kpeter@814: /* -*- C++ -*-
kpeter@814:  *
kpeter@814:  * This file is a part of LEMON, a generic C++ optimization library
kpeter@814:  *
kpeter@814:  * Copyright (C) 2003-2008
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_CANCEL_AND_TIGHTEN_H
kpeter@814: #define LEMON_CANCEL_AND_TIGHTEN_H
kpeter@814: 
kpeter@814: /// \ingroup min_cost_flow
kpeter@814: ///
kpeter@814: /// \file
kpeter@814: /// \brief Cancel and Tighten algorithm for finding a minimum cost flow.
kpeter@814: 
kpeter@814: #include <vector>
kpeter@814: 
kpeter@814: #include <lemon/circulation.h>
kpeter@814: #include <lemon/bellman_ford.h>
kpeter@814: #include <lemon/howard.h>
kpeter@814: #include <lemon/adaptors.h>
kpeter@814: #include <lemon/tolerance.h>
kpeter@814: #include <lemon/math.h>
kpeter@814: 
kpeter@814: #include <lemon/static_graph.h>
kpeter@814: 
kpeter@814: namespace lemon {
kpeter@814: 
kpeter@814:   /// \addtogroup min_cost_flow
kpeter@814:   /// @{
kpeter@814: 
kpeter@814:   /// \brief Implementation of the Cancel and Tighten algorithm for
kpeter@814:   /// finding a minimum cost flow.
kpeter@814:   ///
kpeter@814:   /// \ref CancelAndTighten implements the Cancel and Tighten algorithm for
kpeter@814:   /// finding a minimum cost flow.
kpeter@814:   ///
kpeter@814:   /// \tparam Digraph The digraph type the algorithm runs on.
kpeter@814:   /// \tparam LowerMap The type of the lower bound map.
kpeter@814:   /// \tparam CapacityMap The type of the capacity (upper bound) map.
kpeter@814:   /// \tparam CostMap The type of the cost (length) map.
kpeter@814:   /// \tparam SupplyMap The type of the supply map.
kpeter@814:   ///
kpeter@814:   /// \warning
kpeter@814:   /// - Arc capacities and costs should be \e non-negative \e integers.
kpeter@814:   /// - Supply values should be \e signed \e integers.
kpeter@814:   /// - The value types of the maps should be convertible to each other.
kpeter@814:   /// - \c CostMap::Value must be signed type.
kpeter@814:   ///
kpeter@814:   /// \author Peter Kovacs
kpeter@814:   template < typename Digraph,
kpeter@814:              typename LowerMap = typename Digraph::template ArcMap<int>,
kpeter@814:              typename CapacityMap = typename Digraph::template ArcMap<int>,
kpeter@814:              typename CostMap = typename Digraph::template ArcMap<int>,
kpeter@814:              typename SupplyMap = typename Digraph::template NodeMap<int> >
kpeter@814:   class CancelAndTighten
kpeter@814:   {
kpeter@814:     TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
kpeter@814: 
kpeter@814:     typedef typename CapacityMap::Value Capacity;
kpeter@814:     typedef typename CostMap::Value Cost;
kpeter@814:     typedef typename SupplyMap::Value Supply;
kpeter@814:     typedef typename Digraph::template ArcMap<Capacity> CapacityArcMap;
kpeter@814:     typedef typename Digraph::template NodeMap<Supply> SupplyNodeMap;
kpeter@814: 
kpeter@814:     typedef ResidualDigraph< const Digraph,
kpeter@814:       CapacityArcMap, CapacityArcMap > ResDigraph;
kpeter@814: 
kpeter@814:   public:
kpeter@814: 
kpeter@814:     /// The type of the flow map.
kpeter@814:     typedef typename Digraph::template ArcMap<Capacity> FlowMap;
kpeter@814:     /// The type of the potential map.
kpeter@814:     typedef typename Digraph::template NodeMap<Cost> PotentialMap;
kpeter@814: 
kpeter@814:   private:
kpeter@814: 
kpeter@814:     /// \brief Map adaptor class for handling residual arc costs.
kpeter@814:     ///
kpeter@814:     /// Map adaptor class for handling residual arc costs.
kpeter@814:     class ResidualCostMap : public MapBase<typename ResDigraph::Arc, Cost>
kpeter@814:     {
kpeter@814:       typedef typename ResDigraph::Arc Arc;
kpeter@814:       
kpeter@814:     private:
kpeter@814: 
kpeter@814:       const CostMap &_cost_map;
kpeter@814: 
kpeter@814:     public:
kpeter@814: 
kpeter@814:       ///\e
kpeter@814:       ResidualCostMap(const CostMap &cost_map) : _cost_map(cost_map) {}
kpeter@814: 
kpeter@814:       ///\e
kpeter@814:       Cost operator[](const Arc &e) const {
kpeter@814:         return ResDigraph::forward(e) ? _cost_map[e] : -_cost_map[e];
kpeter@814:       }
kpeter@814: 
kpeter@814:     }; //class ResidualCostMap
kpeter@814: 
kpeter@814:     /// \brief Map adaptor class for handling reduced arc costs.
