kpeter@2577: /* -*- C++ -*-
kpeter@2577:  *
kpeter@2577:  * This file is a part of LEMON, a generic C++ optimization library
kpeter@2577:  *
kpeter@2577:  * Copyright (C) 2003-2008
kpeter@2577:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
kpeter@2577:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
kpeter@2577:  *
kpeter@2577:  * Permission to use, modify and distribute this software is granted
kpeter@2577:  * provided that this copyright notice appears in all copies. For
kpeter@2577:  * precise terms see the accompanying LICENSE file.
kpeter@2577:  *
kpeter@2577:  * This software is provided "AS IS" with no warranty of any kind,
kpeter@2577:  * express or implied, and with no claim as to its suitability for any
kpeter@2577:  * purpose.
kpeter@2577:  *
kpeter@2577:  */
kpeter@2577: 
kpeter@2577: #ifndef LEMON_COST_SCALING_H
kpeter@2577: #define LEMON_COST_SCALING_H
kpeter@2577: 
kpeter@2577: /// \ingroup min_cost_flow
kpeter@2577: /// \file
kpeter@2577: /// \brief Cost scaling algorithm for finding a minimum cost flow.
kpeter@2577: 
kpeter@2577: #include <deque>
kpeter@2577: #include <lemon/graph_adaptor.h>
kpeter@2577: #include <lemon/graph_utils.h>
kpeter@2577: #include <lemon/maps.h>
kpeter@2577: #include <lemon/math.h>
kpeter@2577: 
kpeter@2577: #include <lemon/circulation.h>
kpeter@2577: #include <lemon/bellman_ford.h>
kpeter@2577: 
kpeter@2577: namespace lemon {
kpeter@2577: 
kpeter@2577:   /// \addtogroup min_cost_flow
kpeter@2577:   /// @{
kpeter@2577: 
kpeter@2577:   /// \brief Implementation of the cost scaling algorithm for finding a
kpeter@2577:   /// minimum cost flow.
kpeter@2577:   ///
kpeter@2577:   /// \ref CostScaling implements the cost scaling algorithm performing
kpeter@2625:   /// augment/push and relabel operations for finding a minimum cost
kpeter@2577:   /// flow.
kpeter@2577:   ///
kpeter@2577:   /// \tparam Graph The directed graph type the algorithm runs on.
kpeter@2577:   /// \tparam LowerMap The type of the lower bound map.
kpeter@2577:   /// \tparam CapacityMap The type of the capacity (upper bound) map.
kpeter@2577:   /// \tparam CostMap The type of the cost (length) map.
kpeter@2577:   /// \tparam SupplyMap The type of the supply map.
kpeter@2577:   ///
kpeter@2577:   /// \warning
kpeter@2577:   /// - Edge capacities and costs should be \e non-negative \e integers.
kpeter@2577:   /// - 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@2577:   ///
kpeter@2577:   /// \note Edge costs are multiplied with the number of nodes during
kpeter@2577:   /// the algorithm so overflow problems may arise more easily than with
kpeter@2577:   /// other minimum cost flow algorithms.
kpeter@2577:   /// If it is available, <tt>long long int</tt> type is used instead of
kpeter@2577:   /// <tt>long int</tt> in the inside computations.
kpeter@2577:   ///
kpeter@2577:   /// \author Peter Kovacs
kpeter@2577:   template < typename Graph,
kpeter@2577:              typename LowerMap = typename Graph::template EdgeMap<int>,
kpeter@2577:              typename CapacityMap = typename Graph::template EdgeMap<int>,
kpeter@2577:              typename CostMap = typename Graph::template EdgeMap<int>,
kpeter@2577:              typename SupplyMap = typename Graph::template NodeMap<int> >
kpeter@2577:   class CostScaling
kpeter@2577:   {
kpeter@2577:     GRAPH_TYPEDEFS(typename Graph);
kpeter@2577: 
kpeter@2577:     typedef typename CapacityMap::Value Capacity;
kpeter@2577:     typedef typename CostMap::Value Cost;
kpeter@2577:     typedef typename SupplyMap::Value Supply;
kpeter@2577:     typedef typename Graph::template EdgeMap<Capacity> CapacityEdgeMap;
kpeter@2577:     typedef typename Graph::template NodeMap<Supply> SupplyNodeMap;
kpeter@2577: 
kpeter@2577:     typedef ResGraphAdaptor< const Graph, Capacity,
kpeter@2577:                              CapacityEdgeMap, CapacityEdgeMap > ResGraph;
kpeter@2577:     typedef typename ResGraph::Edge ResEdge;
kpeter@2577: 
kpeter@2577: #if defined __GNUC__ && !defined __STRICT_ANSI__
kpeter@2577:     typedef long long int LCost;
kpeter@2577: #else
kpeter@2577:     typedef long int LCost;
kpeter@2577: #endif
kpeter@2577:     typedef typename Graph::template EdgeMap<LCost> LargeCostMap;
kpeter@2577: 
kpeter@2577:   public:
kpeter@2577: 
kpeter@2577:     /// The type of the flow map.
kpeter@2581:     typedef typename Graph::template EdgeMap<Capacity> FlowMap;
kpeter@2577:     /// The type of the potential map.
