deba@2440: /* -*- C++ -*-
deba@2440:  *
deba@2440:  * This file is a part of LEMON, a generic C++ optimization library
deba@2440:  *
alpar@2553:  * Copyright (C) 2003-2008
deba@2440:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@2440:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@2440:  *
deba@2440:  * Permission to use, modify and distribute this software is granted
deba@2440:  * provided that this copyright notice appears in all copies. For
deba@2440:  * precise terms see the accompanying LICENSE file.
deba@2440:  *
deba@2440:  * This software is provided "AS IS" with no warranty of any kind,
deba@2440:  * express or implied, and with no claim as to its suitability for any
deba@2440:  * purpose.
deba@2440:  *
deba@2440:  */
deba@2440: 
deba@2440: #ifndef LEMON_CYCLE_CANCELING_H
deba@2440: #define LEMON_CYCLE_CANCELING_H
deba@2440: 
deba@2440: /// \ingroup min_cost_flow
deba@2440: ///
deba@2440: /// \file
kpeter@2573: /// \brief Cycle-canceling algorithm for finding a minimum cost flow.
deba@2440: 
deba@2440: #include <vector>
kpeter@2509: #include <lemon/graph_adaptor.h>
kpeter@2573: #include <lemon/path.h>
kpeter@2573: 
deba@2440: #include <lemon/circulation.h>
kpeter@2573: #include <lemon/bellman_ford.h>
kpeter@2573: #include <lemon/min_mean_cycle.h>
kpeter@2556: 
deba@2440: namespace lemon {
deba@2440: 
deba@2440:   /// \addtogroup min_cost_flow
deba@2440:   /// @{
deba@2440: 
kpeter@2556:   /// \brief Implementation of a cycle-canceling algorithm for
kpeter@2556:   /// finding a minimum cost flow.
deba@2440:   ///
kpeter@2556:   /// \ref CycleCanceling implements a cycle-canceling algorithm for
kpeter@2556:   /// finding a minimum cost flow.
deba@2440:   ///
kpeter@2573:   /// \tparam Graph The directed graph type the algorithm runs on.
kpeter@2573:   /// \tparam LowerMap The type of the lower bound map.
kpeter@2573:   /// \tparam CapacityMap The type of the capacity (upper bound) map.
kpeter@2573:   /// \tparam CostMap The type of the cost (length) map.
kpeter@2573:   /// \tparam SupplyMap The type of the supply map.
deba@2440:   ///
deba@2440:   /// \warning
kpeter@2573:   /// - Edge capacities and costs should be \e non-negative \e integers.
kpeter@2573:   /// - Supply values should be \e signed \e integers.
kpeter@2581:   /// - The value types of the maps should be convertible to each other.
kpeter@2581:   /// - \c CostMap::Value must be signed type.
kpeter@2573:   ///
kpeter@2573:   /// \note By default the \ref BellmanFord "Bellman-Ford" algorithm is
kpeter@2573:   /// used for negative cycle detection with limited iteration number.
kpeter@2573:   /// However \ref CycleCanceling also provides the "Minimum Mean
kpeter@2573:   /// Cycle-Canceling" algorithm, which is \e strongly \e polynomial,
kpeter@2573:   /// but rather slower in practice.
kpeter@2573:   /// To use this version of the algorithm, call \ref run() with \c true
kpeter@2573:   /// parameter.