kpeter@814:     ///
kpeter@814:     /// Map adaptor class for handling reduced arc costs.
kpeter@814:     class ReducedCostMap : public MapBase<Arc, Cost>
kpeter@814:     {
kpeter@814:     private:
kpeter@814: 
kpeter@814:       const Digraph &_gr;
kpeter@814:       const CostMap &_cost_map;
kpeter@814:       const PotentialMap &_pot_map;
kpeter@814: 
kpeter@814:     public:
kpeter@814: 
kpeter@814:       ///\e
kpeter@814:       ReducedCostMap( const Digraph &gr,
kpeter@814:                       const CostMap &cost_map,
kpeter@814:                       const PotentialMap &pot_map ) :
kpeter@814:         _gr(gr), _cost_map(cost_map), _pot_map(pot_map) {}
kpeter@814: 
kpeter@814:       ///\e
kpeter@814:       inline Cost operator[](const Arc &e) const {
kpeter@814:         return _cost_map[e] + _pot_map[_gr.source(e)]
kpeter@814:                             - _pot_map[_gr.target(e)];
kpeter@814:       }
kpeter@814: 
kpeter@814:     }; //class ReducedCostMap
kpeter@814: 
kpeter@814:     struct BFOperationTraits {
kpeter@814:       static double zero() { return 0; }
kpeter@814: 
kpeter@814:       static double infinity() {
kpeter@814:         return std::numeric_limits<double>::infinity();
kpeter@814:       }
kpeter@814: 
kpeter@814:       static double plus(const double& left, const double& right) {
kpeter@814:         return left + right;
kpeter@814:       }
kpeter@814: 
kpeter@814:       static bool less(const double& left, const double& right) {
kpeter@814:         return left + 1e-6 < right;
kpeter@814:       }
kpeter@814:     }; // class BFOperationTraits
kpeter@814: 
kpeter@814:   private:
kpeter@814: 
kpeter@814:     // The digraph the algorithm runs on
kpeter@814:     const Digraph &_graph;
kpeter@814:     // The original lower bound map
kpeter@814:     const LowerMap *_lower;
kpeter@814:     // The modified capacity map
kpeter@814:     CapacityArcMap _capacity;
kpeter@814:     // The original cost map
kpeter@814:     const CostMap &_cost;
kpeter@814:     // The modified supply map
kpeter@814:     SupplyNodeMap _supply;
kpeter@814:     bool _valid_supply;
kpeter@814: 
kpeter@814:     // Arc map of the current flow
kpeter@814:     FlowMap *_flow;
kpeter@814:     bool _local_flow;
kpeter@814:     // Node map of the current potentials
kpeter@814:     PotentialMap *_potential;
kpeter@814:     bool _local_potential;
kpeter@814: 
kpeter@814:     // The residual digraph
kpeter@814:     ResDigraph *_res_graph;
kpeter@814:     // The residual cost map
kpeter@814:     ResidualCostMap _res_cost;
kpeter@814: 
kpeter@814:   public:
kpeter@814: 
kpeter@814:     /// \brief General constructor (with lower bounds).
kpeter@814:     ///
kpeter@814:     /// General constructor (with lower bounds).
kpeter@814:     ///
kpeter@814:     /// \param digraph The digraph the algorithm runs on.
kpeter@814:     /// \param lower The lower bounds of the arcs.
kpeter@814:     /// \param capacity The capacities (upper bounds) of the arcs.
kpeter@814:     /// \param cost The cost (length) values of the arcs.
kpeter@814:     /// \param supply The supply values of the nodes (signed).
kpeter@814:     CancelAndTighten( const Digraph &digraph,
kpeter@814:                       const LowerMap &lower,
kpeter@814:                       const CapacityMap &capacity,
kpeter@814:                       const CostMap &cost,
kpeter@814:                       const SupplyMap &supply ) :
kpeter@814:       _graph(digraph), _lower(&lower), _capacity(digraph), _cost(cost),
kpeter@814:       _supply(digraph), _flow(NULL), _local_flow(false),
kpeter@814:       _potential(NULL), _local_potential(false),
kpeter@814:       _res_graph(NULL), _res_cost(_cost)
kpeter@814:     {
kpeter@814:       // Check the sum of supply values
kpeter@814:       Supply sum = 0;
kpeter@814:       for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@814:         _supply[n] = supply[n];
kpeter@814:         sum += _supply[n];
kpeter@814:       }
kpeter@814:       _valid_supply = sum == 0;
kpeter@814: 
kpeter@814:       // Remove non-zero lower bounds
kpeter@814:       for (ArcIt e(_graph); e != INVALID; ++e) {
kpeter@814:         _capacity[e] = capacity[e];
kpeter@814:         if (lower[e] != 0) {
kpeter@814:           _capacity[e] -= lower[e];
kpeter@814:           _supply[_graph.source(e)] -= lower[e];
kpeter@814:           _supply[_graph.target(e)] += lower[e];
kpeter@814:         }
kpeter@814:       }
kpeter@814:     }
kpeter@814: /*
kpeter@814:     /// \brief General constructor (without lower bounds).