kpeter@2577:     typedef typename Graph::template NodeMap<LCost> PotentialMap;
kpeter@2577: 
kpeter@2577:   private:
kpeter@2577: 
kpeter@2577:     /// \brief Map adaptor class for handling residual edge costs.
kpeter@2577:     ///
kpeter@2620:     /// Map adaptor class for handling residual edge costs.
kpeter@2581:     template <typename Map>
kpeter@2581:     class ResidualCostMap : public MapBase<ResEdge, typename Map::Value>
kpeter@2577:     {
kpeter@2577:     private:
kpeter@2577: 
kpeter@2581:       const Map &_cost_map;
kpeter@2577: 
kpeter@2577:     public:
kpeter@2577: 
kpeter@2577:       ///\e
kpeter@2581:       ResidualCostMap(const Map &cost_map) :
kpeter@2577:         _cost_map(cost_map) {}
kpeter@2577: 
kpeter@2577:       ///\e
kpeter@2625:       inline typename Map::Value operator[](const ResEdge &e) const {
kpeter@2625:         return ResGraph::forward(e) ? _cost_map[e] : -_cost_map[e];
kpeter@2577:       }
kpeter@2577: 
kpeter@2577:     }; //class ResidualCostMap
kpeter@2577: 
kpeter@2577:     /// \brief Map adaptor class for handling reduced edge costs.
kpeter@2577:     ///
kpeter@2620:     /// Map adaptor class for handling reduced edge costs.
kpeter@2577:     class ReducedCostMap : public MapBase<Edge, LCost>
kpeter@2577:     {
kpeter@2577:     private:
kpeter@2577: 
kpeter@2577:       const Graph &_gr;
kpeter@2577:       const LargeCostMap &_cost_map;
kpeter@2577:       const PotentialMap &_pot_map;
kpeter@2577: 
kpeter@2577:     public:
kpeter@2577: 
kpeter@2577:       ///\e
kpeter@2577:       ReducedCostMap( const Graph &gr,
kpeter@2577:                       const LargeCostMap &cost_map,
kpeter@2577:                       const PotentialMap &pot_map ) :
kpeter@2577:         _gr(gr), _cost_map(cost_map), _pot_map(pot_map) {}
kpeter@2577: 
kpeter@2577:       ///\e
kpeter@2625:       inline LCost operator[](const Edge &e) const {
kpeter@2577:         return _cost_map[e] + _pot_map[_gr.source(e)]
kpeter@2577:                             - _pot_map[_gr.target(e)];
kpeter@2577:       }
kpeter@2577: 
kpeter@2577:     }; //class ReducedCostMap
kpeter@2577: 
kpeter@2577:   private:
kpeter@2577: 
kpeter@2577:     // The directed graph the algorithm runs on
kpeter@2577:     const Graph &_graph;
kpeter@2577:     // The original lower bound map
kpeter@2577:     const LowerMap *_lower;
kpeter@2577:     // The modified capacity map
kpeter@2577:     CapacityEdgeMap _capacity;
kpeter@2577:     // The original cost map
kpeter@2577:     const CostMap &_orig_cost;
kpeter@2577:     // The scaled cost map
kpeter@2577:     LargeCostMap _cost;
kpeter@2577:     // The modified supply map
kpeter@2577:     SupplyNodeMap _supply;
kpeter@2577:     bool _valid_supply;
kpeter@2577: 
kpeter@2577:     // Edge map of the current flow
kpeter@2581:     FlowMap *_flow;
kpeter@2581:     bool _local_flow;
kpeter@2577:     // Node map of the current potentials
kpeter@2581:     PotentialMap *_potential;
kpeter@2581:     bool _local_potential;
kpeter@2577: 
kpeter@2623:     // The residual cost map
kpeter@2623:     ResidualCostMap<LargeCostMap> _res_cost;
kpeter@2577:     // The residual graph
kpeter@2581:     ResGraph *_res_graph;
kpeter@2577:     // The reduced cost map
kpeter@2581:     ReducedCostMap *_red_cost;
kpeter@2577:     // The excess map
kpeter@2577:     SupplyNodeMap _excess;
kpeter@2577:     // The epsilon parameter used for cost scaling
kpeter@2577:     LCost _epsilon;
kpeter@2625:     // The scaling factor
kpeter@2625:     int _alpha;
kpeter@2577: 
kpeter@2577:   public:
kpeter@2577: 
kpeter@2581:     /// \brief General constructor (with lower bounds).
kpeter@2577:     ///
kpeter@2581:     /// General constructor (with lower bounds).
kpeter@2577:     ///
kpeter@2577:     /// \param graph The directed graph the algorithm runs on.
kpeter@2577:     /// \param lower The lower bounds of the edges.
kpeter@2577:     /// \param capacity The capacities (upper bounds) of the edges.
kpeter@2577:     /// \param cost The cost (length) values of the edges.
kpeter@2577:     /// \param supply The supply values of the nodes (signed).
