kpeter@805: /* -*- C++ -*-
kpeter@805:  *
kpeter@805:  * This file is a part of LEMON, a generic C++ optimization library
kpeter@805:  *
kpeter@805:  * Copyright (C) 2003-2008
kpeter@805:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
kpeter@805:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
kpeter@805:  *
kpeter@805:  * Permission to use, modify and distribute this software is granted
kpeter@805:  * provided that this copyright notice appears in all copies. For
kpeter@805:  * precise terms see the accompanying LICENSE file.
kpeter@805:  *
kpeter@805:  * This software is provided "AS IS" with no warranty of any kind,
kpeter@805:  * express or implied, and with no claim as to its suitability for any
kpeter@805:  * purpose.
kpeter@805:  *
kpeter@805:  */
kpeter@805: 
kpeter@805: #ifndef LEMON_CAPACITY_SCALING_H
kpeter@805: #define LEMON_CAPACITY_SCALING_H
kpeter@805: 
kpeter@805: /// \ingroup min_cost_flow
kpeter@805: ///
kpeter@805: /// \file
kpeter@805: /// \brief Capacity scaling algorithm for finding a minimum cost flow.
kpeter@805: 
kpeter@805: #include <vector>
kpeter@805: #include <lemon/bin_heap.h>
kpeter@805: 
kpeter@805: namespace lemon {
kpeter@805: 
kpeter@805:   /// \addtogroup min_cost_flow
kpeter@805:   /// @{
kpeter@805: 
kpeter@805:   /// \brief Implementation of the capacity scaling algorithm for
kpeter@805:   /// finding a minimum cost flow.
kpeter@805:   ///
kpeter@805:   /// \ref CapacityScaling implements the capacity scaling version
kpeter@805:   /// of the successive shortest path algorithm for finding a minimum
kpeter@805:   /// cost flow.
kpeter@805:   ///
kpeter@805:   /// \tparam Digraph The digraph type the algorithm runs on.
kpeter@805:   /// \tparam LowerMap The type of the lower bound map.
kpeter@805:   /// \tparam CapacityMap The type of the capacity (upper bound) map.
kpeter@805:   /// \tparam CostMap The type of the cost (length) map.
kpeter@805:   /// \tparam SupplyMap The type of the supply map.
kpeter@805:   ///
kpeter@805:   /// \warning
kpeter@805:   /// - Arc capacities and costs should be \e non-negative \e integers.
kpeter@805:   /// - Supply values should be \e signed \e integers.
kpeter@805:   /// - The value types of the maps should be convertible to each other.
kpeter@805:   /// - \c CostMap::Value must be signed type.
kpeter@805:   ///
kpeter@805:   /// \author Peter Kovacs
kpeter@805:   template < typename Digraph,
kpeter@805:              typename LowerMap = typename Digraph::template ArcMap<int>,
kpeter@805:              typename CapacityMap = typename Digraph::template ArcMap<int>,
kpeter@805:              typename CostMap = typename Digraph::template ArcMap<int>,
kpeter@805:              typename SupplyMap = typename Digraph::template NodeMap<int> >
kpeter@805:   class CapacityScaling
kpeter@805:   {
kpeter@805:     TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
kpeter@805: 
kpeter@805:     typedef typename CapacityMap::Value Capacity;
kpeter@805:     typedef typename CostMap::Value Cost;
kpeter@805:     typedef typename SupplyMap::Value Supply;
kpeter@805:     typedef typename Digraph::template ArcMap<Capacity> CapacityArcMap;
kpeter@805:     typedef typename Digraph::template NodeMap<Supply> SupplyNodeMap;
kpeter@805:     typedef typename Digraph::template NodeMap<Arc> PredMap;
kpeter@805: 
kpeter@805:   public:
kpeter@805: 
kpeter@805:     /// The type of the flow map.
