.
kpeter@810:   /// For more information, see \ref Method.
kpeter@809: #ifdef DOXYGEN
kpeter@809:   template <typename GR, typename V, typename C, typename TR>
kpeter@809: #else
kpeter@809:   template < typename GR, typename V = int, typename C = V,
kpeter@809:              typename TR = CostScalingDefaultTraits<GR, V, C> >
kpeter@809: #endif
kpeter@808:   class CostScaling
kpeter@808:   {
kpeter@809:   public:
kpeter@808: 
kpeter@809:     /// The type of the digraph
kpeter@809:     typedef typename TR::Digraph Digraph;
kpeter@809:     /// The type of the flow amounts, capacity bounds and supply values
kpeter@809:     typedef typename TR::Value Value;
kpeter@809:     /// The type of the arc costs
kpeter@809:     typedef typename TR::Cost Cost;
kpeter@808: 
kpeter@809:     /// \brief The large cost type
kpeter@809:     ///
kpeter@809:     /// The large cost type used for internal computations.
kpeter@825:     /// By default, it is \c long \c long if the \c Cost type is integer,
kpeter@809:     /// otherwise it is \c double.
kpeter@809:     typedef typename TR::LargeCost LargeCost;
kpeter@808: 
alpar@1074:     /// \brief The \ref lemon::CostScalingDefaultTraits "traits class"
alpar@1074:     /// of the algorithm
kpeter@809:     typedef TR Traits;
kpeter@808: 
kpeter@808:   public:
kpeter@808: 
kpeter@809:     /// \brief Problem type constants for the \c run() function.
kpeter@809:     ///
kpeter@809:     /// Enum type containing the problem type constants that can be
kpeter@809:     /// returned by the \ref run() function of the algorithm.
kpeter@809:     enum ProblemType {
kpeter@809:       /// The problem has no feasible solution (flow).
kpeter@809:       INFEASIBLE,
kpeter@809:       /// The problem has optimal solution (i.e. it is feasible and
kpeter@809:       /// bounded), and the algorithm has found optimal flow and node
kpeter@809:       /// potentials (primal and dual solutions).
kpeter@809:       OPTIMAL,
kpeter@809:       /// The digraph contains an arc of negative cost and infinite
kpeter@809:       /// upper bound. It means that the objective function is unbounded
kpeter@812:       /// on that arc, however, note that it could actually be bounded
kpeter@809:       /// over the feasible flows, but this algroithm cannot handle
kpeter@809:       /// these cases.
kpeter@809:       UNBOUNDED
kpeter@809:     };
kpeter@808: 
kpeter@810:     /// \brief Constants for selecting the internal method.
kpeter@810:     ///
kpeter@810:     /// Enum type containing constants for selecting the internal method
kpeter@810:     /// for the \ref run() function.
kpeter@810:     ///
kpeter@810:     /// \ref CostScaling provides three internal methods that differ mainly
kpeter@810:     /// in their base operations, which are used in conjunction with the
kpeter@810:     /// relabel operation.
kpeter@810:     /// By default, the so called \ref PARTIAL_AUGMENT
kpeter@919:     /// "Partial Augment-Relabel" method is used, which turned out to be
kpeter@810:     /// the most efficient and the most robust on various test inputs.
kpeter@810:     /// However, the other methods can be selected using the \ref run()
kpeter@810:     /// function with the proper parameter.
kpeter@810:     enum Method {
kpeter@810:       /// Local push operations are used, i.e. flow is moved only on one
kpeter@810:       /// admissible arc at once.
kpeter@810:       PUSH,
kpeter@810:       /// Augment operations are used, i.e. flow is moved on admissible
kpeter@810:       /// paths from a node with excess to a node with deficit.
kpeter@810:       AUGMENT,
alpar@877:       /// Partial augment operations are used, i.e. flow is moved on
kpeter@810:       /// admissible paths started from a node with excess, but the
kpeter@810:       /// lengths of these paths are limited. This method can be viewed
kpeter@810:       /// as a combined version of the previous two operations.
kpeter@810:       PARTIAL_AUGMENT
kpeter@810:     };
kpeter@810: 
kpeter@808:   private:
kpeter@808: 
kpeter@809:     TEMPLATE_DIGRAPH_TYPEDEFS(GR);
kpeter@808: 
kpeter@809:     typedef std::vector<int> IntVector;
kpeter@809:     typedef std::vector<Value> ValueVector;
kpeter@809:     typedef std::vector<Cost> CostVector;
kpeter@809:     typedef std::vector<LargeCost> LargeCostVector;
kpeter@839:     typedef std::vector<char> BoolVector;
kpeter@839:     // Note: vector<char> is used instead of vector<bool> for efficiency reasons
kpeter@808: 
kpeter@809:   private:
alpar@877: 
kpeter@809:     template <typename KT, typename VT>
kpeter@820:     class StaticVectorMap {
kpeter@808:     public:
kpeter@809:       typedef KT Key;
kpeter@809:       typedef VT Value;
alpar@877: 
kpeter@820:       StaticVectorMap(std::vector<Value>& v) : _v(v) {}
alpar@877: 
kpeter@809:       const Value& operator[](const Key& key) const {
kpeter@809:         return _v[StaticDigraph::id(key)];
kpeter@808:       }
kpeter@808: 
kpeter@809:       Value& operator[](const Key& key) {
kpeter@809:         return _v[StaticDigraph::id(key)];
kpeter@809:       }
alpar@877: 
kpeter@809:       void set(const Key& key, const Value& val) {
kpeter@809:         _v[StaticDigraph::id(key)] = val;
kpeter@808:       }
kpeter@808: 
kpeter@809:     private:
kpeter@809:       std::vector<Value>& _v;
kpeter@809:     };
kpeter@809: 
kpeter@820:     typedef StaticVectorMap<StaticDigraph::Arc, LargeCost> LargeCostArcMap;
kpeter@808: 
kpeter@808:   private:
kpeter@808: 
kpeter@809:     // Data related to the underlying digraph
kpeter@809:     const GR &_graph;
kpeter@809:     int _node_num;
kpeter@809:     int _arc_num;
kpeter@809:     int _res_node_num;
kpeter@809:     int _res_arc_num;
kpeter@809:     int _root;
kpeter@808: 
kpeter@809:     // Parameters of the problem
kpeter@809:     bool _have_lower;
kpeter@809:     Value _sum_supply;
kpeter@839:     int _sup_node_num;
kpeter@808: 
kpeter@809:     // Data structures for storing the digraph
kpeter@809:     IntNodeMap _node_id;
kpeter@809:     IntArcMap _arc_idf;
kpeter@809:     IntArcMap _arc_idb;
kpeter@809:     IntVector _first_out;
kpeter@809:     BoolVector _forward;
kpeter@809:     IntVector _source;
kpeter@809:     IntVector _target;
kpeter@809:     IntVector _reverse;
kpeter@809: 
kpeter@809:     // Node and arc data
kpeter@809:     ValueVector _lower;
kpeter@809:     ValueVector _upper;
kpeter@809:     CostVector _scost;
kpeter@809:     ValueVector _supply;
kpeter@809: 
kpeter@809:     ValueVector _res_cap;
kpeter@809:     LargeCostVector _cost;
kpeter@809:     LargeCostVector _pi;
kpeter@809:     ValueVector _excess;
kpeter@809:     IntVector _next_out;
kpeter@809:     std::deque<int> _active_nodes;
kpeter@809: 
kpeter@809:     // Data for scaling
kpeter@809:     LargeCost _epsilon;
kpeter@808:     int _alpha;
kpeter@808: 
kpeter@839:     IntVector _buckets;
kpeter@839:     IntVector _bucket_next;
kpeter@839:     IntVector _bucket_prev;
kpeter@839:     IntVector _rank;
kpeter@839:     int _max_rank;
alpar@877: 
kpeter@809:   public:
alpar@877: 
kpeter@809:     /// \brief Constant for infinite upper bounds (capacities).
kpeter@809:     ///
kpeter@809:     /// Constant for infinite upper bounds (capacities).
kpeter@809:     /// It is \c std::numeric_limits<Value>::infinity() if available,
kpeter@809:     /// \c std::numeric_limits<Value>::max() otherwise.
kpeter@809:     const Value INF;
kpeter@809: 
kpeter@808:   public:
kpeter@808: 
kpeter@809:     /// \name Named Template Parameters
kpeter@809:     /// @{
kpeter@809: 
kpeter@809:     template <typename T>
kpeter@809:     struct SetLargeCostTraits : public Traits {
kpeter@809:       typedef T LargeCost;
kpeter@809:     };
kpeter@809: 
kpeter@809:     /// \brief \ref named-templ-param "Named parameter" for setting
kpeter@809:     /// \c LargeCost type.
kpeter@808:     ///
kpeter@809:     /// \ref named-templ-param "Named parameter" for setting \c LargeCost
kpeter@809:     /// type, which is used for internal computations in the algorithm.