kpeter@2577:     CostScaling( const Graph &graph,
kpeter@2577:                  const LowerMap &lower,
kpeter@2577:                  const CapacityMap &capacity,
kpeter@2577:                  const CostMap &cost,
kpeter@2577:                  const SupplyMap &supply ) :
kpeter@2577:       _graph(graph), _lower(&lower), _capacity(graph), _orig_cost(cost),
kpeter@2623:       _cost(graph), _supply(graph), _flow(NULL), _local_flow(false),
kpeter@2623:       _potential(NULL), _local_potential(false), _res_cost(_cost),
kpeter@2623:       _res_graph(NULL), _red_cost(NULL), _excess(graph, 0)
kpeter@2577:     {
kpeter@2625:       // Remove non-zero lower bounds
kpeter@2577:       _capacity = subMap(capacity, lower);
kpeter@2577:       Supply sum = 0;
kpeter@2577:       for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@2577:         Supply s = supply[n];
kpeter@2577:         for (InEdgeIt e(_graph, n); e != INVALID; ++e)
kpeter@2577:           s += lower[e];
kpeter@2577:         for (OutEdgeIt e(_graph, n); e != INVALID; ++e)
kpeter@2577:           s -= lower[e];
kpeter@2577:         _supply[n] = s;
kpeter@2577:         sum += s;
kpeter@2577:       }
kpeter@2577:       _valid_supply = sum == 0;
kpeter@2577:     }
kpeter@2577: 
kpeter@2581:     /// \brief General constructor (without lower bounds).
kpeter@2577:     ///
kpeter@2581:     /// General constructor (without lower bounds).
kpeter@2577:     ///
kpeter@2577:     /// \param graph The directed graph the algorithm runs on.
kpeter@2577:     /// \param capacity The capacities (upper bounds) of the edges.
kpeter@2577:     /// \param cost The cost (length) values of the edges.
kpeter@2577:     /// \param supply The supply values of the nodes (signed).
kpeter@2577:     CostScaling( const Graph &graph,
kpeter@2577:                  const CapacityMap &capacity,
kpeter@2577:                  const CostMap &cost,
kpeter@2577:                  const SupplyMap &supply ) :
kpeter@2577:       _graph(graph), _lower(NULL), _capacity(capacity), _orig_cost(cost),
kpeter@2623:       _cost(graph), _supply(supply), _flow(NULL), _local_flow(false),
kpeter@2623:       _potential(NULL), _local_potential(false), _res_cost(_cost),
kpeter@2623:       _res_graph(NULL), _red_cost(NULL), _excess(graph, 0)
kpeter@2577:     {
kpeter@2625:       // Check the sum of supply values
kpeter@2577:       Supply sum = 0;
kpeter@2577:       for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n];
kpeter@2577:       _valid_supply = sum == 0;
kpeter@2577:     }
kpeter@2577: 
kpeter@2581:     /// \brief Simple constructor (with lower bounds).
kpeter@2577:     ///
kpeter@2581:     /// Simple constructor (with lower bounds).
kpeter@2577:     ///
kpeter@2577:     /// \param graph The directed graph the algorithm runs on.
kpeter@2577:     /// \param lower The lower bounds of the edges.
kpeter@2577:     /// \param capacity The capacities (upper bounds) of the edges.
kpeter@2577:     /// \param cost The cost (length) values of the edges.
kpeter@2577:     /// \param s The source node.
kpeter@2577:     /// \param t The target node.
kpeter@2577:     /// \param flow_value The required amount of flow from node \c s
kpeter@2577:     /// to node \c t (i.e. the supply of \c s and the demand of \c t).
kpeter@2577:     CostScaling( const Graph &graph,
kpeter@2577:                  const LowerMap &lower,
kpeter@2577:                  const CapacityMap &capacity,
kpeter@2577:                  const CostMap &cost,
kpeter@2577:                  Node s, Node t,
kpeter@2577:                  Supply flow_value ) :
kpeter@2577:       _graph(graph), _lower(&lower), _capacity(graph), _orig_cost(cost),
kpeter@2623:       _cost(graph), _supply(graph), _flow(NULL), _local_flow(false),
kpeter@2623:       _potential(NULL), _local_potential(false), _res_cost(_cost),
kpeter@2623:       _res_graph(NULL), _red_cost(NULL), _excess(graph, 0)
kpeter@2577:     {
kpeter@2625:       // Remove nonzero lower bounds
kpeter@2577:       _capacity = subMap(capacity, lower);
kpeter@2577:       for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@2577:         Supply sum = 0;
kpeter@2577:         if (n == s) sum =  flow_value;
kpeter@2577:         if (n == t) sum = -flow_value;
kpeter@2577:         for (InEdgeIt e(_graph, n); e != INVALID; ++e)
kpeter@2577:           sum += lower[e];
kpeter@2577:         for (OutEdgeIt e(_graph, n); e != INVALID; ++e)
kpeter@2577:           sum -= lower[e];
kpeter@2577:         _supply[n] = sum;
kpeter@2577:       }
kpeter@2577:       _valid_supply = true;
kpeter@2577:     }
kpeter@2577: 
kpeter@2581:     /// \brief Simple constructor (without lower bounds).
kpeter@2577:     ///
kpeter@2581:     /// Simple constructor (without lower bounds).
kpeter@2577:     ///
kpeter@2577:     /// \param graph The directed graph the algorithm runs on.
kpeter@2577:     /// \param capacity The capacities (upper bounds) of the edges.
kpeter@2577:     /// \param cost The cost (length) values of the edges.
kpeter@2577:     /// \param s The source node.
kpeter@2577:     /// \param t The target node.
