alpar@877: /* -*- mode: C++; indent-tabs-mode: nil; -*-
kpeter@814:  *
alpar@877:  * This file is a part of LEMON, a generic C++ optimization library.
kpeter@814:  *
alpar@877:  * Copyright (C) 2003-2010
kpeter@814:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
kpeter@814:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
kpeter@814:  *
kpeter@814:  * Permission to use, modify and distribute this software is granted
kpeter@814:  * provided that this copyright notice appears in all copies. For
kpeter@814:  * precise terms see the accompanying LICENSE file.
kpeter@814:  *
kpeter@814:  * This software is provided "AS IS" with no warranty of any kind,
kpeter@814:  * express or implied, and with no claim as to its suitability for any
kpeter@814:  * purpose.
kpeter@814:  *
kpeter@814:  */
kpeter@814: 
kpeter@814: #ifndef LEMON_CYCLE_CANCELING_H
kpeter@814: #define LEMON_CYCLE_CANCELING_H
kpeter@814: 
kpeter@815: /// \ingroup min_cost_flow_algs
kpeter@814: /// \file
kpeter@815: /// \brief Cycle-canceling algorithms for finding a minimum cost flow.
kpeter@814: 
kpeter@814: #include <vector>
kpeter@815: #include <limits>
kpeter@815: 
kpeter@815: #include <lemon/core.h>
kpeter@815: #include <lemon/maps.h>
kpeter@815: #include <lemon/path.h>
kpeter@815: #include <lemon/math.h>
kpeter@815: #include <lemon/static_graph.h>
kpeter@814: #include <lemon/adaptors.h>
kpeter@814: #include <lemon/circulation.h>
kpeter@814: #include <lemon/bellman_ford.h>
kpeter@864: #include <lemon/howard_mmc.h>
kpeter@1013: #include <lemon/hartmann_orlin_mmc.h>
kpeter@814: 
kpeter@814: namespace lemon {
kpeter@814: 
kpeter@815:   /// \addtogroup min_cost_flow_algs
kpeter@814:   /// @{
kpeter@814: 
kpeter@815:   /// \brief Implementation of cycle-canceling algorithms for
kpeter@815:   /// finding a \ref min_cost_flow "minimum cost flow".
kpeter@814:   ///
kpeter@815:   /// \ref CycleCanceling implements three different cycle-canceling
kpeter@816:   /// algorithms for finding a \ref min_cost_flow "minimum cost flow"
kpeter@816:   /// \ref amo93networkflows, \ref klein67primal,
kpeter@816:   /// \ref goldberg89cyclecanceling.
kpeter@1003:   /// The most efficent one is the \ref CANCEL_AND_TIGHTEN
kpeter@1003:   /// "Cancel-and-Tighten" algorithm, thus it is the default method.
kpeter@1049:   /// It runs in strongly polynomial time O(n<sup>2</sup>e<sup>2</sup>log(n)),
kpeter@1049:   /// but in practice, it is typically orders of magnitude slower than
kpeter@1049:   /// the scaling algorithms and \ref NetworkSimplex.
kpeter@1003:   /// (For more information, see \ref min_cost_flow_algs "the module page".)
kpeter@814:   ///
kpeter@815:   /// Most of the parameters of the problem (except for the digraph)
kpeter@815:   /// can be given using separate functions, and the algorithm can be
kpeter@815:   /// executed using the \ref run() function. If some parameters are not
kpeter@815:   /// specified, then default values will be used.
kpeter@814:   ///
kpeter@815:   /// \tparam GR The digraph type the algorithm runs on.
kpeter@815:   /// \tparam V The number type used for flow amounts, capacity bounds
kpeter@815:   /// and supply values in the algorithm. By default, it is \c int.
kpeter@815:   /// \tparam C The number type used for costs and potentials in the
kpeter@815:   /// algorithm. By default, it is the same as \c V.
kpeter@814:   ///
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@815:   /// be integer.
kpeter@919:   /// \warning This algorithm does not support negative costs for
kpeter@919:   /// arcs having infinite upper bound.
kpeter@814:   ///
kpeter@815:   /// \note For more information about the three available methods,
kpeter@815:   /// see \ref Method.
kpeter@815: #ifdef DOXYGEN
kpeter@815:   template <typename GR, typename V, typename C>
kpeter@815: #else
kpeter@815:   template <typename GR, typename V = int, typename C = V>
kpeter@815: #endif
kpeter@814:   class CycleCanceling
kpeter@814:   {
kpeter@815:   public:
kpeter@814: 
kpeter@815:     /// The type of the digraph
kpeter@815:     typedef GR Digraph;
kpeter@815:     /// The type of the flow amounts, capacity bounds and supply values
kpeter@815:     typedef V Value;
kpeter@815:     /// The type of the arc costs
kpeter@815:     typedef C Cost;
kpeter@814: 
kpeter@814:   public:
kpeter@814: 
kpeter@815:     /// \brief Problem type constants for the \c run() function.
kpeter@815:     ///
kpeter@815:     /// Enum type containing the problem type constants that can be
kpeter@815:     /// returned by the \ref run() function of the algorithm.
kpeter@815:     enum ProblemType {
kpeter@815:       /// The problem has no feasible solution (flow).
kpeter@815:       INFEASIBLE,
kpeter@815:       /// The problem has optimal solution (i.e. it is feasible and
kpeter@815:       /// bounded), and the algorithm has found optimal flow and node
kpeter@815:       /// potentials (primal and dual solutions).
kpeter@815:       OPTIMAL,
kpeter@815:       /// The digraph contains an arc of negative cost and infinite
kpeter@815:       /// upper bound. It means that the objective function is unbounded
kpeter@815:       /// on that arc, however, note that it could actually be bounded
kpeter@815:       /// over the feasible flows, but this algroithm cannot handle
kpeter@815:       /// these cases.
kpeter@815:       UNBOUNDED
kpeter@815:     };
kpeter@815: 
kpeter@815:     /// \brief Constants for selecting the used method.
kpeter@815:     ///
kpeter@815:     /// Enum type containing constants for selecting the used method
kpeter@815:     /// for the \ref run() function.
kpeter@815:     ///
kpeter@815:     /// \ref CycleCanceling provides three different cycle-canceling
kpeter@1003:     /// methods. By default, \ref CANCEL_AND_TIGHTEN "Cancel-and-Tighten"
kpeter@919:     /// is used, which is by far the most efficient and the most robust.
kpeter@815:     /// However, the other methods can be selected using the \ref run()
kpeter@815:     /// function with the proper parameter.
kpeter@815:     enum Method {
kpeter@815:       /// A simple cycle-canceling method, which uses the
kpeter@1003:       /// \ref BellmanFord "Bellman-Ford" algorithm for detecting negative
kpeter@1003:       /// cycles in the residual network.
kpeter@1003:       /// The number of Bellman-Ford iterations is bounded by a successively
kpeter@1003:       /// increased limit.
kpeter@815:       SIMPLE_CYCLE_CANCELING,
kpeter@815:       /// The "Minimum Mean Cycle-Canceling" algorithm, which is a
kpeter@816:       /// well-known strongly polynomial method
kpeter@816:       /// \ref goldberg89cyclecanceling. It improves along a
kpeter@815:       /// \ref min_mean_cycle "minimum mean cycle" in each iteration.