kpeter@809:     /// \c Cost must be convertible to \c LargeCost.
kpeter@809:     template <typename T>
kpeter@809:     struct SetLargeCost
kpeter@809:       : public CostScaling<GR, V, C, SetLargeCostTraits<T> > {
kpeter@809:       typedef  CostScaling<GR, V, C, SetLargeCostTraits<T> > Create;
kpeter@809:     };
kpeter@809: 
kpeter@809:     /// @}
kpeter@809: 
kpeter@863:   protected:
kpeter@863: 
kpeter@863:     CostScaling() {}
kpeter@863: 
kpeter@809:   public:
kpeter@809: 
kpeter@809:     /// \brief Constructor.
kpeter@808:     ///
kpeter@809:     /// The constructor of the class.
kpeter@809:     ///
kpeter@809:     /// \param graph The digraph the algorithm runs on.
kpeter@809:     CostScaling(const GR& graph) :
kpeter@809:       _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph),
kpeter@809:       INF(std::numeric_limits<Value>::has_infinity ?
kpeter@809:           std::numeric_limits<Value>::infinity() :
kpeter@809:           std::numeric_limits<Value>::max())
kpeter@808:     {
kpeter@812:       // Check the number types
kpeter@809:       LEMON_ASSERT(std::numeric_limits<Value>::is_signed,
kpeter@809:         "The flow type of CostScaling must be signed");
kpeter@809:       LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
kpeter@809:         "The cost type of CostScaling must be signed");
alpar@877: 
kpeter@830:       // Reset data structures
kpeter@809:       reset();
kpeter@808:     }
kpeter@808: 
kpeter@809:     /// \name Parameters
kpeter@809:     /// The parameters of the algorithm can be specified using these
kpeter@809:     /// functions.
kpeter@809: 
kpeter@809:     /// @{
kpeter@809: 
kpeter@809:     /// \brief Set the lower bounds on the arcs.
kpeter@808:     ///
kpeter@809:     /// This function sets the lower bounds on the arcs.
kpeter@809:     /// If it is not used before calling \ref run(), the lower bounds
kpeter@809:     /// will be set to zero on all arcs.
kpeter@808:     ///
kpeter@809:     /// \param map An arc map storing the lower bounds.
kpeter@809:     /// Its \c Value type must be convertible to the \c Value type
kpeter@809:     /// of the algorithm.
kpeter@809:     ///
kpeter@809:     /// \return <tt>(*this)</tt>
kpeter@809:     template <typename LowerMap>
kpeter@809:     CostScaling& lowerMap(const LowerMap& map) {
kpeter@809:       _have_lower = true;
kpeter@809:       for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809:         _lower[_arc_idf[a]] = map[a];
kpeter@809:         _lower[_arc_idb[a]] = map[a];
kpeter@808:       }
kpeter@808:       return *this;
kpeter@808:     }
kpeter@808: 
kpeter@809:     /// \brief Set the upper bounds (capacities) on the arcs.
kpeter@808:     ///
kpeter@809:     /// This function sets the upper bounds (capacities) on the arcs.
kpeter@809:     /// If it is not used before calling \ref run(), the upper bounds
kpeter@809:     /// will be set to \ref INF on all arcs (i.e. the flow value will be
kpeter@812:     /// unbounded from above).
kpeter@808:     ///
kpeter@809:     /// \param map An arc map storing the upper bounds.
kpeter@809:     /// Its \c Value type must be convertible to the \c Value type
kpeter@809:     /// of the algorithm.
kpeter@809:     ///
kpeter@809:     /// \return <tt>(*this)</tt>
kpeter@809:     template<typename UpperMap>
kpeter@809:     CostScaling& upperMap(const UpperMap& map) {
kpeter@809:       for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809:         _upper[_arc_idf[a]] = map[a];
kpeter@808:       }
kpeter@808:       return *this;
kpeter@808:     }
kpeter@808: 
kpeter@809:     /// \brief Set the costs of the arcs.
kpeter@809:     ///
kpeter@809:     /// This function sets the costs of the arcs.
kpeter@809:     /// If it is not used before calling \ref run(), the costs
kpeter@809:     /// will be set to \c 1 on all arcs.
kpeter@809:     ///
kpeter@809:     /// \param map An arc map storing the costs.
kpeter@809:     /// Its \c Value type must be convertible to the \c Cost type
kpeter@809:     /// of the algorithm.
kpeter@809:     ///
kpeter@809:     /// \return <tt>(*this)</tt>
kpeter@809:     template<typename CostMap>
kpeter@809:     CostScaling& costMap(const CostMap& map) {
kpeter@809:       for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809:         _scost[_arc_idf[a]] =  map[a];
kpeter@809:         _scost[_arc_idb[a]] = -map[a];
kpeter@809:       }
kpeter@809:       return *this;
kpeter@809:     }
kpeter@809: 
kpeter@809:     /// \brief Set the supply values of the nodes.
kpeter@809:     ///
kpeter@809:     /// This function sets the supply values of the nodes.
kpeter@809:     /// If neither this function nor \ref stSupply() is used before
kpeter@809:     /// calling \ref run(), the supply of each node will be set to zero.
kpeter@809:     ///
kpeter@809:     /// \param map A node map storing the supply values.
kpeter@809:     /// Its \c Value type must be convertible to the \c Value type
kpeter@809:     /// of the algorithm.
kpeter@809:     ///
kpeter@809:     /// \return <tt>(*this)</tt>
kpeter@809:     template<typename SupplyMap>
kpeter@809:     CostScaling& supplyMap(const SupplyMap& map) {
kpeter@809:       for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@809:         _supply[_node_id[n]] = map[n];
kpeter@809:       }
kpeter@809:       return *this;
kpeter@809:     }
kpeter@809: 
kpeter@809:     /// \brief Set single source and target nodes and a supply value.
kpeter@809:     ///
kpeter@809:     /// This function sets a single source node and a single target node
kpeter@809:     /// and the required flow value.
kpeter@809:     /// If neither this function nor \ref supplyMap() is used before
kpeter@809:     /// calling \ref run(), the supply of each node will be set to zero.
kpeter@809:     ///
kpeter@809:     /// Using this function has the same effect as using \ref supplyMap()
kpeter@919:     /// with a map in which \c k is assigned to \c s, \c -k is
kpeter@809:     /// assigned to \c t and all other nodes have zero supply value.
kpeter@809:     ///
kpeter@809:     /// \param s The source node.
kpeter@809:     /// \param t The target node.
kpeter@809:     /// \param k The required amount of flow from node \c s to node \c t
kpeter@809:     /// (i.e. the supply of \c s and the demand of \c t).
kpeter@809:     ///
kpeter@809:     /// \return <tt>(*this)</tt>
kpeter@809:     CostScaling& stSupply(const Node& s, const Node& t, Value k) {
kpeter@809:       for (int i = 0; i != _res_node_num; ++i) {
kpeter@809:         _supply[i] = 0;
kpeter@809:       }
kpeter@809:       _supply[_node_id[s]] =  k;
kpeter@809:       _supply[_node_id[t]] = -k;
kpeter@809:       return *this;
kpeter@809:     }
alpar@877: 
kpeter@809:     /// @}
kpeter@809: 
kpeter@808:     /// \name Execution control
kpeter@809:     /// The algorithm can be executed using \ref run().
kpeter@808: 
kpeter@808:     /// @{
kpeter@808: 
kpeter@808:     /// \brief Run the algorithm.
kpeter@808:     ///
kpeter@809:     /// This function runs the algorithm.
kpeter@809:     /// The paramters can be specified using functions \ref lowerMap(),
kpeter@809:     /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@809:     /// For example,
kpeter@809:     /// \code
kpeter@809:     ///   CostScaling<ListDigraph> cs(graph);
kpeter@809:     ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@809:     ///     .supplyMap(sup).run();
kpeter@809:     /// \endcode
kpeter@809:     ///
kpeter@830:     /// This function can be called more than once. All the given parameters
kpeter@830:     /// are kept for the next call, unless \ref resetParams() or \ref reset()
kpeter@830:     /// is used, thus only the modified parameters have to be set again.
kpeter@830:     /// If the underlying digraph was also modified after the construction
kpeter@830:     /// of the class (or the last \ref reset() call), then the \ref reset()
kpeter@830:     /// function must be called.
kpeter@808:     ///
kpeter@810:     /// \param method The internal method that will be used in the
kpeter@810:     /// algorithm. For more information, see \ref Method.
kpeter@938:     /// \param factor The cost scaling factor. It must be at least two.
kpeter@808:     ///
kpeter@809:     /// \return \c INFEASIBLE if no feasible flow exists,
kpeter@809:     /// \n \c OPTIMAL if the problem has optimal solution
kpeter@809:     /// (i.e. it is feasible and bounded), and the algorithm has found
kpeter@809:     /// optimal flow and node potentials (primal and dual solutions),
kpeter@809:     /// \n \c UNBOUNDED if the digraph contains an arc of negative cost
kpeter@809:     /// and infinite upper bound. It means that the objective function
kpeter@812:     /// is unbounded on that arc, however, note that it could actually be
kpeter@809:     /// bounded over the feasible flows, but this algroithm cannot handle
kpeter@809:     /// these cases.