kpeter@814:     ///
kpeter@814:     /// General constructor (without lower bounds).
kpeter@814:     ///
kpeter@814:     /// \param digraph The digraph the algorithm runs on.
kpeter@814:     /// \param capacity The capacities (upper bounds) of the arcs.
kpeter@814:     /// \param cost The cost (length) values of the arcs.
kpeter@814:     /// \param supply The supply values of the nodes (signed).
kpeter@814:     CancelAndTighten( const Digraph &digraph,
kpeter@814:                       const CapacityMap &capacity,
kpeter@814:                       const CostMap &cost,
kpeter@814:                       const SupplyMap &supply ) :
kpeter@814:       _graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost),
kpeter@814:       _supply(supply), _flow(NULL), _local_flow(false),
kpeter@814:       _potential(NULL), _local_potential(false),
kpeter@814:       _res_graph(NULL), _res_cost(_cost)
kpeter@814:     {
kpeter@814:       // Check the sum of supply values
kpeter@814:       Supply sum = 0;
kpeter@814:       for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n];
kpeter@814:       _valid_supply = sum == 0;
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// \brief Simple constructor (with lower bounds).
kpeter@814:     ///
kpeter@814:     /// Simple constructor (with lower bounds).
kpeter@814:     ///
kpeter@814:     /// \param digraph The digraph the algorithm runs on.
kpeter@814:     /// \param lower The lower bounds of the arcs.
kpeter@814:     /// \param capacity The capacities (upper bounds) of the arcs.
kpeter@814:     /// \param cost The cost (length) values of the arcs.
kpeter@814:     /// \param s The source node.
kpeter@814:     /// \param t The target node.
kpeter@814:     /// \param flow_value The required amount of flow from node \c s
kpeter@814:     /// to node \c t (i.e. the supply of \c s and the demand of \c t).
kpeter@814:     CancelAndTighten( const Digraph &digraph,
kpeter@814:                       const LowerMap &lower,
kpeter@814:                       const CapacityMap &capacity,
kpeter@814:                       const CostMap &cost,
kpeter@814:                       Node s, Node t,
kpeter@814:                       Supply flow_value ) :
kpeter@814:       _graph(digraph), _lower(&lower), _capacity(capacity), _cost(cost),
kpeter@814:       _supply(digraph, 0), _flow(NULL), _local_flow(false),
kpeter@814:       _potential(NULL), _local_potential(false),
kpeter@814:       _res_graph(NULL), _res_cost(_cost)
kpeter@814:     {
kpeter@814:       // Remove non-zero lower bounds
kpeter@814:       _supply[s] =  flow_value;
kpeter@814:       _supply[t] = -flow_value;
kpeter@814:       for (ArcIt e(_graph); e != INVALID; ++e) {
kpeter@814:         if (lower[e] != 0) {
kpeter@814:           _capacity[e] -= lower[e];
kpeter@814:           _supply[_graph.source(e)] -= lower[e];
kpeter@814:           _supply[_graph.target(e)] += lower[e];
kpeter@814:         }
kpeter@814:       }
kpeter@814:       _valid_supply = true;
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// \brief Simple constructor (without lower bounds).
kpeter@814:     ///
kpeter@814:     /// Simple constructor (without lower bounds).
kpeter@814:     ///
kpeter@814:     /// \param digraph The digraph the algorithm runs on.
kpeter@814:     /// \param capacity The capacities (upper bounds) of the arcs.
kpeter@814:     /// \param cost The cost (length) values of the arcs.
kpeter@814:     /// \param s The source node.
kpeter@814:     /// \param t The target node.
kpeter@814:     /// \param flow_value The required amount of flow from node \c s
kpeter@814:     /// to node \c t (i.e. the supply of \c s and the demand of \c t).
kpeter@814:     CancelAndTighten( const Digraph &digraph,
kpeter@814:                       const CapacityMap &capacity,
kpeter@814:                       const CostMap &cost,
kpeter@814:                       Node s, Node t,
kpeter@814:                       Supply flow_value ) :
kpeter@814:       _graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost),
kpeter@814:       _supply(digraph, 0), _flow(NULL), _local_flow(false),
kpeter@814:       _potential(NULL), _local_potential(false),
kpeter@814:       _res_graph(NULL), _res_cost(_cost)
kpeter@814:     {
kpeter@814:       _supply[s] =  flow_value;
kpeter@814:       _supply[t] = -flow_value;
kpeter@814:       _valid_supply = true;
kpeter@814:     }
kpeter@814: */
kpeter@814:     /// Destructor.