kpeter@1003:       /// Its running time complexity is O(n<sup>2</sup>e<sup>3</sup>log(n)).
kpeter@815:       MINIMUM_MEAN_CYCLE_CANCELING,
kpeter@1003:       /// The "Cancel-and-Tighten" algorithm, which can be viewed as an
kpeter@816:       /// improved version of the previous method
kpeter@816:       /// \ref goldberg89cyclecanceling.
kpeter@815:       /// It is faster both in theory and in practice, its running time
kpeter@1003:       /// complexity is O(n<sup>2</sup>e<sup>2</sup>log(n)).
kpeter@815:       CANCEL_AND_TIGHTEN
kpeter@815:     };
kpeter@814: 
kpeter@814:   private:
kpeter@814: 
kpeter@815:     TEMPLATE_DIGRAPH_TYPEDEFS(GR);
alpar@877: 
kpeter@815:     typedef std::vector<int> IntVector;
kpeter@815:     typedef std::vector<double> DoubleVector;
kpeter@815:     typedef std::vector<Value> ValueVector;
kpeter@815:     typedef std::vector<Cost> CostVector;
kpeter@839:     typedef std::vector<char> BoolVector;
kpeter@839:     // Note: vector<char> is used instead of vector<bool> for efficiency reasons
kpeter@814: 
kpeter@815:   private:
alpar@877: 
kpeter@815:     template <typename KT, typename VT>
kpeter@820:     class StaticVectorMap {
kpeter@814:     public:
kpeter@815:       typedef KT Key;
kpeter@815:       typedef VT Value;
alpar@877: 
kpeter@820:       StaticVectorMap(std::vector<Value>& v) : _v(v) {}
alpar@877: 
kpeter@815:       const Value& operator[](const Key& key) const {
kpeter@815:         return _v[StaticDigraph::id(key)];
kpeter@814:       }
kpeter@814: 
kpeter@815:       Value& operator[](const Key& key) {
kpeter@815:         return _v[StaticDigraph::id(key)];
kpeter@815:       }
alpar@877: 
kpeter@815:       void set(const Key& key, const Value& val) {
kpeter@815:         _v[StaticDigraph::id(key)] = val;
kpeter@815:       }
kpeter@815: 
kpeter@815:     private:
kpeter@815:       std::vector<Value>& _v;
kpeter@815:     };
kpeter@815: 
kpeter@820:     typedef StaticVectorMap<StaticDigraph::Node, Cost> CostNodeMap;
kpeter@820:     typedef StaticVectorMap<StaticDigraph::Arc, Cost> CostArcMap;
kpeter@814: 
kpeter@814:   private:
kpeter@814: 
kpeter@814: 
kpeter@815:     // Data related to the underlying digraph
kpeter@815:     const GR &_graph;
kpeter@815:     int _node_num;
kpeter@815:     int _arc_num;
kpeter@815:     int _res_node_num;
kpeter@815:     int _res_arc_num;
kpeter@815:     int _root;
kpeter@814: 
kpeter@815:     // Parameters of the problem
kpeter@815:     bool _have_lower;
kpeter@815:     Value _sum_supply;
kpeter@814: 
kpeter@815:     // Data structures for storing the digraph
kpeter@815:     IntNodeMap _node_id;
kpeter@815:     IntArcMap _arc_idf;
kpeter@815:     IntArcMap _arc_idb;
kpeter@815:     IntVector _first_out;
kpeter@839:     BoolVector _forward;
kpeter@815:     IntVector _source;
kpeter@815:     IntVector _target;
kpeter@815:     IntVector _reverse;
kpeter@814: 
kpeter@815:     // Node and arc data
kpeter@815:     ValueVector _lower;
kpeter@815:     ValueVector _upper;
kpeter@815:     CostVector _cost;
kpeter@815:     ValueVector _supply;
kpeter@815: 
kpeter@815:     ValueVector _res_cap;
kpeter@815:     CostVector _pi;
kpeter@815: 
kpeter@815:     // Data for a StaticDigraph structure
kpeter@815:     typedef std::pair<int, int> IntPair;
kpeter@815:     StaticDigraph _sgr;
kpeter@815:     std::vector<IntPair> _arc_vec;
kpeter@815:     std::vector<Cost> _cost_vec;
kpeter@815:     IntVector _id_vec;
kpeter@815:     CostArcMap _cost_map;
kpeter@815:     CostNodeMap _pi_map;
alpar@877: 
kpeter@815:   public:
alpar@877: 
kpeter@815:     /// \brief Constant for infinite upper bounds (capacities).
kpeter@815:     ///
kpeter@815:     /// Constant for infinite upper bounds (capacities).
kpeter@815:     /// It is \c std::numeric_limits<Value>::infinity() if available,
kpeter@815:     /// \c std::numeric_limits<Value>::max() otherwise.
kpeter@815:     const Value INF;
kpeter@814: 
kpeter@814:   public:
kpeter@814: 
kpeter@815:     /// \brief Constructor.
kpeter@814:     ///
kpeter@815:     /// The constructor of the class.
kpeter@814:     ///
kpeter@815:     /// \param graph The digraph the algorithm runs on.
kpeter@815:     CycleCanceling(const GR& graph) :
kpeter@815:       _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph),
kpeter@815:       _cost_map(_cost_vec), _pi_map(_pi),
kpeter@815:       INF(std::numeric_limits<Value>::has_infinity ?
kpeter@815:           std::numeric_limits<Value>::infinity() :
kpeter@815:           std::numeric_limits<Value>::max())
kpeter@814:     {
kpeter@815:       // Check the number types
kpeter@815:       LEMON_ASSERT(std::numeric_limits<Value>::is_signed,
kpeter@815:         "The flow type of CycleCanceling must be signed");
kpeter@815:       LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
kpeter@815:         "The cost type of CycleCanceling must be signed");
kpeter@815: 
kpeter@830:       // Reset data structures
kpeter@815:       reset();
kpeter@814:     }
kpeter@814: 
kpeter@815:     /// \name Parameters
kpeter@815:     /// The parameters of the algorithm can be specified using these
kpeter@815:     /// functions.
kpeter@815: 
kpeter@815:     /// @{
kpeter@815: 
kpeter@815:     /// \brief Set the lower bounds on the arcs.
kpeter@814:     ///
kpeter@815:     /// This function sets the lower bounds on the arcs.
kpeter@815:     /// If it is not used before calling \ref run(), the lower bounds
kpeter@815:     /// will be set to zero on all arcs.
kpeter@814:     ///
kpeter@815:     /// \param map An arc map storing the lower bounds.
kpeter@815:     /// Its \c Value type must be convertible to the \c Value type
kpeter@815:     /// of the algorithm.
kpeter@815:     ///
kpeter@815:     /// \return <tt>(*this)</tt>
kpeter@815:     template <typename LowerMap>
kpeter@815:     CycleCanceling& lowerMap(const LowerMap& map) {
kpeter@815:       _have_lower = true;
kpeter@815:       for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@815:         _lower[_arc_idf[a]] = map[a];
kpeter@815:         _lower[_arc_idb[a]] = map[a];
kpeter@814:       }
kpeter@814:       return *this;
kpeter@814:     }
kpeter@814: 
kpeter@815:     /// \brief Set the upper bounds (capacities) on the arcs.