kpeter@805:     typedef typename Digraph::template ArcMap<Capacity> FlowMap;
kpeter@805:     /// The type of the potential map.
kpeter@805:     typedef typename Digraph::template NodeMap<Cost> PotentialMap;
kpeter@805: 
kpeter@805:   private:
kpeter@805: 
kpeter@805:     /// \brief Special implementation of the \ref Dijkstra algorithm
kpeter@805:     /// for finding shortest paths in the residual network.
kpeter@805:     ///
kpeter@805:     /// \ref ResidualDijkstra is a special implementation of the
kpeter@805:     /// \ref Dijkstra algorithm for finding shortest paths in the
kpeter@805:     /// residual network of the digraph with respect to the reduced arc
kpeter@805:     /// costs and modifying the node potentials according to the
kpeter@805:     /// distance of the nodes.
kpeter@805:     class ResidualDijkstra
kpeter@805:     {
kpeter@805:       typedef typename Digraph::template NodeMap<int> HeapCrossRef;
kpeter@805:       typedef BinHeap<Cost, HeapCrossRef> Heap;
kpeter@805: 
kpeter@805:     private:
kpeter@805: 
kpeter@805:       // The digraph the algorithm runs on
kpeter@805:       const Digraph &_graph;
kpeter@805: 
kpeter@805:       // The main maps
kpeter@805:       const FlowMap &_flow;
kpeter@805:       const CapacityArcMap &_res_cap;
kpeter@805:       const CostMap &_cost;
kpeter@805:       const SupplyNodeMap &_excess;
kpeter@805:       PotentialMap &_potential;
kpeter@805: 
kpeter@805:       // The distance map
kpeter@805:       PotentialMap _dist;
kpeter@805:       // The pred arc map
kpeter@805:       PredMap &_pred;
kpeter@805:       // The processed (i.e. permanently labeled) nodes
kpeter@805:       std::vector<Node> _proc_nodes;
kpeter@805: 
kpeter@805:     public:
kpeter@805: 
kpeter@805:       /// Constructor.
kpeter@805:       ResidualDijkstra( const Digraph &digraph,
kpeter@805:                         const FlowMap &flow,
kpeter@805:                         const CapacityArcMap &res_cap,
kpeter@805:                         const CostMap &cost,
kpeter@805:                         const SupplyMap &excess,
kpeter@805:                         PotentialMap &potential,
kpeter@805:                         PredMap &pred ) :
kpeter@805:         _graph(digraph), _flow(flow), _res_cap(res_cap), _cost(cost),
kpeter@805:         _excess(excess), _potential(potential), _dist(digraph),
kpeter@805:         _pred(pred)
kpeter@805:       {}
kpeter@805: 
kpeter@805:       /// Run the algorithm from the given source node.
kpeter@805:       Node run(Node s, Capacity delta = 1) {
kpeter@805:         HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP);
kpeter@805:         Heap heap(heap_cross_ref);
kpeter@805:         heap.push(s, 0);
kpeter@805:         _pred[s] = INVALID;
kpeter@805:         _proc_nodes.clear();
kpeter@805: 
kpeter@805:         // Processing nodes
kpeter@805:         while (!heap.empty() && _excess[heap.top()] > -delta) {
kpeter@805:           Node u = heap.top(), v;
kpeter@805:           Cost d = heap.prio() + _potential[u], nd;
kpeter@805:           _dist[u] = heap.prio();
kpeter@805:           heap.pop();
kpeter@805:           _proc_nodes.push_back(u);
kpeter@805: 
kpeter@805:           // Traversing outgoing arcs
kpeter@805:           for (OutArcIt e(_graph, u); e != INVALID; ++e) {
kpeter@805:             if (_res_cap[e] >= delta) {
kpeter@805:               v = _graph.target(e);
kpeter@805:               switch(heap.state(v)) {
kpeter@805:               case Heap::PRE_HEAP:
kpeter@805:                 heap.push(v, d + _cost[e] - _potential[v]);
kpeter@805:                 _pred[v] = e;
kpeter@805:                 break;
kpeter@805:               case Heap::IN_HEAP:
kpeter@805:                 nd = d + _cost[e] - _potential[v];
kpeter@805:                 if (nd < heap[v]) {
kpeter@805:                   heap.decrease(v, nd);
kpeter@805:                   _pred[v] = e;
kpeter@805:                 }
kpeter@805:                 break;
kpeter@805:               case Heap::POST_HEAP:
kpeter@805:                 break;
kpeter@805:               }
kpeter@805:             }
kpeter@805:           }
kpeter@805: 
kpeter@805:           // Traversing incoming arcs
kpeter@805:           for (InArcIt e(_graph, u); e != INVALID; ++e) {
kpeter@805:             if (_flow[e] >= delta) {
kpeter@805:               v = _graph.source(e);
kpeter@805:               switch(heap.state(v)) {
kpeter@805:               case Heap::PRE_HEAP:
kpeter@805:                 heap.push(v, d - _cost[e] - _potential[v]);
kpeter@805:                 _pred[v] = e;
kpeter@805:                 break;
kpeter@805:               case Heap::IN_HEAP:
kpeter@805:                 nd = d - _cost[e] - _potential[v];
kpeter@805:                 if (nd < heap[v]) {
kpeter@805:                   heap.decrease(v, nd);
kpeter@805:                   _pred[v] = e;
kpeter@805:                 }
kpeter@805:                 break;
kpeter@805:               case Heap::POST_HEAP:
kpeter@805:                 break;
kpeter@805:               }
kpeter@805:             }
kpeter@805:           }
kpeter@805:         }
kpeter@805:         if (heap.empty()) return INVALID;
kpeter@805: 
kpeter@805:         // Updating potentials of processed nodes
kpeter@805:         Node t = heap.top();
kpeter@805:         Cost t_dist = heap.prio();
kpeter@805:         for (int i = 0; i < int(_proc_nodes.size()); ++i)
kpeter@805:           _potential[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist;
kpeter@805: 
kpeter@805:         return t;
kpeter@805:       }
kpeter@805: 
kpeter@805:     }; //class ResidualDijkstra
kpeter@805: 
kpeter@805:   private:
kpeter@805: 
kpeter@805:     // The digraph the algorithm runs on
kpeter@805:     const Digraph &_graph;
kpeter@805:     // The original lower bound map
kpeter@805:     const LowerMap *_lower;
kpeter@805:     // The modified capacity map
kpeter@805:     CapacityArcMap _capacity;
kpeter@805:     // The original cost map
kpeter@805:     const CostMap &_cost;
kpeter@805:     // The modified supply map
kpeter@805:     SupplyNodeMap _supply;
kpeter@805:     bool _valid_supply;
kpeter@805: 
kpeter@805:     // Arc map of the current flow
kpeter@805:     FlowMap *_flow;
kpeter@805:     bool _local_flow;
kpeter@805:     // Node map of the current potentials
kpeter@805:     PotentialMap *_potential;
kpeter@805:     bool _local_potential;
kpeter@805: 
kpeter@805:     // The residual capacity map
kpeter@805:     CapacityArcMap _res_cap;
kpeter@805:     // The excess map
kpeter@805:     SupplyNodeMap _excess;
kpeter@805:     // The excess nodes (i.e. nodes with positive excess)
kpeter@805:     std::vector<Node> _excess_nodes;
kpeter@805:     // The deficit nodes (i.e. nodes with negative excess)
kpeter@805:     std::vector<Node> _deficit_nodes;
kpeter@805: 
kpeter@805:     // The delta parameter used for capacity scaling
kpeter@805:     Capacity _delta;
kpeter@805:     // The maximum number of phases
kpeter@805:     int _phase_num;
kpeter@805: 
kpeter@805:     // The pred arc map
kpeter@805:     PredMap _pred;
kpeter@805:     // Implementation of the Dijkstra algorithm for finding augmenting
kpeter@805:     // shortest paths in the residual network
kpeter@805:     ResidualDijkstra *_dijkstra;
kpeter@805: 
kpeter@805:   public:
kpeter@805: 
kpeter@805:     /// \brief General constructor (with lower bounds).