kpeter@814:     ~CancelAndTighten() {
kpeter@814:       if (_local_flow) delete _flow;
kpeter@814:       if (_local_potential) delete _potential;
kpeter@814:       delete _res_graph;
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// \brief Set the flow map.
kpeter@814:     ///
kpeter@814:     /// Set the flow map.
kpeter@814:     ///
kpeter@814:     /// \return \c (*this)
kpeter@814:     CancelAndTighten& flowMap(FlowMap &map) {
kpeter@814:       if (_local_flow) {
kpeter@814:         delete _flow;
kpeter@814:         _local_flow = false;
kpeter@814:       }
kpeter@814:       _flow = &map;
kpeter@814:       return *this;
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// \brief Set the potential map.
kpeter@814:     ///
kpeter@814:     /// Set the potential map.
kpeter@814:     ///
kpeter@814:     /// \return \c (*this)
kpeter@814:     CancelAndTighten& potentialMap(PotentialMap &map) {
kpeter@814:       if (_local_potential) {
kpeter@814:         delete _potential;
kpeter@814:         _local_potential = false;
kpeter@814:       }
kpeter@814:       _potential = &map;
kpeter@814:       return *this;
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// \name Execution control
kpeter@814: 
kpeter@814:     /// @{
kpeter@814: 
kpeter@814:     /// \brief Run the algorithm.
kpeter@814:     ///
kpeter@814:     /// Run the algorithm.
kpeter@814:     ///
kpeter@814:     /// \return \c true if a feasible flow can be found.
kpeter@814:     bool run() {
kpeter@814:       return init() && start();
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// @}
kpeter@814: 
kpeter@814:     /// \name Query Functions
kpeter@814:     /// The result of the algorithm can be obtained using these
kpeter@814:     /// functions.\n
kpeter@814:     /// \ref lemon::CancelAndTighten::run() "run()" must be called before
kpeter@814:     /// using them.
kpeter@814: 
kpeter@814:     /// @{
kpeter@814: 
kpeter@814:     /// \brief Return a const reference to the arc map storing the
kpeter@814:     /// found flow.
kpeter@814:     ///
kpeter@814:     /// Return a const reference to the arc map storing the found flow.
kpeter@814:     ///
kpeter@814:     /// \pre \ref run() must be called before using this function.
kpeter@814:     const FlowMap& flowMap() const {
kpeter@814:       return *_flow;
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// \brief Return a const reference to the node map storing the
kpeter@814:     /// found potentials (the dual solution).
kpeter@814:     ///
kpeter@814:     /// Return a const reference to the node map storing the found
kpeter@814:     /// potentials (the dual solution).
kpeter@814:     ///
kpeter@814:     /// \pre \ref run() must be called before using this function.
kpeter@814:     const PotentialMap& potentialMap() const {
kpeter@814:       return *_potential;
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// \brief Return the flow on the given arc.
kpeter@814:     ///
kpeter@814:     /// Return the flow on the given arc.
kpeter@814:     ///
kpeter@814:     /// \pre \ref run() must be called before using this function.
kpeter@814:     Capacity flow(const Arc& arc) const {
kpeter@814:       return (*_flow)[arc];
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// \brief Return the potential of the given node.
kpeter@814:     ///
kpeter@814:     /// Return the potential of the given node.
kpeter@814:     ///
kpeter@814:     /// \pre \ref run() must be called before using this function.
kpeter@814:     Cost potential(const Node& node) const {
kpeter@814:       return (*_potential)[node];
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// \brief Return the total cost of the found flow.
kpeter@814:     ///
kpeter@814:     /// Return the total cost of the found flow. The complexity of the
kpeter@814:     /// function is \f$ O(e) \f$.
kpeter@814:     ///
kpeter@814:     /// \pre \ref run() must be called before using this function.
kpeter@814:     Cost totalCost() const {
kpeter@814:       Cost c = 0;
kpeter@814:       for (ArcIt e(_graph); e != INVALID; ++e)
kpeter@814:         c += (*_flow)[e] * _cost[e];
kpeter@814:       return c;
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// @}
kpeter@814: 
kpeter@814:   private:
kpeter@814: 
kpeter@814:     /// Initialize the algorithm.