kpeter@814:     ///
kpeter@815:     /// This function sets the upper bounds (capacities) on the arcs.
kpeter@815:     /// If it is not used before calling \ref run(), the upper bounds
kpeter@815:     /// will be set to \ref INF on all arcs (i.e. the flow value will be
kpeter@815:     /// unbounded from above).
kpeter@814:     ///
kpeter@815:     /// \param map An arc map storing the upper bounds.
kpeter@815:     /// Its \c Value type must be convertible to the \c Value type
kpeter@815:     /// of the algorithm.
kpeter@815:     ///
kpeter@815:     /// \return <tt>(*this)</tt>
kpeter@815:     template<typename UpperMap>
kpeter@815:     CycleCanceling& upperMap(const UpperMap& map) {
kpeter@815:       for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@815:         _upper[_arc_idf[a]] = map[a];
kpeter@814:       }
kpeter@814:       return *this;
kpeter@814:     }
kpeter@814: 
kpeter@815:     /// \brief Set the costs of the arcs.
kpeter@815:     ///
kpeter@815:     /// This function sets the costs of the arcs.
kpeter@815:     /// If it is not used before calling \ref run(), the costs
kpeter@815:     /// will be set to \c 1 on all arcs.
kpeter@815:     ///
kpeter@815:     /// \param map An arc map storing the costs.
kpeter@815:     /// Its \c Value type must be convertible to the \c Cost type
kpeter@815:     /// of the algorithm.
kpeter@815:     ///
kpeter@815:     /// \return <tt>(*this)</tt>
kpeter@815:     template<typename CostMap>
kpeter@815:     CycleCanceling& costMap(const CostMap& map) {
kpeter@815:       for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@815:         _cost[_arc_idf[a]] =  map[a];
kpeter@815:         _cost[_arc_idb[a]] = -map[a];
kpeter@815:       }
kpeter@815:       return *this;
kpeter@815:     }
kpeter@815: 
kpeter@815:     /// \brief Set the supply values of the nodes.
kpeter@815:     ///
kpeter@815:     /// This function sets the supply values of the nodes.
kpeter@815:     /// If neither this function nor \ref stSupply() is used before
kpeter@815:     /// calling \ref run(), the supply of each node will be set to zero.
kpeter@815:     ///
kpeter@815:     /// \param map A node map storing the supply values.
kpeter@815:     /// Its \c Value type must be convertible to the \c Value type
kpeter@815:     /// of the algorithm.
kpeter@815:     ///
kpeter@815:     /// \return <tt>(*this)</tt>
kpeter@815:     template<typename SupplyMap>
kpeter@815:     CycleCanceling& supplyMap(const SupplyMap& map) {
kpeter@815:       for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@815:         _supply[_node_id[n]] = map[n];
kpeter@815:       }
kpeter@815:       return *this;
kpeter@815:     }
kpeter@815: 
kpeter@815:     /// \brief Set single source and target nodes and a supply value.
kpeter@815:     ///
kpeter@815:     /// This function sets a single source node and a single target node
kpeter@815:     /// and the required flow value.
kpeter@815:     /// If neither this function nor \ref supplyMap() is used before
kpeter@815:     /// calling \ref run(), the supply of each node will be set to zero.
kpeter@815:     ///
kpeter@815:     /// 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@815:     /// assigned to \c t and all other nodes have zero supply value.
kpeter@815:     ///
kpeter@815:     /// \param s The source node.
kpeter@815:     /// \param t The target node.
kpeter@815:     /// \param k The required amount of flow from node \c s to node \c t
kpeter@815:     /// (i.e. the supply of \c s and the demand of \c t).
kpeter@815:     ///
kpeter@815:     /// \return <tt>(*this)</tt>
kpeter@815:     CycleCanceling& stSupply(const Node& s, const Node& t, Value k) {
kpeter@815:       for (int i = 0; i != _res_node_num; ++i) {
kpeter@815:         _supply[i] = 0;
kpeter@815:       }
kpeter@815:       _supply[_node_id[s]] =  k;
kpeter@815:       _supply[_node_id[t]] = -k;
kpeter@815:       return *this;
kpeter@815:     }
alpar@877: 
kpeter@815:     /// @}
kpeter@815: 
kpeter@814:     /// \name Execution control
kpeter@815:     /// The algorithm can be executed using \ref run().
kpeter@814: 
kpeter@814:     /// @{
kpeter@814: 
kpeter@814:     /// \brief Run the algorithm.
kpeter@814:     ///
kpeter@815:     /// This function runs the algorithm.
kpeter@815:     /// The paramters can be specified using functions \ref lowerMap(),
kpeter@815:     /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@815:     /// For example,
kpeter@815:     /// \code
kpeter@815:     ///   CycleCanceling<ListDigraph> cc(graph);
kpeter@815:     ///   cc.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@815:     ///     .supplyMap(sup).run();
kpeter@815:     /// \endcode
kpeter@814:     ///
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@814:     ///
kpeter@815:     /// \param method The cycle-canceling method that will be used.
kpeter@815:     /// For more information, see \ref Method.
kpeter@815:     ///
kpeter@815:     /// \return \c INFEASIBLE if no feasible flow exists,
kpeter@815:     /// \n \c OPTIMAL if the problem has optimal solution
kpeter@815:     /// (i.e. it is feasible and bounded), and the algorithm has found
kpeter@815:     /// optimal flow and node potentials (primal and dual solutions),
kpeter@815:     /// \n \c UNBOUNDED if the digraph contains an arc of negative cost
kpeter@815:     /// and infinite upper bound. It means that the objective function
kpeter@815:     /// is unbounded on that arc, however, note that it could actually be
kpeter@815:     /// bounded over the feasible flows, but this algroithm cannot handle
kpeter@815:     /// these cases.
kpeter@815:     ///
kpeter@815:     /// \see ProblemType, Method
kpeter@830:     /// \see resetParams(), reset()
kpeter@815:     ProblemType run(Method method = CANCEL_AND_TIGHTEN) {
kpeter@815:       ProblemType pt = init();
kpeter@815:       if (pt != OPTIMAL) return pt;
kpeter@815:       start(method);
kpeter@815:       return OPTIMAL;
kpeter@815:     }
kpeter@815: 
kpeter@815:     /// \brief Reset all the parameters that have been given before.