kpeter@809:     ///
kpeter@810:     /// \see ProblemType, Method
kpeter@830:     /// \see resetParams(), reset()
kpeter@938:     ProblemType run(Method method = PARTIAL_AUGMENT, int factor = 16) {
kpeter@938:       LEMON_ASSERT(factor >= 2, "The scaling factor must be at least 2");
kpeter@810:       _alpha = factor;
kpeter@809:       ProblemType pt = init();
kpeter@809:       if (pt != OPTIMAL) return pt;
kpeter@810:       start(method);
kpeter@809:       return OPTIMAL;
kpeter@809:     }
kpeter@809: 
kpeter@809:     /// \brief Reset all the parameters that have been given before.
kpeter@809:     ///
kpeter@809:     /// This function resets all the paramaters that have been given
kpeter@809:     /// before using functions \ref lowerMap(), \ref upperMap(),
kpeter@809:     /// \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@809:     ///
kpeter@830:     /// It is useful for multiple \ref run() calls. Basically, all the given
kpeter@830:     /// parameters are kept for the next \ref run() call, unless
kpeter@830:     /// \ref resetParams() or \ref reset() is used.
kpeter@830:     /// If the underlying digraph was also modified after the construction
kpeter@830:     /// of the class or the last \ref reset() call, then the \ref reset()
kpeter@830:     /// function must be used, otherwise \ref resetParams() is sufficient.
kpeter@809:     ///
kpeter@809:     /// For example,
kpeter@809:     /// \code
kpeter@809:     ///   CostScaling<ListDigraph> cs(graph);
kpeter@809:     ///
kpeter@809:     ///   // First run
kpeter@809:     ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@809:     ///     .supplyMap(sup).run();
kpeter@809:     ///
kpeter@830:     ///   // Run again with modified cost map (resetParams() is not called,
kpeter@809:     ///   // so only the cost map have to be set again)
kpeter@809:     ///   cost[e] += 100;
kpeter@809:     ///   cs.costMap(cost).run();
kpeter@809:     ///
kpeter@830:     ///   // Run again from scratch using resetParams()
kpeter@809:     ///   // (the lower bounds will be set to zero on all arcs)
kpeter@830:     ///   cs.resetParams();
kpeter@809:     ///   cs.upperMap(capacity).costMap(cost)
kpeter@809:     ///     .supplyMap(sup).run();
kpeter@809:     /// \endcode
kpeter@809:     ///
kpeter@809:     /// \return <tt>(*this)</tt>
kpeter@830:     ///
kpeter@830:     /// \see reset(), run()
kpeter@830:     CostScaling& resetParams() {
kpeter@809:       for (int i = 0; i != _res_node_num; ++i) {
kpeter@809:         _supply[i] = 0;
kpeter@808:       }
kpeter@809:       int limit = _first_out[_root];
kpeter@809:       for (int j = 0; j != limit; ++j) {
kpeter@809:         _lower[j] = 0;
kpeter@809:         _upper[j] = INF;
kpeter@809:         _scost[j] = _forward[j] ? 1 : -1;
kpeter@809:       }
kpeter@809:       for (int j = limit; j != _res_arc_num; ++j) {
kpeter@809:         _lower[j] = 0;
kpeter@809:         _upper[j] = INF;
kpeter@809:         _scost[j] = 0;
kpeter@809:         _scost[_reverse[j]] = 0;
alpar@877:       }
kpeter@809:       _have_lower = false;
kpeter@809:       return *this;
kpeter@808:     }
kpeter@808: 
kpeter@934:     /// \brief Reset the internal data structures and all the parameters
kpeter@934:     /// that have been given before.
kpeter@830:     ///
kpeter@934:     /// This function resets the internal data structures and all the
kpeter@934:     /// paramaters that have been given before using functions \ref lowerMap(),
kpeter@934:     /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@830:     ///
kpeter@934:     /// It is useful for multiple \ref run() calls. By default, all the given
kpeter@934:     /// parameters are kept for the next \ref run() call, unless
kpeter@934:     /// \ref resetParams() or \ref reset() is used.
kpeter@934:     /// If the underlying digraph was also modified after the construction
kpeter@934:     /// of the class or the last \ref reset() call, then the \ref reset()
kpeter@934:     /// function must be used, otherwise \ref resetParams() is sufficient.
kpeter@934:     ///
kpeter@934:     /// See \ref resetParams() for examples.
kpeter@934:     ///
kpeter@830:     /// \return <tt>(*this)</tt>
kpeter@934:     ///
kpeter@934:     /// \see resetParams(), run()
kpeter@830:     CostScaling& reset() {
kpeter@830:       // Resize vectors
kpeter@830:       _node_num = countNodes(_graph);
kpeter@830:       _arc_num = countArcs(_graph);
kpeter@830:       _res_node_num = _node_num + 1;
kpeter@830:       _res_arc_num = 2 * (_arc_num + _node_num);
kpeter@830:       _root = _node_num;
kpeter@830: 
kpeter@830:       _first_out.resize(_res_node_num + 1);
kpeter@830:       _forward.resize(_res_arc_num);
kpeter@830:       _source.resize(_res_arc_num);
kpeter@830:       _target.resize(_res_arc_num);
kpeter@830:       _reverse.resize(_res_arc_num);
kpeter@830: 
kpeter@830:       _lower.resize(_res_arc_num);
kpeter@830:       _upper.resize(_res_arc_num);
kpeter@830:       _scost.resize(_res_arc_num);
kpeter@830:       _supply.resize(_res_node_num);
alpar@877: 
kpeter@830:       _res_cap.resize(_res_arc_num);
kpeter@830:       _cost.resize(_res_arc_num);
kpeter@830:       _pi.resize(_res_node_num);
kpeter@830:       _excess.resize(_res_node_num);
kpeter@830:       _next_out.resize(_res_node_num);
kpeter@830: 
kpeter@830:       // Copy the graph
kpeter@830:       int i = 0, j = 0, k = 2 * _arc_num + _node_num;
kpeter@830:       for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@830:         _node_id[n] = i;
kpeter@830:       }
kpeter@830:       i = 0;
kpeter@830:       for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@830:         _first_out[i] = j;
kpeter@830:         for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) {
kpeter@830:           _arc_idf[a] = j;
kpeter@830:           _forward[j] = true;
kpeter@830:           _source[j] = i;
kpeter@830:           _target[j] = _node_id[_graph.runningNode(a)];
kpeter@830:         }
kpeter@830:         for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) {
kpeter@830:           _arc_idb[a] = j;
kpeter@830:           _forward[j] = false;
kpeter@830:           _source[j] = i;
kpeter@830:           _target[j] = _node_id[_graph.runningNode(a)];
kpeter@830:         }
kpeter@830:         _forward[j] = false;
kpeter@830:         _source[j] = i;
kpeter@830:         _target[j] = _root;
kpeter@830:         _reverse[j] = k;
kpeter@830:         _forward[k] = true;
kpeter@830:         _source[k] = _root;
kpeter@830:         _target[k] = i;
kpeter@830:         _reverse[k] = j;
kpeter@830:         ++j; ++k;
kpeter@830:       }
kpeter@830:       _first_out[i] = j;
kpeter@830:       _first_out[_res_node_num] = k;
kpeter@830:       for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@830:         int fi = _arc_idf[a];
kpeter@830:         int bi = _arc_idb[a];
kpeter@830:         _reverse[fi] = bi;
kpeter@830:         _reverse[bi] = fi;
kpeter@830:       }
alpar@877: 
kpeter@830:       // Reset parameters
kpeter@830:       resetParams();
kpeter@830:       return *this;
kpeter@830:     }
kpeter@830: 
kpeter@808:     /// @}
kpeter@808: 
kpeter@808:     /// \name Query Functions
kpeter@809:     /// The results of the algorithm can be obtained using these
kpeter@808:     /// functions.\n
kpeter@809:     /// The \ref run() function must be called before using them.
kpeter@808: 
kpeter@808:     /// @{
kpeter@808: 
kpeter@809:     /// \brief Return the total cost of the found flow.
kpeter@808:     ///
kpeter@809:     /// This function returns the total cost of the found flow.
kpeter@1080:     /// Its complexity is O(m).
kpeter@809:     ///
kpeter@809:     /// \note The return type of the function can be specified as a
kpeter@809:     /// template parameter. For example,
kpeter@809:     /// \code
kpeter@809:     ///   cs.totalCost<double>();
kpeter@809:     /// \endcode
kpeter@809:     /// It is useful if the total cost cannot be stored in the \c Cost
kpeter@809:     /// type of the algorithm, which is the default return type of the
kpeter@809:     /// function.