kpeter@814:     bool init() {
kpeter@814:       if (!_valid_supply) return false;
kpeter@814: 
kpeter@814:       // Initialize flow and potential maps
kpeter@814:       if (!_flow) {
kpeter@814:         _flow = new FlowMap(_graph);
kpeter@814:         _local_flow = true;
kpeter@814:       }
kpeter@814:       if (!_potential) {
kpeter@814:         _potential = new PotentialMap(_graph);
kpeter@814:         _local_potential = true;
kpeter@814:       }
kpeter@814: 
kpeter@814:       _res_graph = new ResDigraph(_graph, _capacity, *_flow);
kpeter@814: 
kpeter@814:       // Find a feasible flow using Circulation
kpeter@814:       Circulation< Digraph, ConstMap<Arc, Capacity>,
kpeter@814:                    CapacityArcMap, SupplyMap >
kpeter@814:         circulation( _graph, constMap<Arc>(Capacity(0)),
kpeter@814:                      _capacity, _supply );
kpeter@814:       return circulation.flowMap(*_flow).run();
kpeter@814:     }
kpeter@814: 
kpeter@814:     bool start() {
kpeter@814:       const double LIMIT_FACTOR = 0.01;
kpeter@814:       const int MIN_LIMIT = 3;
kpeter@814: 
kpeter@814:       typedef typename Digraph::template NodeMap<double> FloatPotentialMap;
kpeter@814:       typedef typename Digraph::template NodeMap<int> LevelMap;
kpeter@814:       typedef typename Digraph::template NodeMap<bool> BoolNodeMap;
kpeter@814:       typedef typename Digraph::template NodeMap<Node> PredNodeMap;
kpeter@814:       typedef typename Digraph::template NodeMap<Arc> PredArcMap;
kpeter@814:       typedef typename ResDigraph::template ArcMap<double> ResShiftCostMap;
kpeter@814:       FloatPotentialMap pi(_graph);
kpeter@814:       LevelMap level(_graph);
kpeter@814:       BoolNodeMap reached(_graph);
kpeter@814:       BoolNodeMap processed(_graph);
kpeter@814:       PredNodeMap pred_node(_graph);
kpeter@814:       PredArcMap pred_arc(_graph);
kpeter@814:       int node_num = countNodes(_graph);
kpeter@814:       typedef std::pair<Arc, bool> pair;
kpeter@814:       std::vector<pair> stack(node_num);
kpeter@814:       std::vector<Node> proc_vector(node_num);
kpeter@814:       ResShiftCostMap shift_cost(*_res_graph);
kpeter@814: 
kpeter@814:       Tolerance<double> tol;
kpeter@814:       tol.epsilon(1e-6);
kpeter@814: 
kpeter@814:       Timer t1, t2, t3;
kpeter@814:       t1.reset();
kpeter@814:       t2.reset();
kpeter@814:       t3.reset();
kpeter@814: 
kpeter@814:       // Initialize epsilon and the node potentials
kpeter@814:       double epsilon = 0;
kpeter@814:       for (ArcIt e(_graph); e != INVALID; ++e) {
kpeter@814:         if (_capacity[e] - (*_flow)[e] > 0 && _cost[e] < -epsilon)
kpeter@814:           epsilon = -_cost[e];
kpeter@814:         else if ((*_flow)[e] > 0 && _cost[e] > epsilon)
kpeter@814:           epsilon = _cost[e];
kpeter@814:       }
kpeter@814:       for (NodeIt v(_graph); v != INVALID; ++v) {
kpeter@814:         pi[v] = 0;
kpeter@814:       }
kpeter@814: 
kpeter@814:       // Start phases
kpeter@814:       int limit = int(LIMIT_FACTOR * node_num);
kpeter@814:       if (limit < MIN_LIMIT) limit = MIN_LIMIT;
kpeter@814:       int iter = limit;
kpeter@814:       while (epsilon * node_num >= 1) {
kpeter@814:         t1.start();
kpeter@814:         // Find and cancel cycles in the admissible digraph using DFS
kpeter@814:         for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@814:           reached[n] = false;
kpeter@814:           processed[n] = false;
kpeter@814:         }
kpeter@814:         int stack_head = -1;
kpeter@814:         int proc_head = -1;
kpeter@814: 
kpeter@814:         for (NodeIt start(_graph); start != INVALID; ++start) {
kpeter@814:           if (reached[start]) continue;
kpeter@814: 
kpeter@814:           // New start node
kpeter@814:           reached[start] = true;
kpeter@814:           pred_arc[start] = INVALID;
kpeter@814:           pred_node[start] = INVALID;
kpeter@814: 
kpeter@814:           // Find the first admissible residual outgoing arc
kpeter@814:           double p = pi[start];
kpeter@814:           Arc e;
kpeter@814:           _graph.firstOut(e, start);
kpeter@814:           while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 ||
kpeter@814:                   !tol.negative(_cost[e] + p - pi[_graph.target(e)])) )
kpeter@814:             _graph.nextOut(e);
kpeter@814:           if (e != INVALID) {
kpeter@814:             stack[++stack_head] = pair(e, true);
kpeter@814:             goto next_step_1;
kpeter@814:           }
kpeter@814:           _graph.firstIn(e, start);
kpeter@814:           while ( e != INVALID && ((*_flow)[e] == 0 ||
kpeter@814:                   !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) )
kpeter@814:             _graph.nextIn(e);
kpeter@814:           if (e != INVALID) {
kpeter@814:             stack[++stack_head] = pair(e, false);
kpeter@814:             goto next_step_1;
kpeter@814:           }
kpeter@814:           processed[start] = true;
kpeter@814:           proc_vector[++proc_head] = start;
kpeter@814:           continue;
kpeter@814:         next_step_1:
kpeter@814: 
kpeter@814:           while (stack_head >= 0) {
kpeter@814:             Arc se = stack[stack_head].first;
kpeter@814:             bool sf = stack[stack_head].second;
kpeter@814:             Node u, v;
kpeter@814:             if (sf) {
kpeter@814:               u = _graph.source(se);
kpeter@814:               v = _graph.target(se);
kpeter@814:             } else {