kpeter@815:     ///
kpeter@815:     /// This function resets all the paramaters that have been given
kpeter@815:     /// before using functions \ref lowerMap(), \ref upperMap(),
kpeter@815:     /// \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@815:     ///
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@815:     ///
kpeter@815:     /// For example,
kpeter@815:     /// \code
kpeter@815:     ///   CycleCanceling<ListDigraph> cs(graph);
kpeter@815:     ///
kpeter@815:     ///   // First run
kpeter@815:     ///   cc.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@815:     ///     .supplyMap(sup).run();
kpeter@815:     ///
kpeter@830:     ///   // Run again with modified cost map (resetParams() is not called,
kpeter@815:     ///   // so only the cost map have to be set again)
kpeter@815:     ///   cost[e] += 100;
kpeter@815:     ///   cc.costMap(cost).run();
kpeter@815:     ///
kpeter@830:     ///   // Run again from scratch using resetParams()
kpeter@815:     ///   // (the lower bounds will be set to zero on all arcs)
kpeter@830:     ///   cc.resetParams();
kpeter@815:     ///   cc.upperMap(capacity).costMap(cost)
kpeter@815:     ///     .supplyMap(sup).run();
kpeter@815:     /// \endcode
kpeter@815:     ///
kpeter@815:     /// \return <tt>(*this)</tt>
kpeter@830:     ///
kpeter@830:     /// \see reset(), run()
kpeter@830:     CycleCanceling& resetParams() {
kpeter@815:       for (int i = 0; i != _res_node_num; ++i) {
kpeter@815:         _supply[i] = 0;
kpeter@815:       }
kpeter@815:       int limit = _first_out[_root];
kpeter@815:       for (int j = 0; j != limit; ++j) {
kpeter@815:         _lower[j] = 0;
kpeter@815:         _upper[j] = INF;
kpeter@815:         _cost[j] = _forward[j] ? 1 : -1;
kpeter@815:       }
kpeter@815:       for (int j = limit; j != _res_arc_num; ++j) {
kpeter@815:         _lower[j] = 0;
kpeter@815:         _upper[j] = INF;
kpeter@815:         _cost[j] = 0;
kpeter@815:         _cost[_reverse[j]] = 0;
alpar@877:       }
kpeter@815:       _have_lower = false;
kpeter@815:       return *this;
kpeter@814:     }
kpeter@814: 
kpeter@830:     /// \brief Reset the internal data structures and all the parameters
kpeter@830:     /// that have been given before.
kpeter@830:     ///
kpeter@830:     /// This function resets the internal data structures and all the
kpeter@830:     /// paramaters that have been given before using functions \ref lowerMap(),
kpeter@830:     /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@830:     ///
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@830:     ///
kpeter@830:     /// See \ref resetParams() for examples.
kpeter@830:     ///
kpeter@830:     /// \return <tt>(*this)</tt>
kpeter@830:     ///
kpeter@830:     /// \see resetParams(), run()
kpeter@830:     CycleCanceling& 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:       _cost.resize(_res_arc_num);
kpeter@830:       _supply.resize(_res_node_num);
alpar@877: 
kpeter@830:       _res_cap.resize(_res_arc_num);
kpeter@830:       _pi.resize(_res_node_num);
kpeter@830: 
kpeter@830:       _arc_vec.reserve(_res_arc_num);
kpeter@830:       _cost_vec.reserve(_res_arc_num);
kpeter@830:       _id_vec.reserve(_res_arc_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@814:     /// @}
kpeter@814: 
kpeter@814:     /// \name Query Functions
kpeter@815:     /// The results of the algorithm can be obtained using these
kpeter@814:     /// functions.\n
kpeter@815:     /// The \ref run() function must be called before using them.
kpeter@814: 
kpeter@814:     /// @{
kpeter@814: 
kpeter@815:     /// \brief Return the total cost of the found flow.
kpeter@814:     ///
kpeter@815:     /// This function returns the total cost of the found flow.
kpeter@815:     /// Its complexity is O(e).
kpeter@815:     ///
kpeter@815:     /// \note The return type of the function can be specified as a
kpeter@815:     /// template parameter. For example,
kpeter@815:     /// \code
kpeter@815:     ///   cc.totalCost<double>();
kpeter@815:     /// \endcode
kpeter@815:     /// It is useful if the total cost cannot be stored in the \c Cost
kpeter@815:     /// type of the algorithm, which is the default return type of the
kpeter@815:     /// function.
kpeter@814:     ///
kpeter@814:     /// \pre \ref run() must be called before using this function.
kpeter@815:     template <typename Number>
kpeter@815:     Number totalCost() const {
kpeter@815:       Number c = 0;
kpeter@815:       for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@815:         int i = _arc_idb[a];
kpeter@815:         c += static_cast<Number>(_res_cap[i]) *
kpeter@815:              (-static_cast<Number>(_cost[i]));
kpeter@815:       }
kpeter@815:       return c;
kpeter@814:     }
kpeter@814: 
kpeter@815: #ifndef DOXYGEN
kpeter@815:     Cost totalCost() const {
kpeter@815:       return totalCost<Cost>();
kpeter@814:     }
kpeter@815: #endif
kpeter@814: 
kpeter@814:     /// \brief Return the flow on the given arc.
kpeter@814:     ///
kpeter@815:     /// This function returns the flow on the given arc.
kpeter@814:     ///
kpeter@814:     /// \pre \ref run() must be called before using this function.
kpeter@815:     Value flow(const Arc& a) const {
kpeter@815:       return _res_cap[_arc_idb[a]];
kpeter@814:     }
kpeter@814: 
kpeter@1003:     /// \brief Copy the flow values (the primal solution) into the
kpeter@1003:     /// given map.
kpeter@814:     ///
kpeter@815:     /// This function copies the flow value on each arc into the given
kpeter@815:     /// map. The \c Value type of the algorithm must be convertible to
kpeter@815:     /// the \c Value type of the map.
kpeter@814:     ///
kpeter@814:     /// \pre \ref run() must be called before using this function.
kpeter@815:     template <typename FlowMap>
kpeter@815:     void flowMap(FlowMap &map) const {
kpeter@815:       for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@815:         map.set(a, _res_cap[_arc_idb[a]]);
kpeter@815:       }
kpeter@814:     }
kpeter@814: 
kpeter@815:     /// \brief Return the potential (dual value) of the given node.
kpeter@814:     ///
kpeter@815:     /// This function returns the potential (dual value) of the
kpeter@815:     /// given node.
kpeter@814:     ///
kpeter@814:     /// \pre \ref run() must be called before using this function.
kpeter@815:     Cost potential(const Node& n) const {
kpeter@815:       return static_cast<Cost>(_pi[_node_id[n]]);
kpeter@815:     }
kpeter@815: 
kpeter@1003:     /// \brief Copy the potential values (the dual solution) into the
kpeter@1003:     /// given map.
kpeter@815:     ///
kpeter@815:     /// This function copies the potential (dual value) of each node
kpeter@815:     /// into the given map.
kpeter@815:     /// The \c Cost type of the algorithm must be convertible to the
kpeter@815:     /// \c Value type of the map.
kpeter@815:     ///
kpeter@815:     /// \pre \ref run() must be called before using this function.