kpeter@808:     ///
kpeter@808:     /// \pre \ref run() must be called before using this function.
kpeter@809:     template <typename Number>
kpeter@809:     Number totalCost() const {
kpeter@809:       Number c = 0;
kpeter@809:       for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809:         int i = _arc_idb[a];
kpeter@809:         c += static_cast<Number>(_res_cap[i]) *
kpeter@809:              (-static_cast<Number>(_scost[i]));
kpeter@809:       }
kpeter@809:       return c;
kpeter@808:     }
kpeter@808: 
kpeter@809: #ifndef DOXYGEN
kpeter@809:     Cost totalCost() const {
kpeter@809:       return totalCost<Cost>();
kpeter@808:     }
kpeter@809: #endif
kpeter@808: 
kpeter@808:     /// \brief Return the flow on the given arc.
kpeter@808:     ///
kpeter@809:     /// This function returns the flow on the given arc.
kpeter@808:     ///
kpeter@808:     /// \pre \ref run() must be called before using this function.
kpeter@809:     Value flow(const Arc& a) const {
kpeter@809:       return _res_cap[_arc_idb[a]];
kpeter@808:     }
kpeter@808: 
kpeter@1003:     /// \brief Copy the flow values (the primal solution) into the
kpeter@1003:     /// given map.
kpeter@808:     ///
kpeter@809:     /// This function copies the flow value on each arc into the given
kpeter@809:     /// map. The \c Value type of the algorithm must be convertible to
kpeter@809:     /// the \c Value type of the map.
kpeter@808:     ///
kpeter@808:     /// \pre \ref run() must be called before using this function.
kpeter@809:     template <typename FlowMap>
kpeter@809:     void flowMap(FlowMap &map) const {
kpeter@809:       for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809:         map.set(a, _res_cap[_arc_idb[a]]);
kpeter@809:       }
kpeter@808:     }
kpeter@808: 
kpeter@809:     /// \brief Return the potential (dual value) of the given node.
kpeter@808:     ///
kpeter@809:     /// This function returns the potential (dual value) of the
kpeter@809:     /// given node.
kpeter@808:     ///
kpeter@808:     /// \pre \ref run() must be called before using this function.
kpeter@809:     Cost potential(const Node& n) const {
kpeter@809:       return static_cast<Cost>(_pi[_node_id[n]]);
kpeter@809:     }
kpeter@809: 
kpeter@1003:     /// \brief Copy the potential values (the dual solution) into the
kpeter@1003:     /// given map.
kpeter@809:     ///
kpeter@809:     /// This function copies the potential (dual value) of each node
kpeter@809:     /// into the given map.
kpeter@809:     /// The \c Cost type of the algorithm must be convertible to the
kpeter@809:     /// \c Value type of the map.
kpeter@809:     ///
kpeter@809:     /// \pre \ref run() must be called before using this function.
kpeter@809:     template <typename PotentialMap>
kpeter@809:     void potentialMap(PotentialMap &map) const {
kpeter@809:       for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@809:         map.set(n, static_cast<Cost>(_pi[_node_id[n]]));
kpeter@809:       }
kpeter@808:     }
kpeter@808: 
kpeter@808:     /// @}
kpeter@808: 
kpeter@808:   private:
kpeter@808: 
kpeter@809:     // Initialize the algorithm
kpeter@809:     ProblemType init() {
kpeter@821:       if (_res_node_num <= 1) return INFEASIBLE;
kpeter@809: 
kpeter@809:       // Check the sum of supply values
kpeter@809:       _sum_supply = 0;
kpeter@809:       for (int i = 0; i != _root; ++i) {
kpeter@809:         _sum_supply += _supply[i];
kpeter@808:       }
kpeter@809:       if (_sum_supply > 0) return INFEASIBLE;
alpar@877: 
kpeter@1070:       // Check lower and upper bounds
kpeter@1070:       LEMON_DEBUG(checkBoundMaps(),
kpeter@1070:           "Upper bounds must be greater or equal to the lower bounds");
kpeter@1070: 
kpeter@809: 
kpeter@809:       // Initialize vectors
kpeter@809:       for (int i = 0; i != _res_node_num; ++i) {
kpeter@809:         _pi[i] = 0;
kpeter@809:         _excess[i] = _supply[i];
kpeter@809:       }
alpar@877: 
kpeter@809:       // Remove infinite upper bounds and check negative arcs
kpeter@809:       const Value MAX = std::numeric_limits<Value>::max();
kpeter@809:       int last_out;
kpeter@809:       if (_have_lower) {
kpeter@809:         for (int i = 0; i != _root; ++i) {
kpeter@809:           last_out = _first_out[i+1];
kpeter@809:           for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@809:             if (_forward[j]) {
kpeter@809:               Value c = _scost[j] < 0 ? _upper[j] : _lower[j];
kpeter@809:               if (c >= MAX) return UNBOUNDED;
kpeter@809:               _excess[i] -= c;
kpeter@809:               _excess[_target[j]] += c;
kpeter@809:             }
kpeter@809:           }
kpeter@809:         }
kpeter@809:       } else {
kpeter@809:         for (int i = 0; i != _root; ++i) {
kpeter@809:           last_out = _first_out[i+1];
kpeter@809:           for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@809:             if (_forward[j] && _scost[j] < 0) {
kpeter@809:               Value c = _upper[j];
kpeter@809:               if (c >= MAX) return UNBOUNDED;
kpeter@809:               _excess[i] -= c;
kpeter@809:               _excess[_target[j]] += c;
kpeter@809:             }
kpeter@809:           }
kpeter@809:         }
kpeter@809:       }
kpeter@809:       Value ex, max_cap = 0;
kpeter@809:       for (int i = 0; i != _res_node_num; ++i) {
kpeter@809:         ex = _excess[i];
kpeter@809:         _excess[i] = 0;
kpeter@809:         if (ex < 0) max_cap -= ex;
kpeter@809:       }
kpeter@809:       for (int j = 0; j != _res_arc_num; ++j) {
kpeter@809:         if (_upper[j] >= MAX) _upper[j] = max_cap;
kpeter@808:       }
kpeter@808: 
kpeter@809:       // Initialize the large cost vector and the epsilon parameter
kpeter@809:       _epsilon = 0;
kpeter@809:       LargeCost lc;
kpeter@809:       for (int i = 0; i != _root; ++i) {
kpeter@809:         last_out = _first_out[i+1];
kpeter@809:         for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@809:           lc = static_cast<LargeCost>(_scost[j]) * _res_node_num * _alpha;
kpeter@809:           _cost[j] = lc;
kpeter@809:           if (lc > _epsilon) _epsilon = lc;
kpeter@809:         }
kpeter@809:       }
kpeter@809:       _epsilon /= _alpha;
kpeter@808: 
kpeter@809:       // Initialize maps for Circulation and remove non-zero lower bounds
kpeter@809:       ConstMap<Arc, Value> low(0);
kpeter@809:       typedef typename Digraph::template ArcMap<Value> ValueArcMap;
kpeter@809:       typedef typename Digraph::template NodeMap<Value> ValueNodeMap;
kpeter@809:       ValueArcMap cap(_graph), flow(_graph);
kpeter@809:       ValueNodeMap sup(_graph);
kpeter@809:       for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@809:         sup[n] = _supply[_node_id[n]];
kpeter@808:       }
kpeter@809:       if (_have_lower) {
kpeter@809:         for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809:           int j = _arc_idf[a];
kpeter@809:           Value c = _lower[j];
kpeter@809:           cap[a] = _upper[j] - c;
kpeter@809:           sup[_graph.source(a)] -= c;
kpeter@809:           sup[_graph.target(a)] += c;
kpeter@809:         }
kpeter@809:       } else {
kpeter@809:         for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809:           cap[a] = _upper[_arc_idf[a]];
kpeter@809:         }
kpeter@809:       }
kpeter@808: 
kpeter@839:       _sup_node_num = 0;
kpeter@839:       for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@839:         if (sup[n] > 0) ++_sup_node_num;
kpeter@839:       }
kpeter@839: 
kpeter@808:       // Find a feasible flow using Circulation
kpeter@809:       Circulation<Digraph, ConstMap<Arc, Value>, ValueArcMap, ValueNodeMap>
kpeter@809:         circ(_graph, low, cap, sup);
kpeter@809:       if (!circ.flowMap(flow).run()) return INFEASIBLE;
kpeter@809: 
kpeter@809:       // Set residual capacities and handle GEQ supply type
kpeter@809:       if (_sum_supply < 0) {
kpeter@809:         for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809:           Value fa = flow[a];
kpeter@809:           _res_cap[_arc_idf[a]] = cap[a] - fa;
kpeter@809:           _res_cap[_arc_idb[a]] = fa;
kpeter@809:           sup[_graph.source(a)] -= fa;
kpeter@809:           sup[_graph.target(a)] += fa;
kpeter@809:         }
kpeter@809:         for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@809:           _excess[_node_id[n]] = sup[n];
kpeter@809:         }
kpeter@809:         for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
kpeter@809:           int u = _target[a];
kpeter@809:           int ra = _reverse[a];
kpeter@809:           _res_cap[a] = -_sum_supply + 1;
kpeter@809:           _res_cap[ra] = -_excess[u];
kpeter@809:           _cost[a] = 0;
kpeter@809:           _cost[ra] = 0;
kpeter@809:           _excess[u] = 0;
kpeter@809:         }
kpeter@809:       } else {
kpeter@809:         for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@809:           Value fa = flow[a];
kpeter@809:           _res_cap[_arc_idf[a]] = cap[a] - fa;
kpeter@809:           _res_cap[_arc_idb[a]] = fa;
kpeter@809:         }
kpeter@809:         for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
kpeter@809:           int ra = _reverse[a];
kpeter@839:           _res_cap[a] = 0;
kpeter@809:           _res_cap[ra] = 0;
kpeter@809:           _cost[a] = 0;
kpeter@809:           _cost[ra] = 0;
kpeter@809:         }
kpeter@809:       }
alpar@877: 
alpar@877:       // Initialize data structures for buckets
kpeter@839:       _max_rank = _alpha * _res_node_num;
kpeter@839:       _buckets.resize(_max_rank);
kpeter@839:       _bucket_next.resize(_res_node_num + 1);
kpeter@839:       _bucket_prev.resize(_res_node_num + 1);
kpeter@839:       _rank.resize(_res_node_num + 1);
alpar@877: 
kpeter@934:       return OPTIMAL;
kpeter@934:     }
kpeter@1070:     
kpeter@1070:     // Check if the upper bound is greater or equal to the lower bound
kpeter@1070:     // on each arc.