kpeter@2577:     /// \param flow_value The required amount of flow from node \c s
kpeter@2577:     /// to node \c t (i.e. the supply of \c s and the demand of \c t).
kpeter@2577:     CostScaling( const Graph &graph,
kpeter@2577:                  const CapacityMap &capacity,
kpeter@2577:                  const CostMap &cost,
kpeter@2577:                  Node s, Node t,
kpeter@2577:                  Supply flow_value ) :
kpeter@2577:       _graph(graph), _lower(NULL), _capacity(capacity), _orig_cost(cost),
kpeter@2623:       _cost(graph), _supply(graph, 0), _flow(NULL), _local_flow(false),
kpeter@2623:       _potential(NULL), _local_potential(false), _res_cost(_cost),
kpeter@2623:       _res_graph(NULL), _red_cost(NULL), _excess(graph, 0)
kpeter@2577:     {
kpeter@2577:       _supply[s] =  flow_value;
kpeter@2577:       _supply[t] = -flow_value;
kpeter@2577:       _valid_supply = true;
kpeter@2577:     }
kpeter@2577: 
kpeter@2581:     /// Destructor.
kpeter@2581:     ~CostScaling() {
kpeter@2581:       if (_local_flow) delete _flow;
kpeter@2581:       if (_local_potential) delete _potential;
kpeter@2581:       delete _res_graph;
kpeter@2581:       delete _red_cost;
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:     CostScaling& 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:     CostScaling& 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@2577:     ///
kpeter@2620:     /// Run the algorithm.
kpeter@2577:     ///
kpeter@2625:     /// \param partial_augment By default the algorithm performs
kpeter@2625:     /// partial augment and relabel operations in the cost scaling
kpeter@2625:     /// phases. Set this parameter to \c false for using local push and
kpeter@2625:     /// relabel operations instead.
kpeter@2625:     ///
kpeter@2577:     /// \return \c true if a feasible flow can be found.
kpeter@2625:     bool run(bool partial_augment = true) {
kpeter@2625:       if (partial_augment) {
kpeter@2625:         return init() && startPartialAugment();
kpeter@2625:       } else {
kpeter@2625:         return init() && startPushRelabel();
kpeter@2625:       }
kpeter@2577:     }
kpeter@2577: 
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::CostScaling::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@2577:     /// found flow.
kpeter@2577:     ///
kpeter@2620:     /// Return a const reference to the edge map storing the found flow.
kpeter@2577:     ///
kpeter@2577:     /// \pre \ref run() must be called before using this function.
kpeter@2577:     const FlowMap& flowMap() const {
kpeter@2581:       return *_flow;
kpeter@2577:     }
kpeter@2577: 
kpeter@2620:     /// \brief Return a const reference to the node map storing the
kpeter@2577:     /// found potentials (the dual solution).
kpeter@2577:     ///
kpeter@2620:     /// Return a const reference to the node map storing the found
kpeter@2577:     /// potentials (the dual solution).
kpeter@2577:     ///
kpeter@2577:     /// \pre \ref run() must be called before using this function.
kpeter@2577:     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];
kpeter@2577:     }
kpeter@2577: 
kpeter@2620:     /// \brief Return the total cost of the found flow.
kpeter@2577:     ///
kpeter@2620:     /// Return the total cost of the found flow. The complexity of the
kpeter@2577:     /// function is \f$ O(e) \f$.
kpeter@2577:     ///
kpeter@2577:     /// \pre \ref run() must be called before using this function.
kpeter@2577:     Cost totalCost() const {
kpeter@2577:       Cost c = 0;
kpeter@2577:       for (EdgeIt e(_graph); e != INVALID; ++e)
kpeter@2581:         c += (*_flow)[e] * _orig_cost[e];
kpeter@2577:       return c;
kpeter@2577:     }
kpeter@2577: 
kpeter@2581:     /// @}
kpeter@2581: 
kpeter@2577:   private:
kpeter@2577: 
kpeter@2620:     /// Initialize the algorithm.
kpeter@2577:     bool init() {
kpeter@2577:       if (!_valid_supply) return false;
kpeter@2625:       // The scaling factor
kpeter@2625:       _alpha = 8;
kpeter@2577: 
kpeter@2625:       // Initialize 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:       _red_cost = new ReducedCostMap(_graph, _cost, *_potential);
kpeter@2581:       _res_graph = new ResGraph(_graph, _capacity, *_flow);
kpeter@2581: 
kpeter@2625:       // Initialize the scaled cost map and the epsilon parameter
kpeter@2577:       Cost max_cost = 0;
kpeter@2577:       int node_num = countNodes(_graph);
kpeter@2577:       for (EdgeIt e(_graph); e != INVALID; ++e) {
kpeter@2625:         _cost[e] = LCost(_orig_cost[e]) * node_num * _alpha;
kpeter@2577:         if (_orig_cost[e] > max_cost) max_cost = _orig_cost[e];
kpeter@2577:       }
kpeter@2577:       _epsilon = max_cost * node_num;
kpeter@2577: 
kpeter@2625:       // Find a feasible flow using Circulation
kpeter@2577:       Circulation< Graph, ConstMap<Edge, Capacity>, CapacityEdgeMap,
kpeter@2577:                    SupplyMap >
kpeter@2581:         circulation( _graph, constMap<Edge>(Capacity(0)), _capacity,
kpeter@2577:                      _supply );
kpeter@2581:       return circulation.flowMap(*_flow).run();
kpeter@2577:     }
kpeter@2577: 
kpeter@2625:     /// Execute the algorithm performing partial augmentation and
kpeter@2625:     /// relabel operations.