kpeter@805:     ///
kpeter@805:     /// General constructor (with lower bounds).
kpeter@805:     ///
kpeter@805:     /// \param digraph The digraph the algorithm runs on.
kpeter@805:     /// \param lower The lower bounds of the arcs.
kpeter@805:     /// \param capacity The capacities (upper bounds) of the arcs.
kpeter@805:     /// \param cost The cost (length) values of the arcs.
kpeter@805:     /// \param supply The supply values of the nodes (signed).
kpeter@805:     CapacityScaling( const Digraph &digraph,
kpeter@805:                      const LowerMap &lower,
kpeter@805:                      const CapacityMap &capacity,
kpeter@805:                      const CostMap &cost,
kpeter@805:                      const SupplyMap &supply ) :
kpeter@805:       _graph(digraph), _lower(&lower), _capacity(digraph), _cost(cost),
kpeter@805:       _supply(digraph), _flow(NULL), _local_flow(false),
kpeter@805:       _potential(NULL), _local_potential(false),
kpeter@805:       _res_cap(digraph), _excess(digraph), _pred(digraph), _dijkstra(NULL)
kpeter@805:     {
kpeter@805:       Supply sum = 0;
kpeter@805:       for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@805:         _supply[n] = supply[n];
kpeter@805:         _excess[n] = supply[n];
kpeter@805:         sum += supply[n];
kpeter@805:       }
kpeter@805:       _valid_supply = sum == 0;
kpeter@805:       for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@805:         _capacity[a] = capacity[a];
kpeter@805:         _res_cap[a] = capacity[a];
kpeter@805:       }
kpeter@805: 
kpeter@805:       // Remove non-zero lower bounds
kpeter@805:       typename LowerMap::Value lcap;
kpeter@805:       for (ArcIt e(_graph); e != INVALID; ++e) {
kpeter@805:         if ((lcap = lower[e]) != 0) {
kpeter@805:           _capacity[e] -= lcap;
kpeter@805:           _res_cap[e] -= lcap;
kpeter@805:           _supply[_graph.source(e)] -= lcap;
kpeter@805:           _supply[_graph.target(e)] += lcap;
kpeter@805:           _excess[_graph.source(e)] -= lcap;
kpeter@805:           _excess[_graph.target(e)] += lcap;
kpeter@805:         }
kpeter@805:       }
kpeter@805:     }
kpeter@805: /*
kpeter@805:     /// \brief General constructor (without lower bounds).
kpeter@805:     ///
kpeter@805:     /// General constructor (without lower bounds).
kpeter@805:     ///
kpeter@805:     /// \param digraph The digraph the algorithm runs on.
kpeter@805:     /// \param capacity The capacities (upper bounds) of the arcs.
kpeter@805:     /// \param cost The cost (length) values of the arcs.
kpeter@805:     /// \param supply The supply values of the nodes (signed).
kpeter@805:     CapacityScaling( const Digraph &digraph,
kpeter@805:                      const CapacityMap &capacity,
kpeter@805:                      const CostMap &cost,
kpeter@805:                      const SupplyMap &supply ) :
kpeter@805:       _graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost),
kpeter@805:       _supply(supply), _flow(NULL), _local_flow(false),
kpeter@805:       _potential(NULL), _local_potential(false),
kpeter@805:       _res_cap(capacity), _excess(supply), _pred(digraph), _dijkstra(NULL)
kpeter@805:     {
kpeter@805:       // Check the sum of supply values
kpeter@805:       Supply sum = 0;
kpeter@805:       for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n];
kpeter@805:       _valid_supply = sum == 0;
kpeter@805:     }
kpeter@805: 
kpeter@805:     /// \brief Simple constructor (with lower bounds).