kpeter@1070:     bool checkBoundMaps() {
kpeter@1070:       for (int j = 0; j != _res_arc_num; ++j) {
kpeter@1070:         if (_upper[j] < _lower[j]) return false;
kpeter@1070:       }
kpeter@1070:       return true;
kpeter@1070:     }
kpeter@934: 
kpeter@934:     // Execute the algorithm and transform the results
kpeter@934:     void start(Method method) {
kpeter@934:       const int MAX_PARTIAL_PATH_LENGTH = 4;
kpeter@934: 
kpeter@810:       switch (method) {
kpeter@810:         case PUSH:
kpeter@810:           startPush();
kpeter@810:           break;
kpeter@810:         case AUGMENT:
kpeter@931:           startAugment(_res_node_num - 1);
kpeter@810:           break;
kpeter@810:         case PARTIAL_AUGMENT:
kpeter@934:           startAugment(MAX_PARTIAL_PATH_LENGTH);
kpeter@810:           break;
kpeter@809:       }
kpeter@809: 
kpeter@937:       // Compute node potentials (dual solution)
kpeter@937:       for (int i = 0; i != _res_node_num; ++i) {
kpeter@937:         _pi[i] = static_cast<Cost>(_pi[i] / (_res_node_num * _alpha));
kpeter@937:       }
kpeter@937:       bool optimal = true;
kpeter@937:       for (int i = 0; optimal && i != _res_node_num; ++i) {
kpeter@937:         LargeCost pi_i = _pi[i];
kpeter@937:         int last_out = _first_out[i+1];
kpeter@937:         for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@937:           if (_res_cap[j] > 0 && _scost[j] + pi_i - _pi[_target[j]] < 0) {
kpeter@937:             optimal = false;
kpeter@937:             break;
kpeter@937:           }
kpeter@809:         }
kpeter@809:       }
kpeter@809: 
kpeter@937:       if (!optimal) {
kpeter@937:         // Compute node potentials for the original costs with BellmanFord
kpeter@937:         // (if it is necessary)
kpeter@937:         typedef std::pair<int, int> IntPair;
kpeter@937:         StaticDigraph sgr;
kpeter@937:         std::vector<IntPair> arc_vec;
kpeter@937:         std::vector<LargeCost> cost_vec;
kpeter@937:         LargeCostArcMap cost_map(cost_vec);
kpeter@937: 
kpeter@937:         arc_vec.clear();
kpeter@937:         cost_vec.clear();
kpeter@937:         for (int j = 0; j != _res_arc_num; ++j) {
kpeter@937:           if (_res_cap[j] > 0) {
kpeter@937:             int u = _source[j], v = _target[j];
kpeter@937:             arc_vec.push_back(IntPair(u, v));
kpeter@937:             cost_vec.push_back(_scost[j] + _pi[u] - _pi[v]);
kpeter@937:           }
kpeter@937:         }
kpeter@937:         sgr.build(_res_node_num, arc_vec.begin(), arc_vec.end());
kpeter@937: 
kpeter@937:         typename BellmanFord<StaticDigraph, LargeCostArcMap>::Create
kpeter@937:           bf(sgr, cost_map);
kpeter@937:         bf.init(0);
kpeter@937:         bf.start();
kpeter@937: 
kpeter@937:         for (int i = 0; i != _res_node_num; ++i) {
kpeter@937:           _pi[i] += bf.dist(sgr.node(i));
kpeter@937:         }
kpeter@937:       }
kpeter@937: 
kpeter@937:       // Shift potentials to meet the requirements of the GEQ type
kpeter@937:       // optimality conditions
kpeter@937:       LargeCost max_pot = _pi[_root];
kpeter@937:       for (int i = 0; i != _res_node_num; ++i) {
kpeter@937:         if (_pi[i] > max_pot) max_pot = _pi[i];
kpeter@937:       }
kpeter@937:       if (max_pot != 0) {
kpeter@937:         for (int i = 0; i != _res_node_num; ++i) {
kpeter@937:           _pi[i] -= max_pot;
kpeter@937:         }
kpeter@937:       }
kpeter@809: 
kpeter@809:       // Handle non-zero lower bounds
kpeter@809:       if (_have_lower) {
kpeter@809:         int limit = _first_out[_root];
kpeter@809:         for (int j = 0; j != limit; ++j) {
kpeter@809:           if (!_forward[j]) _res_cap[j] += _lower[j];
kpeter@809:         }
kpeter@809:       }
kpeter@808:     }
alpar@877: 
kpeter@839:     // Initialize a cost scaling phase
kpeter@839:     void initPhase() {
kpeter@839:       // Saturate arcs not satisfying the optimality condition
kpeter@839:       for (int u = 0; u != _res_node_num; ++u) {
kpeter@839:         int last_out = _first_out[u+1];
kpeter@839:         LargeCost pi_u = _pi[u];
kpeter@839:         for (int a = _first_out[u]; a != last_out; ++a) {
kpeter@934:           Value delta = _res_cap[a];
kpeter@934:           if (delta > 0) {
kpeter@934:             int v = _target[a];
kpeter@934:             if (_cost[a] + pi_u - _pi[v] < 0) {
kpeter@934:               _excess[u] -= delta;
kpeter@934:               _excess[v] += delta;
kpeter@934:               _res_cap[a] = 0;
kpeter@934:               _res_cap[_reverse[a]] += delta;
kpeter@934:             }
kpeter@839:           }
kpeter@839:         }
kpeter@839:       }
alpar@877: 
kpeter@839:       // Find active nodes (i.e. nodes with positive excess)
kpeter@839:       for (int u = 0; u != _res_node_num; ++u) {
kpeter@839:         if (_excess[u] > 0) _active_nodes.push_back(u);
kpeter@839:       }
kpeter@839: 
kpeter@839:       // Initialize the next arcs
kpeter@839:       for (int u = 0; u != _res_node_num; ++u) {
kpeter@839:         _next_out[u] = _first_out[u];
kpeter@839:       }
kpeter@839:     }
alpar@877: 
kpeter@936:     // Price (potential) refinement heuristic
kpeter@936:     bool priceRefinement() {
kpeter@839: 
kpeter@936:       // Stack for stroing the topological order
kpeter@936:       IntVector stack(_res_node_num);
kpeter@936:       int stack_top;
kpeter@936: 
kpeter@936:       // Perform phases
kpeter@936:       while (topologicalSort(stack, stack_top)) {
kpeter@936: 
kpeter@936:         // Compute node ranks in the acyclic admissible network and
kpeter@936:         // store the nodes in buckets
kpeter@936:         for (int i = 0; i != _res_node_num; ++i) {
kpeter@936:           _rank[i] = 0;
kpeter@839:         }
kpeter@936:         const int bucket_end = _root + 1;
kpeter@936:         for (int r = 0; r != _max_rank; ++r) {
kpeter@936:           _buckets[r] = bucket_end;
kpeter@936:         }
kpeter@936:         int top_rank = 0;
kpeter@936:         for ( ; stack_top >= 0; --stack_top) {
kpeter@936:           int u = stack[stack_top], v;
kpeter@936:           int rank_u = _rank[u];
kpeter@936: 
kpeter@936:           LargeCost rc, pi_u = _pi[u];
kpeter@936:           int last_out = _first_out[u+1];
kpeter@936:           for (int a = _first_out[u]; a != last_out; ++a) {
kpeter@936:             if (_res_cap[a] > 0) {
kpeter@936:               v = _target[a];
kpeter@936:               rc = _cost[a] + pi_u - _pi[v];
kpeter@936:               if (rc < 0) {
kpeter@936:                 LargeCost nrc = static_cast<LargeCost>((-rc - 0.5) / _epsilon);
kpeter@936:                 if (nrc < LargeCost(_max_rank)) {
kpeter@936:                   int new_rank_v = rank_u + static_cast<int>(nrc);
kpeter@936:                   if (new_rank_v > _rank[v]) {
kpeter@936:                     _rank[v] = new_rank_v;
kpeter@936:                   }
kpeter@936:                 }
kpeter@936:               }
kpeter@936:             }
kpeter@936:           }
kpeter@936: 
kpeter@936:           if (rank_u > 0) {
kpeter@936:             top_rank = std::max(top_rank, rank_u);
kpeter@936:             int bfirst = _buckets[rank_u];
kpeter@936:             _bucket_next[u] = bfirst;
kpeter@936:             _bucket_prev[bfirst] = u;
kpeter@936:             _buckets[rank_u] = u;
kpeter@936:           }
kpeter@936:         }
kpeter@936: 
kpeter@936:         // Check if the current flow is epsilon-optimal
kpeter@936:         if (top_rank == 0) {
kpeter@936:           return true;
kpeter@936:         }
kpeter@936: 
kpeter@936:         // Process buckets in top-down order
kpeter@936:         for (int rank = top_rank; rank > 0; --rank) {
kpeter@936:           while (_buckets[rank] != bucket_end) {
kpeter@936:             // Remove the first node from the current bucket