deba@2440:   ///
deba@2440:   /// \author Peter Kovacs
kpeter@2533:   template < typename Graph,
kpeter@2533:              typename LowerMap = typename Graph::template EdgeMap<int>,
kpeter@2573:              typename CapacityMap = typename Graph::template EdgeMap<int>,
kpeter@2533:              typename CostMap = typename Graph::template EdgeMap<int>,
kpeter@2573:              typename SupplyMap = typename Graph::template NodeMap<int> >
deba@2440:   class CycleCanceling
deba@2440:   {
kpeter@2556:     GRAPH_TYPEDEFS(typename Graph);
deba@2440: 
deba@2440:     typedef typename CapacityMap::Value Capacity;
deba@2440:     typedef typename CostMap::Value Cost;
deba@2440:     typedef typename SupplyMap::Value Supply;
kpeter@2556:     typedef typename Graph::template EdgeMap<Capacity> CapacityEdgeMap;
kpeter@2556:     typedef typename Graph::template NodeMap<Supply> SupplyNodeMap;
deba@2440: 
deba@2440:     typedef ResGraphAdaptor< const Graph, Capacity,
kpeter@2556:                              CapacityEdgeMap, CapacityEdgeMap > ResGraph;
deba@2440:     typedef typename ResGraph::Node ResNode;
deba@2440:     typedef typename ResGraph::NodeIt ResNodeIt;
deba@2440:     typedef typename ResGraph::Edge ResEdge;
deba@2440:     typedef typename ResGraph::EdgeIt ResEdgeIt;
deba@2440: 
deba@2440:   public:
deba@2440: 
kpeter@2556:     /// The type of the flow map.
kpeter@2556:     typedef typename Graph::template EdgeMap<Capacity> FlowMap;
kpeter@2581:     /// The type of the potential map.
kpeter@2581:     typedef typename Graph::template NodeMap<Cost> PotentialMap;
deba@2440: 
kpeter@2573:   private:
deba@2440: 
kpeter@2573:     /// \brief Map adaptor class for handling residual edge costs.
kpeter@2573:     ///
kpeter@2620:     /// Map adaptor class for handling residual edge costs.
kpeter@2573:     class ResidualCostMap : public MapBase<ResEdge, Cost>
deba@2440:     {
deba@2440:     private:
deba@2440: 
kpeter@2573:       const CostMap &_cost_map;
deba@2440: 
deba@2440:     public:
deba@2440: 
kpeter@2573:       ///\e
kpeter@2573:       ResidualCostMap(const CostMap &cost_map) : _cost_map(cost_map) {}
deba@2440: 
kpeter@2573:       ///\e
kpeter@2509:       Cost operator[](const ResEdge &e) const {
kpeter@2573:         return ResGraph::forward(e) ? _cost_map[e] : -_cost_map[e];
deba@2440:       }
deba@2440: 
kpeter@2573:     }; //class ResidualCostMap
deba@2440: 
kpeter@2573:   private:
deba@2440: 
kpeter@2573:     // The maximum number of iterations for the first execution of the
kpeter@2573:     // Bellman-Ford algorithm. It should be at least 2.
kpeter@2593:     static const int BF_FIRST_LIMIT  = 2;
kpeter@2573:     // The iteration limit for the Bellman-Ford algorithm is multiplied
kpeter@2593:     // by BF_LIMIT_FACTOR/100 in every round.
kpeter@2593:     static const int BF_LIMIT_FACTOR = 150;
deba@2440: 
kpeter@2573:   private:
deba@2440: 
kpeter@2573:     // The directed graph the algorithm runs on
kpeter@2573:     const Graph &_graph;
kpeter@2573:     // The original lower bound map
kpeter@2573:     const LowerMap *_lower;
kpeter@2573:     // The modified capacity map
kpeter@2573:     CapacityEdgeMap _capacity;
kpeter@2573:     // The original cost map
kpeter@2573:     const CostMap &_cost;
kpeter@2573:     // The modified supply map
kpeter@2573:     SupplyNodeMap _supply;
kpeter@2573:     bool _valid_supply;
kpeter@2573: 
kpeter@2573:     // Edge map of the current flow
kpeter@2581:     FlowMap *_flow;
kpeter@2581:     bool _local_flow;
kpeter@2581:     // Node map of the current potentials
kpeter@2581:     PotentialMap *_potential;
kpeter@2581:     bool _local_potential;
kpeter@2573: 
kpeter@2573:     // The residual graph
kpeter@2581:     ResGraph *_res_graph;
kpeter@2573:     // The residual cost map
kpeter@2573:     ResidualCostMap _res_cost;
kpeter@2573: 
kpeter@2573:   public:
deba@2440: 
kpeter@2581:     /// \brief General constructor (with lower bounds).
deba@2440:     ///
kpeter@2581:     /// General constructor (with lower bounds).
deba@2440:     ///
kpeter@2573:     /// \param graph The directed graph the algorithm runs on.