kpeter@815:     template <typename PotentialMap>
kpeter@815:     void potentialMap(PotentialMap &map) const {
kpeter@815:       for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@815:         map.set(n, static_cast<Cost>(_pi[_node_id[n]]));
kpeter@815:       }
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// @}
kpeter@814: 
kpeter@814:   private:
kpeter@814: 
kpeter@815:     // Initialize the algorithm
kpeter@815:     ProblemType init() {
kpeter@815:       if (_res_node_num <= 1) return INFEASIBLE;
kpeter@814: 
kpeter@815:       // Check the sum of supply values
kpeter@815:       _sum_supply = 0;
kpeter@815:       for (int i = 0; i != _root; ++i) {
kpeter@815:         _sum_supply += _supply[i];
kpeter@814:       }
kpeter@815:       if (_sum_supply > 0) return INFEASIBLE;
alpar@877: 
kpeter@815: 
kpeter@815:       // Initialize vectors
kpeter@815:       for (int i = 0; i != _res_node_num; ++i) {
kpeter@815:         _pi[i] = 0;
kpeter@815:       }
kpeter@815:       ValueVector excess(_supply);
alpar@877: 
kpeter@815:       // Remove infinite upper bounds and check negative arcs
kpeter@815:       const Value MAX = std::numeric_limits<Value>::max();
kpeter@815:       int last_out;
kpeter@815:       if (_have_lower) {
kpeter@815:         for (int i = 0; i != _root; ++i) {
kpeter@815:           last_out = _first_out[i+1];
kpeter@815:           for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@815:             if (_forward[j]) {
kpeter@815:               Value c = _cost[j] < 0 ? _upper[j] : _lower[j];
kpeter@815:               if (c >= MAX) return UNBOUNDED;
kpeter@815:               excess[i] -= c;
kpeter@815:               excess[_target[j]] += c;
kpeter@815:             }
kpeter@815:           }
kpeter@815:         }
kpeter@815:       } else {
kpeter@815:         for (int i = 0; i != _root; ++i) {
kpeter@815:           last_out = _first_out[i+1];
kpeter@815:           for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@815:             if (_forward[j] && _cost[j] < 0) {
kpeter@815:               Value c = _upper[j];
kpeter@815:               if (c >= MAX) return UNBOUNDED;
kpeter@815:               excess[i] -= c;
kpeter@815:               excess[_target[j]] += c;
kpeter@815:             }
kpeter@815:           }
kpeter@815:         }
kpeter@815:       }
kpeter@815:       Value ex, max_cap = 0;
kpeter@815:       for (int i = 0; i != _res_node_num; ++i) {
kpeter@815:         ex = excess[i];
kpeter@815:         if (ex < 0) max_cap -= ex;
kpeter@815:       }
kpeter@815:       for (int j = 0; j != _res_arc_num; ++j) {
kpeter@815:         if (_upper[j] >= MAX) _upper[j] = max_cap;
kpeter@814:       }
kpeter@814: 
kpeter@815:       // Initialize maps for Circulation and remove non-zero lower bounds
kpeter@815:       ConstMap<Arc, Value> low(0);
kpeter@815:       typedef typename Digraph::template ArcMap<Value> ValueArcMap;
kpeter@815:       typedef typename Digraph::template NodeMap<Value> ValueNodeMap;
kpeter@815:       ValueArcMap cap(_graph), flow(_graph);
kpeter@815:       ValueNodeMap sup(_graph);
kpeter@815:       for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@815:         sup[n] = _supply[_node_id[n]];
kpeter@815:       }
kpeter@815:       if (_have_lower) {
kpeter@815:         for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@815:           int j = _arc_idf[a];
kpeter@815:           Value c = _lower[j];
kpeter@815:           cap[a] = _upper[j] - c;
kpeter@815:           sup[_graph.source(a)] -= c;
kpeter@815:           sup[_graph.target(a)] += c;
kpeter@815:         }
kpeter@815:       } else {
kpeter@815:         for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@815:           cap[a] = _upper[_arc_idf[a]];
kpeter@815:         }
kpeter@815:       }
kpeter@814: 
kpeter@815:       // Find a feasible flow using Circulation
kpeter@815:       Circulation<Digraph, ConstMap<Arc, Value>, ValueArcMap, ValueNodeMap>
kpeter@815:         circ(_graph, low, cap, sup);
kpeter@815:       if (!circ.flowMap(flow).run()) return INFEASIBLE;
kpeter@815: 
kpeter@815:       // Set residual capacities and handle GEQ supply type
kpeter@815:       if (_sum_supply < 0) {
kpeter@815:         for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@815:           Value fa = flow[a];
kpeter@815:           _res_cap[_arc_idf[a]] = cap[a] - fa;
kpeter@815:           _res_cap[_arc_idb[a]] = fa;
kpeter@815:           sup[_graph.source(a)] -= fa;
kpeter@815:           sup[_graph.target(a)] += fa;
kpeter@815:         }
kpeter@815:         for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@815:           excess[_node_id[n]] = sup[n];
kpeter@815:         }
kpeter@815:         for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
kpeter@815:           int u = _target[a];
kpeter@815:           int ra = _reverse[a];
kpeter@815:           _res_cap[a] = -_sum_supply + 1;
kpeter@815:           _res_cap[ra] = -excess[u];
kpeter@815:           _cost[a] = 0;
kpeter@815:           _cost[ra] = 0;
kpeter@815:         }
kpeter@815:       } else {
kpeter@815:         for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@815:           Value fa = flow[a];
kpeter@815:           _res_cap[_arc_idf[a]] = cap[a] - fa;
kpeter@815:           _res_cap[_arc_idb[a]] = fa;
kpeter@815:         }
kpeter@815:         for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
kpeter@815:           int ra = _reverse[a];
kpeter@815:           _res_cap[a] = 1;
kpeter@815:           _res_cap[ra] = 0;
kpeter@815:           _cost[a] = 0;
kpeter@815:           _cost[ra] = 0;
kpeter@815:         }
kpeter@815:       }
alpar@877: 
kpeter@815:       return OPTIMAL;
kpeter@815:     }
alpar@877: 
kpeter@815:     // Build a StaticDigraph structure containing the current
kpeter@815:     // residual network
kpeter@815:     void buildResidualNetwork() {
kpeter@815:       _arc_vec.clear();
kpeter@815:       _cost_vec.clear();
kpeter@815:       _id_vec.clear();
kpeter@815:       for (int j = 0; j != _res_arc_num; ++j) {
kpeter@815:         if (_res_cap[j] > 0) {
kpeter@815:           _arc_vec.push_back(IntPair(_source[j], _target[j]));
kpeter@815:           _cost_vec.push_back(_cost[j]);
kpeter@815:           _id_vec.push_back(j);
kpeter@815:         }
kpeter@815:       }
kpeter@815:       _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end());
kpeter@814:     }
kpeter@814: 
kpeter@815:     // Execute the algorithm and transform the results
kpeter@815:     void start(Method method) {
kpeter@815:       // Execute the algorithm