kpeter@936:             int u = _buckets[rank];
kpeter@936:             _buckets[rank] = _bucket_next[u];
kpeter@936: 
kpeter@936:             // Search the outgoing arcs of u
kpeter@936:             LargeCost rc, pi_u = _pi[u];
kpeter@936:             int last_out = _first_out[u+1];
kpeter@936:             int v, old_rank_v, new_rank_v;
kpeter@936:             for (int a = _first_out[u]; a != last_out; ++a) {
kpeter@936:               if (_res_cap[a] > 0) {
kpeter@936:                 v = _target[a];
kpeter@936:                 old_rank_v = _rank[v];
kpeter@936: 
kpeter@936:                 if (old_rank_v < rank) {
kpeter@936: 
kpeter@936:                   // Compute the new rank of node v
kpeter@936:                   rc = _cost[a] + pi_u - _pi[v];
kpeter@936:                   if (rc < 0) {
kpeter@936:                     new_rank_v = rank;
kpeter@936:                   } else {
kpeter@936:                     LargeCost nrc = rc / _epsilon;
kpeter@936:                     new_rank_v = 0;
kpeter@936:                     if (nrc < LargeCost(_max_rank)) {
kpeter@936:                       new_rank_v = rank - 1 - static_cast<int>(nrc);
kpeter@936:                     }
kpeter@936:                   }
kpeter@936: 
kpeter@936:                   // Change the rank of node v
kpeter@936:                   if (new_rank_v > old_rank_v) {
kpeter@936:                     _rank[v] = new_rank_v;
kpeter@936: 
kpeter@936:                     // Remove v from its old bucket
kpeter@936:                     if (old_rank_v > 0) {
kpeter@936:                       if (_buckets[old_rank_v] == v) {
kpeter@936:                         _buckets[old_rank_v] = _bucket_next[v];
kpeter@936:                       } else {
kpeter@936:                         int pv = _bucket_prev[v], nv = _bucket_next[v];
kpeter@936:                         _bucket_next[pv] = nv;
kpeter@936:                         _bucket_prev[nv] = pv;
kpeter@936:                       }
kpeter@936:                     }
kpeter@936: 
kpeter@936:                     // Insert v into its new bucket
kpeter@936:                     int nv = _buckets[new_rank_v];
kpeter@936:                     _bucket_next[v] = nv;
kpeter@936:                     _bucket_prev[nv] = v;
kpeter@936:                     _buckets[new_rank_v] = v;
kpeter@936:                   }
kpeter@936:                 }
kpeter@936:               }
kpeter@936:             }
kpeter@936: 
kpeter@936:             // Refine potential of node u
kpeter@936:             _pi[u] -= rank * _epsilon;
kpeter@936:           }
kpeter@936:         }
kpeter@936: 
kpeter@839:       }
kpeter@839: 
kpeter@936:       return false;
kpeter@936:     }
kpeter@936: 
kpeter@936:     // Find and cancel cycles in the admissible network and
kpeter@936:     // determine topological order using DFS
kpeter@936:     bool topologicalSort(IntVector &stack, int &stack_top) {
kpeter@936:       const int MAX_CYCLE_CANCEL = 1;
kpeter@936: 
kpeter@936:       BoolVector reached(_res_node_num, false);
kpeter@936:       BoolVector processed(_res_node_num, false);
kpeter@936:       IntVector pred(_res_node_num);
kpeter@936:       for (int i = 0; i != _res_node_num; ++i) {
kpeter@936:         _next_out[i] = _first_out[i];
kpeter@839:       }
kpeter@936:       stack_top = -1;
kpeter@936: 
kpeter@936:       int cycle_cnt = 0;
kpeter@936:       for (int start = 0; start != _res_node_num; ++start) {
kpeter@936:         if (reached[start]) continue;
kpeter@936: 
kpeter@936:         // Start DFS search from this start node
kpeter@936:         pred[start] = -1;
kpeter@936:         int tip = start, v;
kpeter@936:         while (true) {
kpeter@936:           // Check the outgoing arcs of the current tip node
kpeter@936:           reached[tip] = true;
kpeter@936:           LargeCost pi_tip = _pi[tip];
kpeter@936:           int a, last_out = _first_out[tip+1];
kpeter@936:           for (a = _next_out[tip]; a != last_out; ++a) {
kpeter@936:             if (_res_cap[a] > 0) {
kpeter@936:               v = _target[a];
kpeter@936:               if (_cost[a] + pi_tip - _pi[v] < 0) {
kpeter@936:                 if (!reached[v]) {
kpeter@936:                   // A new node is reached
kpeter@936:                   reached[v] = true;
kpeter@936:                   pred[v] = tip;
kpeter@936:                   _next_out[tip] = a;
kpeter@936:                   tip = v;
kpeter@936:                   a = _next_out[tip];
kpeter@936:                   last_out = _first_out[tip+1];
kpeter@936:                   break;
kpeter@936:                 }
kpeter@936:                 else if (!processed[v]) {
kpeter@936:                   // A cycle is found
kpeter@936:                   ++cycle_cnt;
kpeter@936:                   _next_out[tip] = a;
kpeter@936: 
kpeter@936:                   // Find the minimum residual capacity along the cycle
kpeter@936:                   Value d, delta = _res_cap[a];
kpeter@936:                   int u, delta_node = tip;
kpeter@936:                   for (u = tip; u != v; ) {
kpeter@936:                     u = pred[u];
kpeter@936:                     d = _res_cap[_next_out[u]];
kpeter@936:                     if (d <= delta) {
kpeter@936:                       delta = d;
kpeter@936:                       delta_node = u;
kpeter@936:                     }
kpeter@936:                   }
kpeter@936: 
kpeter@936:                   // Augment along the cycle
kpeter@936:                   _res_cap[a] -= delta;
kpeter@936:                   _res_cap[_reverse[a]] += delta;
kpeter@936:                   for (u = tip; u != v; ) {
kpeter@936:                     u = pred[u];
kpeter@936:                     int ca = _next_out[u];
kpeter@936:                     _res_cap[ca] -= delta;
kpeter@936:                     _res_cap[_reverse[ca]] += delta;
kpeter@936:                   }
kpeter@936: 
kpeter@936:                   // Check the maximum number of cycle canceling
kpeter@936:                   if (cycle_cnt >= MAX_CYCLE_CANCEL) {
kpeter@936:                     return false;
kpeter@936:                   }
kpeter@936: 
kpeter@936:                   // Roll back search to delta_node
kpeter@936:                   if (delta_node != tip) {
kpeter@936:                     for (u = tip; u != delta_node; u = pred[u]) {
kpeter@936:                       reached[u] = false;
kpeter@936:                     }
kpeter@936:                     tip = delta_node;
kpeter@936:                     a = _next_out[tip] + 1;
kpeter@936:                     last_out = _first_out[tip+1];
kpeter@936:                     break;
kpeter@936:                   }
kpeter@936:                 }
kpeter@936:               }
kpeter@936:             }
kpeter@936:           }
kpeter@936: 
kpeter@936:           // Step back to the previous node
kpeter@936:           if (a == last_out) {
kpeter@936:             processed[tip] = true;
kpeter@936:             stack[++stack_top] = tip;
kpeter@936:             tip = pred[tip];
kpeter@936:             if (tip < 0) {
kpeter@936:               // Finish DFS from the current start node
kpeter@936:               break;
kpeter@936:             }
kpeter@936:             ++_next_out[tip];
kpeter@936:           }
kpeter@936:         }
kpeter@936: 
kpeter@936:       }
kpeter@936: 
kpeter@936:       return (cycle_cnt == 0);
kpeter@839:     }
kpeter@839: 
kpeter@839:     // Global potential update heuristic
kpeter@839:     void globalUpdate() {
kpeter@934:       const int bucket_end = _root + 1;
alpar@877: 
kpeter@839:       // Initialize buckets
kpeter@839:       for (int r = 0; r != _max_rank; ++r) {
kpeter@839:         _buckets[r] = bucket_end;
kpeter@839:       }
kpeter@839:       Value total_excess = 0;