kpeter@2573:     /// \param lower The lower bounds of the edges.
kpeter@2573:     /// \param capacity The capacities (upper bounds) of the edges.
kpeter@2573:     /// \param cost The cost (length) values of the edges.
kpeter@2573:     /// \param supply The supply values of the nodes (signed).
kpeter@2573:     CycleCanceling( const Graph &graph,
kpeter@2573:                     const LowerMap &lower,
kpeter@2573:                     const CapacityMap &capacity,
kpeter@2573:                     const CostMap &cost,
kpeter@2573:                     const SupplyMap &supply ) :
kpeter@2629:       _graph(graph), _lower(&lower), _capacity(capacity), _cost(cost),
kpeter@2629:       _supply(supply), _flow(NULL), _local_flow(false),
kpeter@2623:       _potential(NULL), _local_potential(false), _res_graph(NULL),
kpeter@2623:       _res_cost(_cost)
deba@2440:     {
kpeter@2629:       // Check the sum of supply values
deba@2440:       Supply sum = 0;
kpeter@2629:       for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n];
kpeter@2629:       _valid_supply = sum == 0;
kpeter@2629: 
kpeter@2629:       // Remove non-zero lower bounds
kpeter@2629:       for (EdgeIt e(_graph); e != INVALID; ++e) {
kpeter@2629:         if (lower[e] != 0) {
kpeter@2629:           _capacity[e] -= lower[e];
kpeter@2629:           _supply[_graph.source(e)] -= lower[e];
kpeter@2629:           _supply[_graph.target(e)] += lower[e];
kpeter@2629:         }
deba@2440:       }
deba@2440:     }
deba@2440: 
kpeter@2581:     /// \brief General constructor (without lower bounds).
deba@2440:     ///
kpeter@2581:     /// General constructor (without lower bounds).
deba@2440:     ///
kpeter@2573:     /// \param graph The directed graph the algorithm runs on.
kpeter@2573:     /// \param capacity The capacities (upper bounds) of the edges.
kpeter@2573:     /// \param cost The cost (length) values of the edges.
kpeter@2573:     /// \param supply The supply values of the nodes (signed).
kpeter@2573:     CycleCanceling( const Graph &graph,
kpeter@2573:                     const CapacityMap &capacity,
kpeter@2573:                     const CostMap &cost,
kpeter@2573:                     const SupplyMap &supply ) :
kpeter@2573:       _graph(graph), _lower(NULL), _capacity(capacity), _cost(cost),
kpeter@2623:       _supply(supply), _flow(NULL), _local_flow(false),
kpeter@2623:       _potential(NULL), _local_potential(false), _res_graph(NULL),
kpeter@2623:       _res_cost(_cost)
deba@2440:     {
kpeter@2629:       // Check the sum of supply values
deba@2440:       Supply sum = 0;
kpeter@2573:       for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n];
kpeter@2573:       _valid_supply = sum == 0;
deba@2440:     }
deba@2440: 
kpeter@2581:     /// \brief Simple constructor (with lower bounds).
deba@2440:     ///
kpeter@2581:     /// Simple constructor (with lower bounds).
deba@2440:     ///
kpeter@2573:     /// \param graph The directed graph the algorithm runs on.
kpeter@2573:     /// \param lower The lower bounds of the edges.
kpeter@2573:     /// \param capacity The capacities (upper bounds) of the edges.
kpeter@2573:     /// \param cost The cost (length) values of the edges.
kpeter@2573:     /// \param s The source node.
kpeter@2573:     /// \param t The target node.
kpeter@2573:     /// \param flow_value The required amount of flow from node \c s
kpeter@2573:     /// to node \c t (i.e. the supply of \c s and the demand of \c t).