kpeter@815:       switch (method) {
kpeter@815:         case SIMPLE_CYCLE_CANCELING:
kpeter@815:           startSimpleCycleCanceling();
kpeter@815:           break;
kpeter@815:         case MINIMUM_MEAN_CYCLE_CANCELING:
kpeter@815:           startMinMeanCycleCanceling();
kpeter@815:           break;
kpeter@815:         case CANCEL_AND_TIGHTEN:
kpeter@815:           startCancelAndTighten();
kpeter@815:           break;
kpeter@815:       }
kpeter@814: 
kpeter@815:       // Compute node potentials
kpeter@815:       if (method != SIMPLE_CYCLE_CANCELING) {
kpeter@815:         buildResidualNetwork();
kpeter@815:         typename BellmanFord<StaticDigraph, CostArcMap>
kpeter@815:           ::template SetDistMap<CostNodeMap>::Create bf(_sgr, _cost_map);
kpeter@815:         bf.distMap(_pi_map);
kpeter@815:         bf.init(0);
kpeter@815:         bf.start();
kpeter@814:       }
kpeter@815: 
kpeter@815:       // Handle non-zero lower bounds
kpeter@815:       if (_have_lower) {
kpeter@815:         int limit = _first_out[_root];
kpeter@815:         for (int j = 0; j != limit; ++j) {
kpeter@815:           if (!_forward[j]) _res_cap[j] += _lower[j];
kpeter@815:         }
kpeter@815:       }
kpeter@814:     }
kpeter@814: 
kpeter@815:     // Execute the "Simple Cycle Canceling" method
kpeter@815:     void startSimpleCycleCanceling() {
kpeter@815:       // Constants for computing the iteration limits
kpeter@815:       const int BF_FIRST_LIMIT  = 2;
kpeter@815:       const double BF_LIMIT_FACTOR = 1.5;
alpar@877: 
kpeter@820:       typedef StaticVectorMap<StaticDigraph::Arc, Value> FilterMap;
kpeter@815:       typedef FilterArcs<StaticDigraph, FilterMap> ResDigraph;
kpeter@820:       typedef StaticVectorMap<StaticDigraph::Node, StaticDigraph::Arc> PredMap;
kpeter@815:       typedef typename BellmanFord<ResDigraph, CostArcMap>
kpeter@815:         ::template SetDistMap<CostNodeMap>
kpeter@815:         ::template SetPredMap<PredMap>::Create BF;
alpar@877: 
kpeter@815:       // Build the residual network
kpeter@815:       _arc_vec.clear();
kpeter@815:       _cost_vec.clear();
kpeter@815:       for (int j = 0; j != _res_arc_num; ++j) {
kpeter@815:         _arc_vec.push_back(IntPair(_source[j], _target[j]));
kpeter@815:         _cost_vec.push_back(_cost[j]);
kpeter@815:       }
kpeter@815:       _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end());
kpeter@815: 
kpeter@815:       FilterMap filter_map(_res_cap);
kpeter@815:       ResDigraph rgr(_sgr, filter_map);
kpeter@815:       std::vector<int> cycle;
kpeter@815:       std::vector<StaticDigraph::Arc> pred(_res_arc_num);
kpeter@815:       PredMap pred_map(pred);
kpeter@815:       BF bf(rgr, _cost_map);
kpeter@815:       bf.distMap(_pi_map).predMap(pred_map);
kpeter@814: 
kpeter@814:       int length_bound = BF_FIRST_LIMIT;
kpeter@814:       bool optimal = false;
kpeter@814:       while (!optimal) {
kpeter@814:         bf.init(0);
kpeter@814:         int iter_num = 0;
kpeter@814:         bool cycle_found = false;
kpeter@814:         while (!cycle_found) {
kpeter@815:           // Perform some iterations of the Bellman-Ford algorithm
kpeter@815:           int curr_iter_num = iter_num + length_bound <= _node_num ?
kpeter@815:             length_bound : _node_num - iter_num;
kpeter@814:           iter_num += curr_iter_num;
kpeter@814:           int real_iter_num = curr_iter_num;
kpeter@814:           for (int i = 0; i < curr_iter_num; ++i) {
kpeter@814:             if (bf.processNextWeakRound()) {
kpeter@814:               real_iter_num = i;
kpeter@814:               break;
kpeter@814:             }
kpeter@814:           }
kpeter@814:           if (real_iter_num < curr_iter_num) {
kpeter@814:             // Optimal flow is found
kpeter@814:             optimal = true;
kpeter@814:             break;
kpeter@814:           } else {
kpeter@815:             // Search for node disjoint negative cycles
kpeter@815:             std::vector<int> state(_res_node_num, 0);
kpeter@814:             int id = 0;
kpeter@815:             for (int u = 0; u != _res_node_num; ++u) {
kpeter@815:               if (state[u] != 0) continue;
kpeter@815:               ++id;
kpeter@815:               int v = u;
kpeter@815:               for (; v != -1 && state[v] == 0; v = pred[v] == INVALID ?
kpeter@815:                    -1 : rgr.id(rgr.source(pred[v]))) {
kpeter@815:                 state[v] = id;
kpeter@814:               }
kpeter@815:               if (v != -1 && state[v] == id) {
kpeter@815:                 // A negative cycle is found
kpeter@814:                 cycle_found = true;
kpeter@814:                 cycle.clear();
kpeter@815:                 StaticDigraph::Arc a = pred[v];
kpeter@815:                 Value d, delta = _res_cap[rgr.id(a)];
kpeter@815:                 cycle.push_back(rgr.id(a));
kpeter@815:                 while (rgr.id(rgr.source(a)) != v) {
kpeter@815:                   a = pred_map[rgr.source(a)];
kpeter@815:                   d = _res_cap[rgr.id(a)];
kpeter@815:                   if (d < delta) delta = d;
kpeter@815:                   cycle.push_back(rgr.id(a));
kpeter@814:                 }
kpeter@814: 
kpeter@815:                 // Augment along the cycle
kpeter@815:                 for (int i = 0; i < int(cycle.size()); ++i) {
kpeter@815:                   int j = cycle[i];
kpeter@815:                   _res_cap[j] -= delta;
kpeter@815:                   _res_cap[_reverse[j]] += delta;
kpeter@815:                 }
kpeter@814:               }
kpeter@814:             }
kpeter@814:           }
kpeter@814: 
kpeter@815:           // Increase iteration limit if no cycle is found
kpeter@815:           if (!cycle_found) {
kpeter@815:             length_bound = static_cast<int>(length_bound * BF_LIMIT_FACTOR);
kpeter@815:           }
kpeter@814:         }
kpeter@814:       }
kpeter@814:     }
kpeter@814: 
kpeter@815:     // Execute the "Minimum Mean Cycle Canceling" method
kpeter@815:     void startMinMeanCycleCanceling() {
kpeter@1013:       typedef Path<StaticDigraph> SPath;
kpeter@815:       typedef typename SPath::ArcIt SPathArcIt;
kpeter@864:       typedef typename HowardMmc<StaticDigraph, CostArcMap>
kpeter@1013:         ::template SetPath<SPath>::Create HwMmc;
kpeter@1013:       typedef typename HartmannOrlinMmc<StaticDigraph, CostArcMap>
kpeter@1013:         ::template SetPath<SPath>::Create HoMmc;
kpeter@1013: 
kpeter@1013:       const double HW_ITER_LIMIT_FACTOR = 1.0;
kpeter@1013:       const int HW_ITER_LIMIT_MIN_VALUE = 5;
kpeter@1013: 
kpeter@1013:       const int hw_iter_limit =