kpeter@934:       int b0 = bucket_end;
kpeter@839:       for (int i = 0; i != _res_node_num; ++i) {
kpeter@839:         if (_excess[i] < 0) {
kpeter@839:           _rank[i] = 0;
kpeter@934:           _bucket_next[i] = b0;
kpeter@934:           _bucket_prev[b0] = i;
kpeter@934:           b0 = i;
kpeter@839:         } else {
kpeter@839:           total_excess += _excess[i];
kpeter@839:           _rank[i] = _max_rank;
kpeter@839:         }
kpeter@839:       }
kpeter@839:       if (total_excess == 0) return;
kpeter@934:       _buckets[0] = b0;
kpeter@839: 
kpeter@839:       // Search the buckets
kpeter@839:       int r = 0;
kpeter@839:       for ( ; r != _max_rank; ++r) {
kpeter@839:         while (_buckets[r] != bucket_end) {
kpeter@839:           // Remove the first node from the current bucket
kpeter@839:           int u = _buckets[r];
kpeter@839:           _buckets[r] = _bucket_next[u];
alpar@877: 
kpeter@1049:           // Search the incoming arcs of u
kpeter@839:           LargeCost pi_u = _pi[u];
kpeter@839:           int last_out = _first_out[u+1];
kpeter@839:           for (int a = _first_out[u]; a != last_out; ++a) {
kpeter@839:             int ra = _reverse[a];
kpeter@839:             if (_res_cap[ra] > 0) {
kpeter@839:               int v = _source[ra];
kpeter@839:               int old_rank_v = _rank[v];
kpeter@839:               if (r < old_rank_v) {
kpeter@839:                 // Compute the new rank of v
kpeter@839:                 LargeCost nrc = (_cost[ra] + _pi[v] - pi_u) / _epsilon;
kpeter@839:                 int new_rank_v = old_rank_v;
kpeter@934:                 if (nrc < LargeCost(_max_rank)) {
kpeter@934:                   new_rank_v = r + 1 + static_cast<int>(nrc);
kpeter@934:                 }
alpar@877: 
kpeter@839:                 // Change the rank of v
kpeter@839:                 if (new_rank_v < old_rank_v) {
kpeter@839:                   _rank[v] = new_rank_v;
kpeter@839:                   _next_out[v] = _first_out[v];
alpar@877: 
kpeter@839:                   // Remove v from its old bucket
kpeter@839:                   if (old_rank_v < _max_rank) {
kpeter@839:                     if (_buckets[old_rank_v] == v) {
kpeter@839:                       _buckets[old_rank_v] = _bucket_next[v];
kpeter@839:                     } else {
kpeter@934:                       int pv = _bucket_prev[v], nv = _bucket_next[v];
kpeter@934:                       _bucket_next[pv] = nv;
kpeter@934:                       _bucket_prev[nv] = pv;
kpeter@839:                     }
kpeter@839:                   }
alpar@877: 
kpeter@934:                   // Insert v into its new bucket
kpeter@934:                   int nv = _buckets[new_rank_v];
kpeter@934:                   _bucket_next[v] = nv;
kpeter@934:                   _bucket_prev[nv] = v;
kpeter@839:                   _buckets[new_rank_v] = v;
kpeter@839:                 }
kpeter@839:               }
kpeter@839:             }
kpeter@839:           }
kpeter@839: 
kpeter@839:           // Finish search if there are no more active nodes
kpeter@839:           if (_excess[u] > 0) {
kpeter@839:             total_excess -= _excess[u];
kpeter@839:             if (total_excess <= 0) break;
kpeter@839:           }
kpeter@839:         }
kpeter@839:         if (total_excess <= 0) break;
kpeter@839:       }
alpar@877: 
kpeter@839:       // Relabel nodes
kpeter@839:       for (int u = 0; u != _res_node_num; ++u) {
kpeter@839:         int k = std::min(_rank[u], r);
kpeter@839:         if (k > 0) {
kpeter@839:           _pi[u] -= _epsilon * k;
kpeter@839:           _next_out[u] = _first_out[u];
kpeter@839:         }
kpeter@839:       }
kpeter@839:     }
kpeter@808: 
kpeter@810:     /// Execute the algorithm performing augment and relabel operations
kpeter@931:     void startAugment(int max_length) {
kpeter@808:       // Paramters for heuristics
kpeter@936:       const int PRICE_REFINEMENT_LIMIT = 2;
kpeter@935:       const double GLOBAL_UPDATE_FACTOR = 1.0;
kpeter@935:       const int global_update_skip = static_cast<int>(GLOBAL_UPDATE_FACTOR *
kpeter@839:         (_res_node_num + _sup_node_num * _sup_node_num));
kpeter@935:       int next_global_update_limit = global_update_skip;
alpar@877: 
kpeter@809:       // Perform cost scaling phases
kpeter@935:       IntVector path;
kpeter@935:       BoolVector path_arc(_res_arc_num, false);
kpeter@935:       int relabel_cnt = 0;
kpeter@936:       int eps_phase_cnt = 0;
kpeter@808:       for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
kpeter@808:                                         1 : _epsilon / _alpha )
kpeter@808:       {
kpeter@936:         ++eps_phase_cnt;
kpeter@936: 
kpeter@936:         // Price refinement heuristic
kpeter@936:         if (eps_phase_cnt >= PRICE_REFINEMENT_LIMIT) {
kpeter@936:           if (priceRefinement()) continue;
kpeter@808:         }
alpar@877: 
kpeter@839:         // Initialize current phase
kpeter@839:         initPhase();
alpar@877: 
kpeter@808:         // Perform partial augment and relabel operations
kpeter@809:         while (true) {
kpeter@808:           // Select an active node (FIFO selection)
kpeter@809:           while (_active_nodes.size() > 0 &&
kpeter@809:                  _excess[_active_nodes.front()] <= 0) {
kpeter@809:             _active_nodes.pop_front();
kpeter@808:           }
kpeter@809:           if (_active_nodes.size() == 0) break;
kpeter@809:           int start = _active_nodes.front();
kpeter@808: 
kpeter@808:           // Find an augmenting path from the start node
kpeter@809:           int tip = start;
kpeter@935:           while (int(path.size()) < max_length && _excess[tip] >= 0) {
kpeter@809:             int u;
kpeter@935:             LargeCost rc, min_red_cost = std::numeric_limits<LargeCost>::max();
kpeter@935:             LargeCost pi_tip = _pi[tip];
kpeter@839:             int last_out = _first_out[tip+1];
kpeter@809:             for (int a = _next_out[tip]; a != last_out; ++a) {
kpeter@935:               if (_res_cap[a] > 0) {
kpeter@935:                 u = _target[a];
kpeter@935:                 rc = _cost[a] + pi_tip - _pi[u];
kpeter@935:                 if (rc < 0) {
kpeter@935:                   path.push_back(a);
kpeter@935:                   _next_out[tip] = a;
kpeter@935:                   if (path_arc[a]) {
kpeter@935:                     goto augment;   // a cycle is found, stop path search
kpeter@935:                   }
kpeter@935:                   tip = u;
kpeter@935:                   path_arc[a] = true;
kpeter@935:                   goto next_step;
kpeter@935:                 }
kpeter@935:                 else if (rc < min_red_cost) {
kpeter@935:                   min_red_cost = rc;
kpeter@935:                 }
kpeter@808:               }
kpeter@808:             }
kpeter@808: 
kpeter@808:             // Relabel tip node
kpeter@839:             if (tip != start) {
kpeter@839:               int ra = _reverse[path.back()];
kpeter@935:               min_red_cost =
kpeter@935:                 std::min(min_red_cost, _cost[ra] + pi_tip - _pi[_target[ra]]);
kpeter@839:             }
kpeter@935:             last_out = _next_out[tip];
kpeter@809:             for (int a = _first_out[tip]; a != last_out; ++a) {
kpeter@935:               if (_res_cap[a] > 0) {
kpeter@935:                 rc = _cost[a] + pi_tip - _pi[_target[a]];
kpeter@935:                 if (rc < min_red_cost) {
kpeter@935:                   min_red_cost = rc;
kpeter@935:                 }
kpeter@809:               }
kpeter@808:             }
kpeter@809:             _pi[tip] -= min_red_cost + _epsilon;
kpeter@809:             _next_out[tip] = _first_out[tip];
kpeter@839:             ++relabel_cnt;
kpeter@808: 