kpeter@814:               u = _graph.target(se);
kpeter@814:               v = _graph.source(se);
kpeter@814:             }
kpeter@814: 
kpeter@814:             if (!reached[v]) {
kpeter@814:               // A new node is reached
kpeter@814:               reached[v] = true;
kpeter@814:               pred_node[v] = u;
kpeter@814:               pred_arc[v] = se;
kpeter@814:               // Find the first admissible residual outgoing arc
kpeter@814:               double p = pi[v];
kpeter@814:               Arc e;
kpeter@814:               _graph.firstOut(e, v);
kpeter@814:               while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 ||
kpeter@814:                       !tol.negative(_cost[e] + p - pi[_graph.target(e)])) )
kpeter@814:                 _graph.nextOut(e);
kpeter@814:               if (e != INVALID) {
kpeter@814:                 stack[++stack_head] = pair(e, true);
kpeter@814:                 goto next_step_2;
kpeter@814:               }
kpeter@814:               _graph.firstIn(e, v);
kpeter@814:               while ( e != INVALID && ((*_flow)[e] == 0 ||
kpeter@814:                       !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) )
kpeter@814:                 _graph.nextIn(e);
kpeter@814:               stack[++stack_head] = pair(e, false);
kpeter@814:             next_step_2: ;
kpeter@814:             } else {
kpeter@814:               if (!processed[v]) {
kpeter@814:                 // A cycle is found
kpeter@814:                 Node n, w = u;
kpeter@814:                 Capacity d, delta = sf ? _capacity[se] - (*_flow)[se] :
kpeter@814:                                          (*_flow)[se];
kpeter@814:                 for (n = u; n != v; n = pred_node[n]) {
kpeter@814:                   d = _graph.target(pred_arc[n]) == n ?
kpeter@814:                       _capacity[pred_arc[n]] - (*_flow)[pred_arc[n]] :
kpeter@814:                       (*_flow)[pred_arc[n]];
kpeter@814:                   if (d <= delta) {
kpeter@814:                     delta = d;
kpeter@814:                     w = pred_node[n];
kpeter@814:                   }
kpeter@814:                 }
kpeter@814: 
kpeter@814: /*
kpeter@814:                 std::cout << "CYCLE FOUND: ";
kpeter@814:                 if (sf)
kpeter@814:                   std::cout << _cost[se] + pi[_graph.source(se)] - pi[_graph.target(se)];
kpeter@814:                 else
kpeter@814:                   std::cout << _graph.id(se) << ":" << -(_cost[se] + pi[_graph.source(se)] - pi[_graph.target(se)]);
kpeter@814:                 for (n = u; n != v; n = pred_node[n]) {
kpeter@814:                   if (_graph.target(pred_arc[n]) == n)
kpeter@814:                     std::cout << " " << _cost[pred_arc[n]] + pi[_graph.source(pred_arc[n])] - pi[_graph.target(pred_arc[n])];
kpeter@814:                   else
kpeter@814:                     std::cout << " " << -(_cost[pred_arc[n]] + pi[_graph.source(pred_arc[n])] - pi[_graph.target(pred_arc[n])]);
kpeter@814:                 }
kpeter@814:                 std::cout << "\n";
kpeter@814: */
kpeter@814:                 // Augment along the cycle
kpeter@814:                 (*_flow)[se] = sf ? (*_flow)[se] + delta :
kpeter@814:                                     (*_flow)[se] - delta;
kpeter@814:                 for (n = u; n != v; n = pred_node[n]) {
kpeter@814:                   if (_graph.target(pred_arc[n]) == n)
kpeter@814:                     (*_flow)[pred_arc[n]] += delta;
kpeter@814:                   else
kpeter@814:                     (*_flow)[pred_arc[n]] -= delta;
kpeter@814:                 }
kpeter@814:                 for (n = u; stack_head > 0 && n != w; n = pred_node[n]) {
kpeter@814:                   --stack_head;
kpeter@814:                   reached[n] = false;
kpeter@814:                 }
kpeter@814:                 u = w;
kpeter@814:               }
kpeter@814:               v = u;
kpeter@814: 
kpeter@814:               // Find the next admissible residual outgoing arc
kpeter@814:               double p = pi[v];
kpeter@814:               Arc e = stack[stack_head].first;
kpeter@814:               if (!stack[stack_head].second) {
kpeter@814:                 _graph.nextIn(e);
kpeter@814:                 goto in_arc_3;
kpeter@814:               }
kpeter@814:               _graph.nextOut(e);
kpeter@814:               while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 ||
kpeter@814:                       !tol.negative(_cost[e] + p - pi[_graph.target(e)])) )
kpeter@814:                 _graph.nextOut(e);
kpeter@814:               if (e != INVALID) {
kpeter@814:                 stack[stack_head] = pair(e, true);
kpeter@814:                 goto next_step_3;
kpeter@814:               }
kpeter@814:               _graph.firstIn(e, v);
kpeter@814:             in_arc_3:
kpeter@814:               while ( e != INVALID && ((*_flow)[e] == 0 ||
kpeter@814:                       !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) )
kpeter@814:                 _graph.nextIn(e);
kpeter@814:               stack[stack_head] = pair(e, false);
kpeter@814:             next_step_3: ;
kpeter@814:             }
kpeter@814: 
kpeter@814:             while (stack_head >= 0 && stack[stack_head].first == INVALID) {
kpeter@814:               processed[v] = true;
kpeter@814:               proc_vector[++proc_head] = v;
kpeter@814:               if (--stack_head >= 0) {
kpeter@814:                 v = stack[stack_head].second ?