kpeter@1013:           std::max(static_cast<int>(HW_ITER_LIMIT_FACTOR * _node_num),
kpeter@1013:                    HW_ITER_LIMIT_MIN_VALUE);
alpar@877: 
kpeter@815:       SPath cycle;
kpeter@1013:       HwMmc hw_mmc(_sgr, _cost_map);
kpeter@1013:       hw_mmc.cycle(cycle);
kpeter@815:       buildResidualNetwork();
kpeter@1013:       while (true) {
kpeter@1013:         
kpeter@1013:         typename HwMmc::TerminationCause hw_tc =
kpeter@1013:             hw_mmc.findCycleMean(hw_iter_limit);
kpeter@1013:         if (hw_tc == HwMmc::ITERATION_LIMIT) {
kpeter@1013:           // Howard's algorithm reached the iteration limit, start a
kpeter@1013:           // strongly polynomial algorithm instead
kpeter@1013:           HoMmc ho_mmc(_sgr, _cost_map);
kpeter@1013:           ho_mmc.cycle(cycle);
kpeter@1013:           // Find a minimum mean cycle (Hartmann-Orlin algorithm)
kpeter@1013:           if (!(ho_mmc.findCycleMean() && ho_mmc.cycleCost() < 0)) break;
kpeter@1013:           ho_mmc.findCycle();
kpeter@1013:         } else {
kpeter@1013:           // Find a minimum mean cycle (Howard algorithm)
kpeter@1013:           if (!(hw_tc == HwMmc::OPTIMAL && hw_mmc.cycleCost() < 0)) break;
kpeter@1013:           hw_mmc.findCycle();
kpeter@1013:         }
kpeter@1013:         
kpeter@815:         // Compute delta value
kpeter@815:         Value delta = INF;
kpeter@815:         for (SPathArcIt a(cycle); a != INVALID; ++a) {
kpeter@815:           Value d = _res_cap[_id_vec[_sgr.id(a)]];
kpeter@815:           if (d < delta) delta = d;
kpeter@815:         }
kpeter@814: 
kpeter@815:         // Augment along the cycle
kpeter@815:         for (SPathArcIt a(cycle); a != INVALID; ++a) {
kpeter@815:           int j = _id_vec[_sgr.id(a)];
kpeter@815:           _res_cap[j] -= delta;
kpeter@815:           _res_cap[_reverse[j]] += delta;
kpeter@815:         }
kpeter@815: 
alpar@877:         // Rebuild the residual network
kpeter@815:         buildResidualNetwork();
kpeter@815:       }
kpeter@815:     }
kpeter@815: 
kpeter@1003:     // Execute the "Cancel-and-Tighten" method
kpeter@815:     void startCancelAndTighten() {
kpeter@815:       // Constants for the min mean cycle computations
kpeter@815:       const double LIMIT_FACTOR = 1.0;
kpeter@815:       const int MIN_LIMIT = 5;
kpeter@1013:       const double HW_ITER_LIMIT_FACTOR = 1.0;
kpeter@1013:       const int HW_ITER_LIMIT_MIN_VALUE = 5;
kpeter@1013: 
kpeter@1013:       const int hw_iter_limit =
kpeter@1013:           std::max(static_cast<int>(HW_ITER_LIMIT_FACTOR * _node_num),
kpeter@1013:                    HW_ITER_LIMIT_MIN_VALUE);
kpeter@815: 
kpeter@815:       // Contruct auxiliary data vectors
kpeter@815:       DoubleVector pi(_res_node_num, 0.0);
kpeter@815:       IntVector level(_res_node_num);
kpeter@839:       BoolVector reached(_res_node_num);
kpeter@839:       BoolVector processed(_res_node_num);
kpeter@815:       IntVector pred_node(_res_node_num);
kpeter@815:       IntVector pred_arc(_res_node_num);
kpeter@815:       std::vector<int> stack(_res_node_num);
kpeter@815:       std::vector<int> proc_vector(_res_node_num);
kpeter@815: 
kpeter@815:       // Initialize epsilon
kpeter@815:       double epsilon = 0;
kpeter@815:       for (int a = 0; a != _res_arc_num; ++a) {
kpeter@815:         if (_res_cap[a] > 0 && -_cost[a] > epsilon)
kpeter@815:           epsilon = -_cost[a];
kpeter@815:       }
kpeter@815: 
kpeter@815:       // Start phases
kpeter@815:       Tolerance<double> tol;
kpeter@815:       tol.epsilon(1e-6);
kpeter@815:       int limit = int(LIMIT_FACTOR * std::sqrt(double(_res_node_num)));
kpeter@815:       if (limit < MIN_LIMIT) limit = MIN_LIMIT;
kpeter@815:       int iter = limit;
kpeter@815:       while (epsilon * _res_node_num >= 1) {
kpeter@815:         // Find and cancel cycles in the admissible network using DFS
kpeter@815:         for (int u = 0; u != _res_node_num; ++u) {
kpeter@815:           reached[u] = false;
kpeter@815:           processed[u] = false;
kpeter@815:         }
kpeter@815:         int stack_head = -1;
kpeter@815:         int proc_head = -1;
kpeter@815:         for (int start = 0; start != _res_node_num; ++start) {
kpeter@815:           if (reached[start]) continue;
kpeter@815: 
kpeter@815:           // New start node
kpeter@815:           reached[start] = true;
kpeter@815:           pred_arc[start] = -1;
kpeter@815:           pred_node[start] = -1;
kpeter@815: 
kpeter@815:           // Find the first admissible outgoing arc
kpeter@815:           double p = pi[start];
kpeter@815:           int a = _first_out[start];
kpeter@815:           int last_out = _first_out[start+1];
kpeter@815:           for (; a != last_out && (_res_cap[a] == 0 ||
kpeter@815:                !tol.negative(_cost[a] + p - pi[_target[a]])); ++a) ;
kpeter@815:           if (a == last_out) {
kpeter@815:             processed[start] = true;
kpeter@815:             proc_vector[++proc_head] = start;
kpeter@815:             continue;
kpeter@815:           }
kpeter@815:           stack[++stack_head] = a;
kpeter@815: 
kpeter@815:           while (stack_head >= 0) {
kpeter@815:             int sa = stack[stack_head];
kpeter@815:             int u = _source[sa];
kpeter@815:             int v = _target[sa];
kpeter@815: 
kpeter@815:             if (!reached[v]) {
kpeter@815:               // A new node is reached
kpeter@815:               reached[v] = true;
kpeter@815:               pred_node[v] = u;
kpeter@815:               pred_arc[v] = sa;
kpeter@815:               p = pi[v];
kpeter@815:               a = _first_out[v];
kpeter@815:               last_out = _first_out[v+1];
kpeter@815:               for (; a != last_out && (_res_cap[a] == 0 ||
kpeter@815:                    !tol.negative(_cost[a] + p - pi[_target[a]])); ++a) ;
kpeter@815:               stack[++stack_head] = a == last_out ? -1 : a;
kpeter@815:             } else {
kpeter@815:               if (!processed[v]) {
kpeter@815:                 // A cycle is found
kpeter@815:                 int n, w = u;
kpeter@815:                 Value d, delta = _res_cap[sa];
kpeter@815:                 for (n = u; n != v; n = pred_node[n]) {
kpeter@815:                   d = _res_cap[pred_arc[n]];
kpeter@815:                   if (d <= delta) {
kpeter@815:                     delta = d;
kpeter@815:                     w = pred_node[n];
kpeter@815:                   }
kpeter@815:                 }
kpeter@815: 
kpeter@815:                 // Augment along the cycle
kpeter@815:                 _res_cap[sa] -= delta;