kpeter@2625:     bool startPartialAugment() {
kpeter@2625:       // Paramters for heuristics
kpeter@2625:       const int BF_HEURISTIC_EPSILON_BOUND = 1000;
kpeter@2625:       const int BF_HEURISTIC_BOUND_FACTOR  = 3;
kpeter@2625:       // Maximum augment path length
kpeter@2625:       const int MAX_PATH_LENGTH = 4;
kpeter@2577: 
kpeter@2625:       // Variables
kpeter@2625:       typename Graph::template NodeMap<Edge> pred_edge(_graph);
kpeter@2625:       typename Graph::template NodeMap<bool> forward(_graph);
kpeter@2625:       typename Graph::template NodeMap<OutEdgeIt> next_out(_graph);
kpeter@2625:       typename Graph::template NodeMap<InEdgeIt> next_in(_graph);
kpeter@2625:       typename Graph::template NodeMap<bool> next_dir(_graph);
kpeter@2577:       std::deque<Node> active_nodes;
kpeter@2625:       std::vector<Node> path_nodes;
kpeter@2577: 
kpeter@2577:       int node_num = countNodes(_graph);
kpeter@2625:       for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
kpeter@2625:                                         1 : _epsilon / _alpha )
kpeter@2577:       {
kpeter@2625:         // "Early Termination" heuristic: use Bellman-Ford algorithm
kpeter@2625:         // to check if the current flow is optimal
kpeter@2577:         if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) {
kpeter@2581:           typedef ShiftMap< ResidualCostMap<LargeCostMap> > ShiftCostMap;
kpeter@2625:           ShiftCostMap shift_cost(_res_cost, 1);
kpeter@2581:           BellmanFord<ResGraph, ShiftCostMap> bf(*_res_graph, shift_cost);
kpeter@2577:           bf.init(0);
kpeter@2577:           bool done = false;
kpeter@2577:           int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(node_num));
kpeter@2577:           for (int i = 0; i < K && !done; ++i)
kpeter@2577:             done = bf.processNextWeakRound();
kpeter@2625:           if (done) break;
kpeter@2577:         }
kpeter@2577: 
kpeter@2625:         // Saturate edges not satisfying the optimality condition
kpeter@2577:         Capacity delta;
kpeter@2577:         for (EdgeIt e(_graph); e != INVALID; ++e) {
kpeter@2581:           if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) {
kpeter@2581:             delta = _capacity[e] - (*_flow)[e];
kpeter@2577:             _excess[_graph.source(e)] -= delta;
kpeter@2577:             _excess[_graph.target(e)] += delta;
kpeter@2581:             (*_flow)[e] = _capacity[e];
kpeter@2577:           }
kpeter@2581:           if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) {
kpeter@2581:             _excess[_graph.target(e)] -= (*_flow)[e];
kpeter@2581:             _excess[_graph.source(e)] += (*_flow)[e];
kpeter@2581:             (*_flow)[e] = 0;
kpeter@2577:           }
kpeter@2577:         }
kpeter@2577: 
kpeter@2625:         // Find active nodes (i.e. nodes with positive excess)
kpeter@2625:         for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@2577:           if (_excess[n] > 0) active_nodes.push_back(n);
kpeter@2625:         }
kpeter@2577: 
kpeter@2625:         // Initialize the next edge maps
kpeter@2625:         for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@2625:           next_out[n] = OutEdgeIt(_graph, n);
kpeter@2625:           next_in[n] = InEdgeIt(_graph, n);
kpeter@2625:           next_dir[n] = true;
kpeter@2625:         }
kpeter@2625: 
kpeter@2625:         // Perform partial augment and relabel operations
kpeter@2577:         while (active_nodes.size() > 0) {
kpeter@2625:           // Select an active node (FIFO selection)
kpeter@2625:           if (_excess[active_nodes[0]] <= 0) {
kpeter@2625:             active_nodes.pop_front();
kpeter@2625:             continue;
kpeter@2625:           }
kpeter@2625:           Node start = active_nodes[0];
kpeter@2625:           path_nodes.clear();
kpeter@2625:           path_nodes.push_back(start);
kpeter@2625: 
kpeter@2625:           // Find an augmenting path from the start node
kpeter@2625:           Node u, tip = start;
kpeter@2625:           LCost min_red_cost;
kpeter@2625:           while ( _excess[tip] >= 0 &&
kpeter@2625:                   int(path_nodes.size()) <= MAX_PATH_LENGTH )
kpeter@2625:           {
kpeter@2625:             if (next_dir[tip]) {