kpeter@808:             // Step back
kpeter@808:             if (tip != start) {
kpeter@935:               int pa = path.back();
kpeter@935:               path_arc[pa] = false;
kpeter@935:               tip = _source[pa];
kpeter@839:               path.pop_back();
kpeter@808:             }
kpeter@808: 
kpeter@809:           next_step: ;
kpeter@808:           }
kpeter@808: 
kpeter@808:           // Augment along the found path (as much flow as possible)
kpeter@935:         augment:
kpeter@809:           Value delta;
kpeter@839:           int pa, u, v = start;
kpeter@839:           for (int i = 0; i != int(path.size()); ++i) {
kpeter@839:             pa = path[i];
kpeter@809:             u = v;
kpeter@839:             v = _target[pa];
kpeter@935:             path_arc[pa] = false;
kpeter@809:             delta = std::min(_res_cap[pa], _excess[u]);
kpeter@809:             _res_cap[pa] -= delta;
kpeter@809:             _res_cap[_reverse[pa]] += delta;
kpeter@809:             _excess[u] -= delta;
kpeter@809:             _excess[v] += delta;
kpeter@935:             if (_excess[v] > 0 && _excess[v] <= delta) {
kpeter@809:               _active_nodes.push_back(v);
kpeter@935:             }
kpeter@808:           }
kpeter@935:           path.clear();
kpeter@839: 
kpeter@839:           // Global update heuristic
kpeter@935:           if (relabel_cnt >= next_global_update_limit) {
kpeter@839:             globalUpdate();
kpeter@935:             next_global_update_limit += global_update_skip;
kpeter@839:           }
kpeter@808:         }
kpeter@935: 
kpeter@808:       }
kpeter@935: 
kpeter@808:     }
kpeter@808: 
kpeter@809:     /// Execute the algorithm performing push and relabel operations
kpeter@810:     void startPush() {
kpeter@808:       // Paramters for heuristics
kpeter@936:       const int PRICE_REFINEMENT_LIMIT = 2;
kpeter@839:       const double GLOBAL_UPDATE_FACTOR = 2.0;
kpeter@808: 
kpeter@935:       const int global_update_skip = static_cast<int>(GLOBAL_UPDATE_FACTOR *
kpeter@839:         (_res_node_num + _sup_node_num * _sup_node_num));
kpeter@935:       int next_global_update_limit = global_update_skip;
alpar@877: 
kpeter@809:       // Perform cost scaling phases
kpeter@809:       BoolVector hyper(_res_node_num, false);
kpeter@839:       LargeCostVector hyper_cost(_res_node_num);
kpeter@935:       int relabel_cnt = 0;
kpeter@936:       int eps_phase_cnt = 0;
kpeter@808:       for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
kpeter@808:                                         1 : _epsilon / _alpha )
kpeter@808:       {
kpeter@936:         ++eps_phase_cnt;
kpeter@936: 
kpeter@936:         // Price refinement heuristic
kpeter@936:         if (eps_phase_cnt >= PRICE_REFINEMENT_LIMIT) {
kpeter@936:           if (priceRefinement()) continue;
kpeter@808:         }
alpar@877: 
kpeter@839:         // Initialize current phase
kpeter@839:         initPhase();
kpeter@808: 
kpeter@808:         // Perform push and relabel operations
kpeter@809:         while (_active_nodes.size() > 0) {
kpeter@839:           LargeCost min_red_cost, rc, pi_n;
kpeter@809:           Value delta;
kpeter@809:           int n, t, a, last_out = _res_arc_num;
kpeter@809: 
kpeter@839:         next_node:
kpeter@808:           // Select an active node (FIFO selection)
kpeter@809:           n = _active_nodes.front();
kpeter@839:           last_out = _first_out[n+1];
kpeter@839:           pi_n = _pi[n];
alpar@877: 
kpeter@808:           // Perform push operations if there are admissible arcs
kpeter@809:           if (_excess[n] > 0) {
kpeter@809:             for (a = _next_out[n]; a != last_out; ++a) {
kpeter@809:               if (_res_cap[a] > 0 &&
kpeter@839:                   _cost[a] + pi_n - _pi[_target[a]] < 0) {
kpeter@809:                 delta = std::min(_res_cap[a], _excess[n]);
kpeter@809:                 t = _target[a];
kpeter@808: 
kpeter@808:                 // Push-look-ahead heuristic
kpeter@809:                 Value ahead = -_excess[t];
kpeter@839:                 int last_out_t = _first_out[t+1];
kpeter@839:                 LargeCost pi_t = _pi[t];
kpeter@809:                 for (int ta = _next_out[t]; ta != last_out_t; ++ta) {
alpar@877:                   if (_res_cap[ta] > 0 &&
kpeter@839:                       _cost[ta] + pi_t - _pi[_target[ta]] < 0)
kpeter@809:                     ahead += _res_cap[ta];
kpeter@809:                   if (ahead >= delta) break;
kpeter@808:                 }
kpeter@808:                 if (ahead < 0) ahead = 0;
kpeter@808: 
kpeter@808:                 // Push flow along the arc
kpeter@839:                 if (ahead < delta && !hyper[t]) {
kpeter@809:                   _res_cap[a] -= ahead;
kpeter@809:                   _res_cap[_reverse[a]] += ahead;
kpeter@808:                   _excess[n] -= ahead;
kpeter@808:                   _excess[t] += ahead;
kpeter@809:                   _active_nodes.push_front(t);
kpeter@808:                   hyper[t] = true;
kpeter@839:                   hyper_cost[t] = _cost[a] + pi_n - pi_t;
kpeter@809:                   _next_out[n] = a;
kpeter@809:                   goto next_node;
kpeter@808:                 } else {
kpeter@809:                   _res_cap[a] -= delta;
kpeter@809:                   _res_cap[_reverse[a]] += delta;
kpeter@808:                   _excess[n] -= delta;
kpeter@808:                   _excess[t] += delta;
kpeter@808:                   if (_excess[t] > 0 && _excess[t] <= delta)
kpeter@809:                     _active_nodes.push_back(t);
kpeter@808:                 }
kpeter@808: 
kpeter@809:                 if (_excess[n] == 0) {
kpeter@809:                   _next_out[n] = a;
kpeter@809:                   goto remove_nodes;
kpeter@809:                 }
kpeter@808:               }
kpeter@808:             }
kpeter@809:             _next_out[n] = a;
kpeter@808:           }
kpeter@808: 
kpeter@808:           // Relabel the node if it is still active (or hyper)
kpeter@809:           if (_excess[n] > 0 || hyper[n]) {
kpeter@839:              min_red_cost = hyper[n] ? -hyper_cost[n] :
kpeter@839:                std::numeric_limits<LargeCost>::max();
kpeter@809:             for (int a = _first_out[n]; a != last_out; ++a) {
kpeter@935:               if (_res_cap[a] > 0) {
kpeter@935:                 rc = _cost[a] + pi_n - _pi[_target[a]];
kpeter@935:                 if (rc < min_red_cost) {
kpeter@935:                   min_red_cost = rc;
kpeter@935:                 }
kpeter@809:               }
kpeter@808:             }
kpeter@809:             _pi[n] -= min_red_cost + _epsilon;
kpeter@839:             _next_out[n] = _first_out[n];
kpeter@808:             hyper[n] = false;
kpeter@839:             ++relabel_cnt;
kpeter@808:           }
alpar@877: 
kpeter@808:           // Remove nodes that are not active nor hyper
kpeter@809:         remove_nodes:
kpeter@809:           while ( _active_nodes.size() > 0 &&
kpeter@809:                   _excess[_active_nodes.front()] <= 0 &&
kpeter@809:                   !hyper[_active_nodes.front()] ) {
kpeter@809:             _active_nodes.pop_front();
kpeter@808:           }
alpar@877: 
kpeter@839:           // Global update heuristic
kpeter@935:           if (relabel_cnt >= next_global_update_limit) {
kpeter@839:             globalUpdate();
kpeter@839:             for (int u = 0; u != _res_node_num; ++u)
kpeter@839:               hyper[u] = false;
kpeter@935:             next_global_update_limit += global_update_skip;
kpeter@839:           }
kpeter@808:         }
kpeter@808:       }
kpeter@808:     }
kpeter@808: 
kpeter@808:   }; //class CostScaling
kpeter@808: 
kpeter@808:   ///@}
kpeter@808: 
kpeter@808: } //namespace lemon
kpeter@808: 
kpeter@808: #endif //LEMON_COST_SCALING_H