kpeter@814:                     _graph.source(stack[stack_head].first) :
kpeter@814:                     _graph.target(stack[stack_head].first);
kpeter@814:                 // Find the next admissible residual outgoing arc
kpeter@814:                 double p = pi[v];
kpeter@814:                 Arc e = stack[stack_head].first;
kpeter@814:                 if (!stack[stack_head].second) {
kpeter@814:                   _graph.nextIn(e);
kpeter@814:                   goto in_arc_4;
kpeter@814:                 }
kpeter@814:                 _graph.nextOut(e);
kpeter@814:                 while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 ||
kpeter@814:                         !tol.negative(_cost[e] + p - pi[_graph.target(e)])) )
kpeter@814:                   _graph.nextOut(e);
kpeter@814:                 if (e != INVALID) {
kpeter@814:                   stack[stack_head] = pair(e, true);
kpeter@814:                   goto next_step_4;
kpeter@814:                 }
kpeter@814:                 _graph.firstIn(e, v);
kpeter@814:               in_arc_4:
kpeter@814:                 while ( e != INVALID && ((*_flow)[e] == 0 ||
kpeter@814:                         !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) )
kpeter@814:                   _graph.nextIn(e);
kpeter@814:                 stack[stack_head] = pair(e, false);
kpeter@814:               next_step_4: ;
kpeter@814:               }
kpeter@814:             }
kpeter@814:           }
kpeter@814:         }
kpeter@814:         t1.stop();
kpeter@814: 
kpeter@814:         // Tighten potentials and epsilon
kpeter@814:         if (--iter > 0) {
kpeter@814:           // Compute levels
kpeter@814:           t2.start();
kpeter@814:           for (int i = proc_head; i >= 0; --i) {
kpeter@814:             Node v = proc_vector[i];
kpeter@814:             double p = pi[v];
kpeter@814:             int l = 0;
kpeter@814:             for (InArcIt e(_graph, v); e != INVALID; ++e) {
kpeter@814:               Node u = _graph.source(e);
kpeter@814:               if ( _capacity[e] - (*_flow)[e] > 0 &&
kpeter@814:                    tol.negative(_cost[e] + pi[u] - p) &&
kpeter@814:                    level[u] + 1 > l ) l = level[u] + 1;
kpeter@814:             }
kpeter@814:             for (OutArcIt e(_graph, v); e != INVALID; ++e) {
kpeter@814:               Node u = _graph.target(e);
kpeter@814:               if ( (*_flow)[e] > 0 &&
kpeter@814:                    tol.negative(-_cost[e] + pi[u] - p) &&
kpeter@814:                    level[u] + 1 > l ) l = level[u] + 1;
kpeter@814:             }
kpeter@814:             level[v] = l;
kpeter@814:           }
kpeter@814: 
kpeter@814:           // Modify potentials
kpeter@814:           double p, q = -1;
kpeter@814:           for (ArcIt e(_graph); e != INVALID; ++e) {
kpeter@814:             Node u = _graph.source(e);
kpeter@814:             Node v = _graph.target(e);
kpeter@814:             if (_capacity[e] - (*_flow)[e] > 0 && level[u] - level[v] > 0) {
kpeter@814:               p = (_cost[e] + pi[u] - pi[v] + epsilon) /
kpeter@814:                   (level[u] - level[v] + 1);
kpeter@814:               if (q < 0 || p < q) q = p;
kpeter@814:             }
kpeter@814:             else if ((*_flow)[e] > 0 && level[v] - level[u] > 0) {
kpeter@814:               p = (-_cost[e] - pi[u] + pi[v] + epsilon) /
kpeter@814:                   (level[v] - level[u] + 1);
kpeter@814:               if (q < 0 || p < q) q = p;
kpeter@814:             }
kpeter@814:           }
kpeter@814:           for (NodeIt v(_graph); v != INVALID; ++v) {
kpeter@814:             pi[v] -= q * level[v];
kpeter@814:           }
kpeter@814: 
kpeter@814:           // Modify epsilon
kpeter@814:           epsilon = 0;
kpeter@814:           for (ArcIt e(_graph); e != INVALID; ++e) {