kpeter@2573:     CycleCanceling( const Graph &graph,
kpeter@2573:                     const LowerMap &lower,
kpeter@2573:                     const CapacityMap &capacity,
kpeter@2573:                     const CostMap &cost,
kpeter@2573:                     Node s, Node t,
kpeter@2573:                     Supply flow_value ) :
kpeter@2629:       _graph(graph), _lower(&lower), _capacity(capacity), _cost(cost),
kpeter@2629:       _supply(graph, 0), _flow(NULL), _local_flow(false),
kpeter@2623:       _potential(NULL), _local_potential(false), _res_graph(NULL),
kpeter@2623:       _res_cost(_cost)
deba@2440:     {
kpeter@2629:       // Remove non-zero lower bounds
kpeter@2629:       _supply[s] =  flow_value;
kpeter@2629:       _supply[t] = -flow_value;
kpeter@2629:       for (EdgeIt e(_graph); e != INVALID; ++e) {
kpeter@2629:         if (lower[e] != 0) {
kpeter@2629:           _capacity[e] -= lower[e];
kpeter@2629:           _supply[_graph.source(e)] -= lower[e];
kpeter@2629:           _supply[_graph.target(e)] += lower[e];
kpeter@2629:         }
deba@2440:       }
kpeter@2573:       _valid_supply = true;
deba@2440:     }
deba@2440: 
kpeter@2581:     /// \brief Simple constructor (without lower bounds).
deba@2440:     ///
kpeter@2581:     /// Simple constructor (without lower bounds).
deba@2440:     ///
kpeter@2573:     /// \param graph The directed graph the algorithm runs on.
kpeter@2573:     /// \param capacity The capacities (upper bounds) of the edges.
kpeter@2573:     /// \param cost The cost (length) values of the edges.
kpeter@2573:     /// \param s The source node.
kpeter@2573:     /// \param t The target node.
kpeter@2573:     /// \param flow_value The required amount of flow from node \c s
kpeter@2573:     /// to node \c t (i.e. the supply of \c s and the demand of \c t).
kpeter@2573:     CycleCanceling( const Graph &graph,
kpeter@2573:                     const CapacityMap &capacity,
kpeter@2573:                     const CostMap &cost,
kpeter@2573:                     Node s, Node t,
kpeter@2573:                     Supply flow_value ) :
kpeter@2573:       _graph(graph), _lower(NULL), _capacity(capacity), _cost(cost),
kpeter@2623:       _supply(graph, 0), _flow(NULL), _local_flow(false),
kpeter@2623:       _potential(NULL), _local_potential(false), _res_graph(NULL),
kpeter@2623:       _res_cost(_cost)
deba@2440:     {
kpeter@2573:       _supply[s] =  flow_value;
kpeter@2573:       _supply[t] = -flow_value;
kpeter@2573:       _valid_supply = true;
deba@2440:     }
deba@2440: 
kpeter@2581:     /// Destructor.
kpeter@2581:     ~CycleCanceling() {
kpeter@2581:       if (_local_flow) delete _flow;
kpeter@2581:       if (_local_potential) delete _potential;
kpeter@2581:       delete _res_graph;
kpeter@2581:     }
kpeter@2581: 
kpeter@2620:     /// \brief Set the flow map.
kpeter@2581:     ///
kpeter@2620:     /// Set the flow map.
kpeter@2581:     ///
kpeter@2581:     /// \return \c (*this)
kpeter@2581:     CycleCanceling& flowMap(FlowMap &map) {
kpeter@2581:       if (_local_flow) {
kpeter@2581:         delete _flow;
kpeter@2581:         _local_flow = false;
kpeter@2581:       }
kpeter@2581:       _flow = &map;
kpeter@2581:       return *this;
kpeter@2581:     }
kpeter@2581: 
kpeter@2620:     /// \brief Set the potential map.
kpeter@2581:     ///
kpeter@2620:     /// Set the potential map.
kpeter@2581:     ///
kpeter@2581:     /// \return \c (*this)
kpeter@2581:     CycleCanceling& potentialMap(PotentialMap &map) {
kpeter@2581:       if (_local_potential) {
kpeter@2581:         delete _potential;
kpeter@2581:         _local_potential = false;
kpeter@2581:       }
kpeter@2581:       _potential = &map;
kpeter@2581:       return *this;
kpeter@2581:     }
kpeter@2581: 
kpeter@2581:     /// \name Execution control
kpeter@2581: 
kpeter@2581:     /// @{
kpeter@2581: 
kpeter@2620:     /// \brief Run the algorithm.