kpeter@2625:               for (OutEdgeIt e = next_out[tip]; e != INVALID; ++e) {
kpeter@2625:                 if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) {
kpeter@2625:                   u = _graph.target(e);
kpeter@2625:                   pred_edge[u] = e;
kpeter@2625:                   forward[u] = true;
kpeter@2625:                   next_out[tip] = e;
kpeter@2625:                   tip = u;
kpeter@2625:                   path_nodes.push_back(tip);
kpeter@2625:                   goto next_step;
kpeter@2625:                 }
kpeter@2625:               }
kpeter@2625:               next_dir[tip] = false;
kpeter@2625:             }
kpeter@2625:             for (InEdgeIt e = next_in[tip]; e != INVALID; ++e) {
kpeter@2625:               if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) {
kpeter@2625:                 u = _graph.source(e);
kpeter@2625:                 pred_edge[u] = e;
kpeter@2625:                 forward[u] = false;
kpeter@2625:                 next_in[tip] = e;
kpeter@2625:                 tip = u;
kpeter@2625:                 path_nodes.push_back(tip);
kpeter@2625:                 goto next_step;
kpeter@2625:               }
kpeter@2625:             }
kpeter@2625: 
kpeter@2625:             // Relabel tip node
kpeter@2625:             min_red_cost = std::numeric_limits<LCost>::max() / 2;
kpeter@2625:             for (OutEdgeIt oe(_graph, tip); oe != INVALID; ++oe) {
kpeter@2625:               if ( _capacity[oe] - (*_flow)[oe] > 0 &&
kpeter@2625:                    (*_red_cost)[oe] < min_red_cost )
kpeter@2625:                 min_red_cost = (*_red_cost)[oe];
kpeter@2625:             }
kpeter@2625:             for (InEdgeIt ie(_graph, tip); ie != INVALID; ++ie) {
kpeter@2625:               if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < min_red_cost)
kpeter@2625:                 min_red_cost = -(*_red_cost)[ie];
kpeter@2625:             }
kpeter@2625:             (*_potential)[tip] -= min_red_cost + _epsilon;
kpeter@2625: 
kpeter@2625:             // Reset the next edge maps
kpeter@2625:             next_out[tip] = OutEdgeIt(_graph, tip);
kpeter@2625:             next_in[tip] = InEdgeIt(_graph, tip);
kpeter@2625:             next_dir[tip] = true;
kpeter@2625: 
kpeter@2625:             // Step back
kpeter@2625:             if (tip != start) {
kpeter@2625:               path_nodes.pop_back();
kpeter@2625:               tip = path_nodes[path_nodes.size()-1];
kpeter@2625:             }
kpeter@2625: 
kpeter@2625:           next_step:
kpeter@2625:             continue;
kpeter@2625:           }
kpeter@2625: 
kpeter@2625:           // Augment along the found path (as much flow as possible)
kpeter@2625:           Capacity delta;
kpeter@2625:           for (int i = 1; i < int(path_nodes.size()); ++i) {
kpeter@2625:             u = path_nodes[i];
kpeter@2625:             delta = forward[u] ?
kpeter@2625:               _capacity[pred_edge[u]] - (*_flow)[pred_edge[u]] :
kpeter@2625:               (*_flow)[pred_edge[u]];
kpeter@2625:             delta = std::min(delta, _excess[path_nodes[i-1]]);
kpeter@2625:             (*_flow)[pred_edge[u]] += forward[u] ? delta : -delta;
kpeter@2625:             _excess[path_nodes[i-1]] -= delta;
kpeter@2625:             _excess[u] += delta;
kpeter@2625:             if (_excess[u] > 0 && _excess[u] <= delta) active_nodes.push_back(u);
kpeter@2625:           }
kpeter@2625:         }
kpeter@2625:       }
kpeter@2625: 
kpeter@2625:       // Compute node potentials for the original costs
kpeter@2625:       ResidualCostMap<CostMap> res_cost(_orig_cost);
kpeter@2625:       BellmanFord< ResGraph, ResidualCostMap<CostMap> >
kpeter@2625:         bf(*_res_graph, res_cost);
kpeter@2625:       bf.init(0); bf.start();
kpeter@2625:       for (NodeIt n(_graph); n != INVALID; ++n)
kpeter@2625:         (*_potential)[n] = bf.dist(n);
kpeter@2625: 
kpeter@2625:       // Handle non-zero lower bounds
kpeter@2625:       if (_lower) {
kpeter@2625:         for (EdgeIt e(_graph); e != INVALID; ++e)
kpeter@2625:           (*_flow)[e] += (*_lower)[e];
kpeter@2625:       }
kpeter@2625:       return true;
kpeter@2625:     }
kpeter@2625: 
kpeter@2625:     /// Execute the algorithm performing push and relabel operations.