kpeter@814:             double curr = _cost[e] + pi[_graph.source(e)]
kpeter@814:                                    - pi[_graph.target(e)];
kpeter@814:             if (_capacity[e] - (*_flow)[e] > 0 && curr < -epsilon)
kpeter@814:               epsilon = -curr;
kpeter@814:             else if ((*_flow)[e] > 0 && curr > epsilon)
kpeter@814:               epsilon = curr;
kpeter@814:           }
kpeter@814:           t2.stop();
kpeter@814:         } else {
kpeter@814:           // Set epsilon to the minimum cycle mean
kpeter@814:           t3.start();
kpeter@814: 
kpeter@814: /**/
kpeter@814:           StaticDigraph static_graph;
kpeter@814:           typename ResDigraph::template NodeMap<typename StaticDigraph::Node> node_ref(*_res_graph);
kpeter@814:           typename ResDigraph::template ArcMap<typename StaticDigraph::Arc> arc_ref(*_res_graph);
kpeter@814:           static_graph.build(*_res_graph, node_ref, arc_ref);
kpeter@814:           typename StaticDigraph::template NodeMap<double> static_pi(static_graph);
kpeter@814:           typename StaticDigraph::template ArcMap<double> static_cost(static_graph);
kpeter@814: 
kpeter@814:           for (typename ResDigraph::ArcIt e(*_res_graph); e != INVALID; ++e)
kpeter@814:             static_cost[arc_ref[e]] = _res_cost[e];
kpeter@814: 
kpeter@814:           Howard<StaticDigraph, typename StaticDigraph::template ArcMap<double> >
kpeter@814:             mmc(static_graph, static_cost);
kpeter@814:           mmc.findMinMean();
kpeter@814:           epsilon = -mmc.cycleMean();
kpeter@814: /**/
kpeter@814: 
kpeter@814: /*
kpeter@814:           Howard<ResDigraph, ResidualCostMap> mmc(*_res_graph, _res_cost);
kpeter@814:           mmc.findMinMean();
kpeter@814:           epsilon = -mmc.cycleMean();
kpeter@814: */
kpeter@814: 
kpeter@814:           // Compute feasible potentials for the current epsilon
kpeter@814:           for (typename StaticDigraph::ArcIt e(static_graph); e != INVALID; ++e)
kpeter@814:             static_cost[e] += epsilon;
kpeter@814:           typename BellmanFord<StaticDigraph, typename StaticDigraph::template ArcMap<double> >::
kpeter@814:             template SetDistMap<typename StaticDigraph::template NodeMap<double> >::
kpeter@814:             template SetOperationTraits<BFOperationTraits>::Create
kpeter@814:               bf(static_graph, static_cost);
kpeter@814:           bf.distMap(static_pi).init(0);
kpeter@814:           bf.start();
kpeter@814:           for (NodeIt n(_graph); n != INVALID; ++n)
kpeter@814:             pi[n] = static_pi[node_ref[n]];
kpeter@814:           
kpeter@814: /*
kpeter@814:           for (typename ResDigraph::ArcIt e(*_res_graph); e != INVALID; ++e)
kpeter@814:             shift_cost[e] = _res_cost[e] + epsilon;
kpeter@814:           typename BellmanFord<ResDigraph, ResShiftCostMap>::
kpeter@814:             template SetDistMap<FloatPotentialMap>::
kpeter@814:             template SetOperationTraits<BFOperationTraits>::Create
kpeter@814:               bf(*_res_graph, shift_cost);
kpeter@814:           bf.distMap(pi).init(0);
kpeter@814:           bf.start();
kpeter@814: */
kpeter@814: 
kpeter@814:           iter = limit;
kpeter@814:           t3.stop();
kpeter@814:         }
kpeter@814:       }
kpeter@814: 
kpeter@814: //      std::cout << t1.realTime() << " " << t2.realTime() << " " << t3.realTime() << "\n";
kpeter@814: 
kpeter@814:       // Handle non-zero lower bounds
kpeter@814:       if (_lower) {
kpeter@814:         for (ArcIt e(_graph); e != INVALID; ++e)
kpeter@814:           (*_flow)[e] += (*_lower)[e];
kpeter@814:       }
kpeter@814:       return true;
kpeter@814:     }
kpeter@814: 
kpeter@814:   }; //class CancelAndTighten
kpeter@814: 
kpeter@814:   ///@}
kpeter@814: 
kpeter@814: } //namespace lemon
kpeter@814: 
kpeter@814: #endif //LEMON_CANCEL_AND_TIGHTEN_H