kpeter@2556:     ///
kpeter@2620:     /// Run the algorithm.
kpeter@2556:     ///
kpeter@2573:     /// \param min_mean_cc Set this parameter to \c true to run the
kpeter@2573:     /// "Minimum Mean Cycle-Canceling" algorithm, which is strongly
kpeter@2573:     /// polynomial, but rather slower in practice.
kpeter@2573:     ///
kpeter@2556:     /// \return \c true if a feasible flow can be found.
kpeter@2573:     bool run(bool min_mean_cc = false) {
kpeter@2573:       return init() && start(min_mean_cc);
kpeter@2556:     }
kpeter@2556: 
kpeter@2581:     /// @}
kpeter@2581: 
kpeter@2581:     /// \name Query Functions
kpeter@2581:     /// The result of the algorithm can be obtained using these
kpeter@2620:     /// functions.\n
kpeter@2620:     /// \ref lemon::CycleCanceling::run() "run()" must be called before
kpeter@2620:     /// using them.
kpeter@2581: 
kpeter@2581:     /// @{
kpeter@2581: 
kpeter@2620:     /// \brief Return a const reference to the edge map storing the
kpeter@2573:     /// found flow.
deba@2440:     ///
kpeter@2620:     /// Return a const reference to the edge map storing the found flow.
deba@2440:     ///
deba@2440:     /// \pre \ref run() must be called before using this function.
deba@2440:     const FlowMap& flowMap() const {
kpeter@2581:       return *_flow;
kpeter@2581:     }
kpeter@2581: 
kpeter@2620:     /// \brief Return a const reference to the node map storing the
kpeter@2581:     /// found potentials (the dual solution).
kpeter@2581:     ///
kpeter@2620:     /// Return a const reference to the node map storing the found
kpeter@2581:     /// potentials (the dual solution).
kpeter@2581:     ///
kpeter@2581:     /// \pre \ref run() must be called before using this function.
kpeter@2581:     const PotentialMap& potentialMap() const {
kpeter@2581:       return *_potential;
kpeter@2581:     }
kpeter@2581: 
kpeter@2620:     /// \brief Return the flow on the given edge.
kpeter@2581:     ///
kpeter@2620:     /// Return the flow on the given edge.
kpeter@2581:     ///
kpeter@2581:     /// \pre \ref run() must be called before using this function.
kpeter@2581:     Capacity flow(const Edge& edge) const {
kpeter@2581:       return (*_flow)[edge];
kpeter@2581:     }
kpeter@2581: 
kpeter@2620:     /// \brief Return the potential of the given node.
kpeter@2581:     ///
kpeter@2620:     /// Return the potential of the given node.
kpeter@2581:     ///
kpeter@2581:     /// \pre \ref run() must be called before using this function.
kpeter@2581:     Cost potential(const Node& node) const {
kpeter@2581:       return (*_potential)[node];
deba@2440:     }
deba@2440: 
kpeter@2620:     /// \brief Return the total cost of the found flow.
deba@2440:     ///
kpeter@2620:     /// Return the total cost of the found flow. The complexity of the
deba@2440:     /// function is \f$ O(e) \f$.
deba@2440:     ///
deba@2440:     /// \pre \ref run() must be called before using this function.
deba@2440:     Cost totalCost() const {
deba@2440:       Cost c = 0;
kpeter@2573:       for (EdgeIt e(_graph); e != INVALID; ++e)
kpeter@2581:         c += (*_flow)[e] * _cost[e];
deba@2440:       return c;
deba@2440:     }
deba@2440: 
kpeter@2581:     /// @}
kpeter@2581: 
kpeter@2573:   private:
deba@2440: 
kpeter@2620:     /// Initialize the algorithm.