kpeter@2625:     bool startPushRelabel() {
kpeter@2625:       // Paramters for heuristics
kpeter@2625:       const int BF_HEURISTIC_EPSILON_BOUND = 1000;
kpeter@2625:       const int BF_HEURISTIC_BOUND_FACTOR  = 3;
kpeter@2625: 
kpeter@2625:       typename Graph::template NodeMap<bool> hyper(_graph, false);
kpeter@2625:       typename Graph::template NodeMap<Edge> pred_edge(_graph);
kpeter@2625:       typename Graph::template NodeMap<bool> forward(_graph);
kpeter@2625:       typename Graph::template NodeMap<OutEdgeIt> next_out(_graph);
kpeter@2625:       typename Graph::template NodeMap<InEdgeIt> next_in(_graph);
kpeter@2625:       typename Graph::template NodeMap<bool> next_dir(_graph);
kpeter@2625:       std::deque<Node> active_nodes;
kpeter@2625: 
kpeter@2625:       int node_num = countNodes(_graph);
kpeter@2625:       for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
kpeter@2625:                                         1 : _epsilon / _alpha )
kpeter@2625:       {
kpeter@2625:         // "Early Termination" heuristic: use Bellman-Ford algorithm
kpeter@2625:         // to check if the current flow is optimal
kpeter@2625:         if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) {
kpeter@2625:           typedef ShiftMap< ResidualCostMap<LargeCostMap> > ShiftCostMap;
kpeter@2625:           ShiftCostMap shift_cost(_res_cost, 1);
kpeter@2625:           BellmanFord<ResGraph, ShiftCostMap> bf(*_res_graph, shift_cost);
kpeter@2625:           bf.init(0);
kpeter@2625:           bool done = false;
kpeter@2625:           int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(node_num));
kpeter@2625:           for (int i = 0; i < K && !done; ++i)
kpeter@2625:             done = bf.processNextWeakRound();
kpeter@2625:           if (done) break;
kpeter@2625:         }
kpeter@2625: 
kpeter@2625:         // Saturate edges not satisfying the optimality condition
kpeter@2625:         Capacity delta;
kpeter@2625:         for (EdgeIt e(_graph); e != INVALID; ++e) {
kpeter@2625:           if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) {
kpeter@2625:             delta = _capacity[e] - (*_flow)[e];
kpeter@2625:             _excess[_graph.source(e)] -= delta;
kpeter@2625:             _excess[_graph.target(e)] += delta;
kpeter@2625:             (*_flow)[e] = _capacity[e];
kpeter@2625:           }
kpeter@2625:           if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) {
kpeter@2625:             _excess[_graph.target(e)] -= (*_flow)[e];
kpeter@2625:             _excess[_graph.source(e)] += (*_flow)[e];
kpeter@2625:             (*_flow)[e] = 0;
kpeter@2625:           }
kpeter@2625:         }
kpeter@2625: 
kpeter@2625:         // Find active nodes (i.e. nodes with positive excess)
kpeter@2625:         for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@2625:           if (_excess[n] > 0) active_nodes.push_back(n);
kpeter@2625:         }
kpeter@2625: 
kpeter@2625:         // Initialize the next edge maps
kpeter@2625:         for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@2625:           next_out[n] = OutEdgeIt(_graph, n);
kpeter@2625:           next_in[n] = InEdgeIt(_graph, n);
kpeter@2625:           next_dir[n] = true;
kpeter@2625:         }
kpeter@2625: 
kpeter@2625:         // Perform push and relabel operations
kpeter@2625:         while (active_nodes.size() > 0) {
kpeter@2625:           // Select an active node (FIFO selection)
kpeter@2577:           Node n = active_nodes[0], t;
kpeter@2577:           bool relabel_enabled = true;
kpeter@2577: 
kpeter@2625:           // Perform push operations if there are admissible edges
kpeter@2625:           if (_excess[n] > 0 && next_dir[n]) {
kpeter@2625:             OutEdgeIt e = next_out[n];
kpeter@2625:             for ( ; e != INVALID; ++e) {
kpeter@2581:               if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) {
kpeter@2625:                 delta = std::min(_capacity[e] - (*_flow)[e], _excess[n]);
kpeter@2577:                 t = _graph.target(e);
kpeter@2577: 
kpeter@2577:                 // Push-look-ahead heuristic
kpeter@2577:                 Capacity ahead = -_excess[t];
kpeter@2577:                 for (OutEdgeIt oe(_graph, t); oe != INVALID; ++oe) {
kpeter@2581:                   if (_capacity[oe] - (*_flow)[oe] > 0 && (*_red_cost)[oe] < 0)
kpeter@2581:                     ahead += _capacity[oe] - (*_flow)[oe];
kpeter@2577:                 }
kpeter@2577:                 for (InEdgeIt ie(_graph, t); ie != INVALID; ++ie) {
kpeter@2581:                   if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < 0)
kpeter@2581:                     ahead += (*_flow)[ie];
kpeter@2577:                 }
kpeter@2577:                 if (ahead < 0) ahead = 0;
kpeter@2577: 
kpeter@2625:                 // Push flow along the edge
kpeter@2577:                 if (ahead < delta) {
kpeter@2581:                   (*_flow)[e] += ahead;
kpeter@2577:                   _excess[n] -= ahead;
kpeter@2577:                   _excess[t] += ahead;
kpeter@2577:                   active_nodes.push_front(t);
kpeter@2577:                   hyper[t] = true;
kpeter@2577:                   relabel_enabled = false;
kpeter@2577:                   break;