kpeter@815:                 _res_cap[_reverse[sa]] += delta;
kpeter@815:                 for (n = u; n != v; n = pred_node[n]) {
kpeter@815:                   int pa = pred_arc[n];
kpeter@815:                   _res_cap[pa] -= delta;
kpeter@815:                   _res_cap[_reverse[pa]] += delta;
kpeter@815:                 }
kpeter@815:                 for (n = u; stack_head > 0 && n != w; n = pred_node[n]) {
kpeter@815:                   --stack_head;
kpeter@815:                   reached[n] = false;
kpeter@815:                 }
kpeter@815:                 u = w;
kpeter@815:               }
kpeter@815:               v = u;
kpeter@815: 
kpeter@815:               // Find the next admissible outgoing arc
kpeter@815:               p = pi[v];
kpeter@815:               a = stack[stack_head] + 1;
kpeter@815:               last_out = _first_out[v+1];
kpeter@815:               for (; a != last_out && (_res_cap[a] == 0 ||
kpeter@815:                    !tol.negative(_cost[a] + p - pi[_target[a]])); ++a) ;
kpeter@815:               stack[stack_head] = a == last_out ? -1 : a;
kpeter@815:             }
kpeter@815: 
kpeter@815:             while (stack_head >= 0 && stack[stack_head] == -1) {
kpeter@815:               processed[v] = true;
kpeter@815:               proc_vector[++proc_head] = v;
kpeter@815:               if (--stack_head >= 0) {
kpeter@815:                 // Find the next admissible outgoing arc
kpeter@815:                 v = _source[stack[stack_head]];
kpeter@815:                 p = pi[v];
kpeter@815:                 a = stack[stack_head] + 1;
kpeter@815:                 last_out = _first_out[v+1];
kpeter@815:                 for (; a != last_out && (_res_cap[a] == 0 ||
kpeter@815:                      !tol.negative(_cost[a] + p - pi[_target[a]])); ++a) ;
kpeter@815:                 stack[stack_head] = a == last_out ? -1 : a;
kpeter@815:               }
kpeter@815:             }
kpeter@815:           }
kpeter@815:         }
kpeter@815: 
kpeter@815:         // Tighten potentials and epsilon
kpeter@815:         if (--iter > 0) {
kpeter@815:           for (int u = 0; u != _res_node_num; ++u) {
kpeter@815:             level[u] = 0;
kpeter@815:           }
kpeter@815:           for (int i = proc_head; i > 0; --i) {
kpeter@815:             int u = proc_vector[i];
kpeter@815:             double p = pi[u];
kpeter@815:             int l = level[u] + 1;
kpeter@815:             int last_out = _first_out[u+1];
kpeter@815:             for (int a = _first_out[u]; a != last_out; ++a) {
kpeter@815:               int v = _target[a];
kpeter@815:               if (_res_cap[a] > 0 && tol.negative(_cost[a] + p - pi[v]) &&
kpeter@815:                   l > level[v]) level[v] = l;
kpeter@815:             }
kpeter@814:           }
kpeter@814: 
kpeter@815:           // Modify potentials
kpeter@815:           double q = std::numeric_limits<double>::max();
kpeter@815:           for (int u = 0; u != _res_node_num; ++u) {
kpeter@815:             int lu = level[u];
kpeter@815:             double p, pu = pi[u];
kpeter@815:             int last_out = _first_out[u+1];
kpeter@815:             for (int a = _first_out[u]; a != last_out; ++a) {
kpeter@815:               if (_res_cap[a] == 0) continue;
kpeter@815:               int v = _target[a];
kpeter@815:               int ld = lu - level[v];
kpeter@815:               if (ld > 0) {
kpeter@815:                 p = (_cost[a] + pu - pi[v] + epsilon) / (ld + 1);
kpeter@815:                 if (p < q) q = p;
kpeter@815:               }
kpeter@815:             }
kpeter@815:           }
kpeter@815:           for (int u = 0; u != _res_node_num; ++u) {
kpeter@815:             pi[u] -= q * level[u];
kpeter@815:           }
kpeter@814: 
kpeter@815:           // Modify epsilon
kpeter@815:           epsilon = 0;
kpeter@815:           for (int u = 0; u != _res_node_num; ++u) {
kpeter@815:             double curr, pu = pi[u];
kpeter@815:             int last_out = _first_out[u+1];
kpeter@815:             for (int a = _first_out[u]; a != last_out; ++a) {
kpeter@815:               if (_res_cap[a] == 0) continue;
kpeter@815:               curr = _cost[a] + pu - pi[_target[a]];
kpeter@815:               if (-curr > epsilon) epsilon = -curr;
kpeter@815:             }
kpeter@815:           }
kpeter@815:         } else {
kpeter@1013:           typedef HowardMmc<StaticDigraph, CostArcMap> HwMmc;
kpeter@1013:           typedef HartmannOrlinMmc<StaticDigraph, CostArcMap> HoMmc;
kpeter@815:           typedef typename BellmanFord<StaticDigraph, CostArcMap>
kpeter@815:             ::template SetDistMap<CostNodeMap>::Create BF;
kpeter@815: 
kpeter@815:           // Set epsilon to the minimum cycle mean
kpeter@1013:           Cost cycle_cost = 0;
kpeter@1013:           int cycle_size = 1;
kpeter@815:           buildResidualNetwork();
kpeter@1013:           HwMmc hw_mmc(_sgr, _cost_map);
kpeter@1013:           if (hw_mmc.findCycleMean(hw_iter_limit) == HwMmc::ITERATION_LIMIT) {
kpeter@1013:             // Howard's algorithm reached the iteration limit, start a
kpeter@1013:             // strongly polynomial algorithm instead
kpeter@1013:             HoMmc ho_mmc(_sgr, _cost_map);
kpeter@1013:             ho_mmc.findCycleMean();
kpeter@1013:             epsilon = -ho_mmc.cycleMean();
kpeter@1013:             cycle_cost = ho_mmc.cycleCost();
kpeter@1013:             cycle_size = ho_mmc.cycleSize();
kpeter@1013:           } else {
kpeter@1013:             // Set epsilon
kpeter@1013:             epsilon = -hw_mmc.cycleMean();
kpeter@1013:             cycle_cost = hw_mmc.cycleCost();
kpeter@1013:             cycle_size = hw_mmc.cycleSize();
kpeter@1013:           }
alpar@877: 
kpeter@815:           // Compute feasible potentials for the current epsilon
kpeter@815:           for (int i = 0; i != int(_cost_vec.size()); ++i) {
kpeter@815:             _cost_vec[i] = cycle_size * _cost_vec[i] - cycle_cost;
kpeter@815:           }
kpeter@815:           BF bf(_sgr, _cost_map);
kpeter@815:           bf.distMap(_pi_map);
kpeter@815:           bf.init(0);
kpeter@815:           bf.start();
kpeter@815:           for (int u = 0; u != _res_node_num; ++u) {
kpeter@815:             pi[u] = static_cast<double>(_pi[u]) / cycle_size;
kpeter@815:           }
alpar@877: 
kpeter@815:           iter = limit;
kpeter@814:         }
kpeter@814:       }
kpeter@814:     }
kpeter@814: 
kpeter@814:   }; //class CycleCanceling
kpeter@814: 
kpeter@814:   ///@}
kpeter@814: 
kpeter@814: } //namespace lemon
kpeter@814: 
kpeter@814: #endif //LEMON_CYCLE_CANCELING_H