deba@2440:     bool init() {
kpeter@2573:       if (!_valid_supply) return false;
deba@2440: 
kpeter@2581:       // Initializing flow and potential maps
kpeter@2581:       if (!_flow) {
kpeter@2581:         _flow = new FlowMap(_graph);
kpeter@2581:         _local_flow = true;
kpeter@2581:       }
kpeter@2581:       if (!_potential) {
kpeter@2581:         _potential = new PotentialMap(_graph);
kpeter@2581:         _local_potential = true;
kpeter@2581:       }
kpeter@2581: 
kpeter@2581:       _res_graph = new ResGraph(_graph, _capacity, *_flow);
kpeter@2581: 
kpeter@2573:       // Finding a feasible flow using Circulation
kpeter@2556:       Circulation< Graph, ConstMap<Edge, Capacity>, CapacityEdgeMap,
kpeter@2556:                    SupplyMap >
kpeter@2581:         circulation( _graph, constMap<Edge>(Capacity(0)), _capacity,
kpeter@2573:                      _supply );
kpeter@2581:       return circulation.flowMap(*_flow).run();
deba@2440:     }
deba@2440: 
kpeter@2573:     bool start(bool min_mean_cc) {
kpeter@2573:       if (min_mean_cc)
kpeter@2581:         startMinMean();
kpeter@2573:       else
kpeter@2581:         start();
kpeter@2581: 
kpeter@2581:       // Handling non-zero lower bounds
kpeter@2581:       if (_lower) {
kpeter@2581:         for (EdgeIt e(_graph); e != INVALID; ++e)
kpeter@2581:           (*_flow)[e] += (*_lower)[e];
kpeter@2581:       }
kpeter@2581:       return true;
kpeter@2573:     }
kpeter@2573: 
kpeter@2620:     /// \brief Execute the algorithm using \ref BellmanFord.
kpeter@2573:     ///
kpeter@2620:     /// Execute the algorithm using the \ref BellmanFord
kpeter@2573:     /// "Bellman-Ford" algorithm for negative cycle detection with
kpeter@2573:     /// successively larger limit for the number of iterations.
kpeter@2581:     void start() {
kpeter@2581:       typename BellmanFord<ResGraph, ResidualCostMap>::PredMap pred(*_res_graph);
kpeter@2581:       typename ResGraph::template NodeMap<int> visited(*_res_graph);
deba@2440:       std::vector<ResEdge> cycle;
kpeter@2573:       int node_num = countNodes(_graph);
deba@2440: 
kpeter@2573:       int length_bound = BF_FIRST_LIMIT;
deba@2440:       bool optimal = false;
deba@2440:       while (!optimal) {
kpeter@2581:         BellmanFord<ResGraph, ResidualCostMap> bf(*_res_graph, _res_cost);
kpeter@2556:         bf.predMap(pred);
kpeter@2556:         bf.init(0);
kpeter@2556:         int iter_num = 0;
kpeter@2556:         bool cycle_found = false;
kpeter@2556:         while (!cycle_found) {
kpeter@2556:           int curr_iter_num = iter_num + length_bound <= node_num ?
kpeter@2556:                               length_bound : node_num - iter_num;
kpeter@2556:           iter_num += curr_iter_num;
kpeter@2556:           int real_iter_num = curr_iter_num;
kpeter@2556:           for (int i = 0; i < curr_iter_num; ++i) {
kpeter@2556:             if (bf.processNextWeakRound()) {
kpeter@2556:               real_iter_num = i;
kpeter@2556:               break;
kpeter@2556:             }
kpeter@2556:           }
kpeter@2556:           if (real_iter_num < curr_iter_num) {
kpeter@2581:             // Optimal flow is found
kpeter@2556:             optimal = true;
kpeter@2581:             // Setting node potentials
kpeter@2581:             for (NodeIt n(_graph); n != INVALID; ++n)
kpeter@2581:               (*_potential)[n] = bf.dist(n);
kpeter@2556:             break;
kpeter@2556:           } else {
kpeter@2556:             // Searching for node disjoint negative cycles
kpeter@2581:             for (ResNodeIt n(*_res_graph); n != INVALID; ++n)
kpeter@2556:               visited[n] = 0;
kpeter@2556:             int id = 0;
kpeter@2581:             for (ResNodeIt n(*_res_graph); n != INVALID; ++n) {
kpeter@2556:               if (visited[n] > 0) continue;
kpeter@2556:               visited[n] = ++id;
kpeter@2556:               ResNode u = pred[n] == INVALID ?