kpeter@2577:                 } else {
kpeter@2581:                   (*_flow)[e] += delta;
kpeter@2577:                   _excess[n] -= delta;
kpeter@2577:                   _excess[t] += delta;
kpeter@2577:                   if (_excess[t] > 0 && _excess[t] <= delta)
kpeter@2577:                     active_nodes.push_back(t);
kpeter@2577:                 }
kpeter@2577: 
kpeter@2577:                 if (_excess[n] == 0) break;
kpeter@2577:               }
kpeter@2577:             }
kpeter@2625:             if (e != INVALID) {
kpeter@2625:               next_out[n] = e;
kpeter@2625:             } else {
kpeter@2625:               next_dir[n] = false;
kpeter@2625:             }
kpeter@2577:           }
kpeter@2577: 
kpeter@2625:           if (_excess[n] > 0 && !next_dir[n]) {
kpeter@2625:             InEdgeIt e = next_in[n];
kpeter@2625:             for ( ; e != INVALID; ++e) {
kpeter@2581:               if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) {
kpeter@2625:                 delta = std::min((*_flow)[e], _excess[n]);
kpeter@2577:                 t = _graph.source(e);
kpeter@2577: 
kpeter@2577:                 // Push-look-ahead heuristic
kpeter@2577:                 Capacity ahead = -_excess[t];
kpeter@2577:                 for (OutEdgeIt oe(_graph, t); oe != INVALID; ++oe) {
kpeter@2581:                   if (_capacity[oe] - (*_flow)[oe] > 0 && (*_red_cost)[oe] < 0)
kpeter@2581:                     ahead += _capacity[oe] - (*_flow)[oe];
kpeter@2577:                 }
kpeter@2577:                 for (InEdgeIt ie(_graph, t); ie != INVALID; ++ie) {
kpeter@2581:                   if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < 0)
kpeter@2581:                     ahead += (*_flow)[ie];
kpeter@2577:                 }
kpeter@2577:                 if (ahead < 0) ahead = 0;
kpeter@2577: 
kpeter@2625:                 // Push flow along the edge
kpeter@2577:                 if (ahead < delta) {
kpeter@2581:                   (*_flow)[e] -= ahead;
kpeter@2577:                   _excess[n] -= ahead;
kpeter@2577:                   _excess[t] += ahead;
kpeter@2577:                   active_nodes.push_front(t);
kpeter@2577:                   hyper[t] = true;
kpeter@2577:                   relabel_enabled = false;
kpeter@2577:                   break;
kpeter@2577:                 } else {
kpeter@2581:                   (*_flow)[e] -= delta;
kpeter@2577:                   _excess[n] -= delta;
kpeter@2577:                   _excess[t] += delta;
kpeter@2577:                   if (_excess[t] > 0 && _excess[t] <= delta)
kpeter@2577:                     active_nodes.push_back(t);
kpeter@2577:                 }
kpeter@2577: 
kpeter@2577:                 if (_excess[n] == 0) break;
kpeter@2577:               }
kpeter@2577:             }
kpeter@2625:             next_in[n] = e;
kpeter@2577:           }
kpeter@2577: 
kpeter@2625:           // Relabel the node if it is still active (or hyper)
kpeter@2577:           if (relabel_enabled && (_excess[n] > 0 || hyper[n])) {
kpeter@2625:             LCost min_red_cost = std::numeric_limits<LCost>::max() / 2;
kpeter@2577:             for (OutEdgeIt oe(_graph, n); oe != INVALID; ++oe) {
kpeter@2581:               if ( _capacity[oe] - (*_flow)[oe] > 0 &&
kpeter@2581:                    (*_red_cost)[oe] < min_red_cost )
kpeter@2581:                 min_red_cost = (*_red_cost)[oe];
kpeter@2577:             }
kpeter@2577:             for (InEdgeIt ie(_graph, n); ie != INVALID; ++ie) {
kpeter@2581:               if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < min_red_cost)
kpeter@2581:                 min_red_cost = -(*_red_cost)[ie];
kpeter@2577:             }
kpeter@2581:             (*_potential)[n] -= min_red_cost + _epsilon;
kpeter@2577:             hyper[n] = false;
kpeter@2625: 
kpeter@2625:             // Reset the next edge maps
kpeter@2625:             next_out[n] = OutEdgeIt(_graph, n);
kpeter@2625:             next_in[n] = InEdgeIt(_graph, n);
kpeter@2625:             next_dir[n] = true;
kpeter@2577:           }
kpeter@2577: 
kpeter@2625:           // Remove nodes that are not active nor hyper
kpeter@2577:           while ( active_nodes.size() > 0 &&
kpeter@2577:                   _excess[active_nodes[0]] <= 0 &&
kpeter@2577:                   !hyper[active_nodes[0]] ) {
kpeter@2577:             active_nodes.pop_front();
kpeter@2577:           }
kpeter@2577:         }
kpeter@2577:       }
kpeter@2577: 
kpeter@2625:       // Compute node potentials for the original costs
kpeter@2581:       ResidualCostMap<CostMap> res_cost(_orig_cost);
kpeter@2581:       BellmanFord< ResGraph, ResidualCostMap<CostMap> >
kpeter@2581:         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);
kpeter@2581: 
kpeter@2625:       // Handle non-zero lower bounds
kpeter@2577:       if (_lower) {
kpeter@2577:         for (EdgeIt e(_graph); e != INVALID; ++e)
kpeter@2581:           (*_flow)[e] += (*_lower)[e];
kpeter@2577:       }
kpeter@2577:       return true;
kpeter@2577:     }
kpeter@2577: 
kpeter@2577:   }; //class CostScaling
kpeter@2577: 
kpeter@2577:   ///@}
kpeter@2577: 
kpeter@2577: } //namespace lemon
kpeter@2577: 
kpeter@2577: #endif //LEMON_COST_SCALING_H