kpeter@2581:                           INVALID : _res_graph->source(pred[n]);
kpeter@2556:               while (u != INVALID && visited[u] == 0) {
kpeter@2556:                 visited[u] = id;
kpeter@2556:                 u = pred[u] == INVALID ?
kpeter@2581:                     INVALID : _res_graph->source(pred[u]);
kpeter@2556:               }
kpeter@2556:               if (u != INVALID && visited[u] == id) {
kpeter@2556:                 // Finding the negative cycle
kpeter@2556:                 cycle_found = true;
kpeter@2556:                 cycle.clear();
kpeter@2556:                 ResEdge e = pred[u];
kpeter@2556:                 cycle.push_back(e);
kpeter@2581:                 Capacity d = _res_graph->rescap(e);
kpeter@2581:                 while (_res_graph->source(e) != u) {
kpeter@2581:                   cycle.push_back(e = pred[_res_graph->source(e)]);
kpeter@2581:                   if (_res_graph->rescap(e) < d)
kpeter@2581:                     d = _res_graph->rescap(e);
kpeter@2556:                 }
kpeter@2573: 
kpeter@2556:                 // Augmenting along the cycle
kpeter@2573:                 for (int i = 0; i < int(cycle.size()); ++i)
kpeter@2581:                   _res_graph->augment(cycle[i], d);
kpeter@2556:               }
kpeter@2556:             }
kpeter@2556:           }
deba@2440: 
kpeter@2556:           if (!cycle_found)
kpeter@2593:             length_bound = length_bound * BF_LIMIT_FACTOR / 100;
kpeter@2556:         }
deba@2440:       }
deba@2440:     }
deba@2440: 
kpeter@2620:     /// \brief Execute the algorithm using \ref MinMeanCycle.
kpeter@2573:     ///
kpeter@2620:     /// Execute the algorithm using \ref MinMeanCycle for negative
kpeter@2573:     /// cycle detection.
kpeter@2581:     void startMinMean() {
deba@2440:       typedef Path<ResGraph> ResPath;
kpeter@2581:       MinMeanCycle<ResGraph, ResidualCostMap> mmc(*_res_graph, _res_cost);
deba@2440:       ResPath cycle;
deba@2440: 
deba@2440:       mmc.cyclePath(cycle).init();
deba@2440:       if (mmc.findMinMean()) {
kpeter@2556:         while (mmc.cycleLength() < 0) {
kpeter@2556:           // Finding the cycle
kpeter@2556:           mmc.findCycle();
deba@2440: 
kpeter@2556:           // Finding the largest flow amount that can be augmented
kpeter@2556:           // along the cycle
kpeter@2556:           Capacity delta = 0;
kpeter@2556:           for (typename ResPath::EdgeIt e(cycle); e != INVALID; ++e) {
kpeter@2581:             if (delta == 0 || _res_graph->rescap(e) < delta)
kpeter@2581:               delta = _res_graph->rescap(e);
kpeter@2556:           }
deba@2440: 
kpeter@2556:           // Augmenting along the cycle
kpeter@2556:           for (typename ResPath::EdgeIt e(cycle); e != INVALID; ++e)
kpeter@2581:             _res_graph->augment(e, delta);
deba@2440: 
kpeter@2556:           // Finding the minimum cycle mean for the modified residual
kpeter@2556:           // graph
kpeter@2556:           mmc.reset();
kpeter@2556:           if (!mmc.findMinMean()) break;
kpeter@2556:         }
deba@2440:       }
deba@2440: 
kpeter@2581:       // Computing node potentials
kpeter@2581:       BellmanFord<ResGraph, ResidualCostMap> bf(*_res_graph, _res_cost);
kpeter@2581:       bf.init(0); bf.start();
kpeter@2581:       for (NodeIt n(_graph); n != INVALID; ++n)
kpeter@2581:         (*_potential)[n] = bf.dist(n);
deba@2440:     }
deba@2440: 
deba@2440:   }; //class CycleCanceling
deba@2440: 
deba@2440:   ///@}
deba@2440: 
deba@2440: } //namespace lemon
deba@2440: 
deba@2440: #endif //LEMON_CYCLE_CANCELING_H