kpeter@805:     ///
kpeter@805:     /// Simple constructor (with lower bounds).
kpeter@805:     ///
kpeter@805:     /// \param digraph The digraph the algorithm runs on.
kpeter@805:     /// \param lower The lower bounds of the arcs.
kpeter@805:     /// \param capacity The capacities (upper bounds) of the arcs.
kpeter@805:     /// \param cost The cost (length) values of the arcs.
kpeter@805:     /// \param s The source node.
kpeter@805:     /// \param t The target node.
kpeter@805:     /// \param flow_value The required amount of flow from node \c s
kpeter@805:     /// to node \c t (i.e. the supply of \c s and the demand of \c t).
kpeter@805:     CapacityScaling( const Digraph &digraph,
kpeter@805:                      const LowerMap &lower,
kpeter@805:                      const CapacityMap &capacity,
kpeter@805:                      const CostMap &cost,
kpeter@805:                      Node s, Node t,
kpeter@805:                      Supply flow_value ) :
kpeter@805:       _graph(digraph), _lower(&lower), _capacity(capacity), _cost(cost),
kpeter@805:       _supply(digraph, 0), _flow(NULL), _local_flow(false),
kpeter@805:       _potential(NULL), _local_potential(false),
kpeter@805:       _res_cap(capacity), _excess(digraph, 0), _pred(digraph), _dijkstra(NULL)
kpeter@805:     {
kpeter@805:       // Remove non-zero lower bounds
kpeter@805:       _supply[s] = _excess[s] =  flow_value;
kpeter@805:       _supply[t] = _excess[t] = -flow_value;
kpeter@805:       typename LowerMap::Value lcap;
kpeter@805:       for (ArcIt e(_graph); e != INVALID; ++e) {
kpeter@805:         if ((lcap = lower[e]) != 0) {
kpeter@805:           _capacity[e] -= lcap;
kpeter@805:           _res_cap[e] -= lcap;
kpeter@805:           _supply[_graph.source(e)] -= lcap;
kpeter@805:           _supply[_graph.target(e)] += lcap;
kpeter@805:           _excess[_graph.source(e)] -= lcap;
kpeter@805:           _excess[_graph.target(e)] += lcap;
kpeter@805:         }
kpeter@805:       }
kpeter@805:       _valid_supply = true;
kpeter@805:     }
kpeter@805: 
kpeter@805:     /// \brief Simple constructor (without lower bounds).
kpeter@805:     ///
kpeter@805:     /// Simple constructor (without lower bounds).
kpeter@805:     ///
kpeter@805:     /// \param digraph The digraph the algorithm runs on.
kpeter@805:     /// \param capacity The capacities (upper bounds) of the arcs.
kpeter@805:     /// \param cost The cost (length) values of the arcs.
kpeter@805:     /// \param s The source node.
kpeter@805:     /// \param t The target node.
kpeter@805:     /// \param flow_value The required amount of flow from node \c s
kpeter@805:     /// to node \c t (i.e. the supply of \c s and the demand of \c t).
kpeter@805:     CapacityScaling( const Digraph &digraph,
kpeter@805:                      const CapacityMap &capacity,
kpeter@805:                      const CostMap &cost,
kpeter@805:                      Node s, Node t,
kpeter@805:                      Supply flow_value ) :
kpeter@805:       _graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost),
kpeter@805:       _supply(digraph, 0), _flow(NULL), _local_flow(false),
kpeter@805:       _potential(NULL), _local_potential(false),
kpeter@805:       _res_cap(capacity), _excess(digraph, 0), _pred(digraph), _dijkstra(NULL)
kpeter@805:     {
kpeter@805:       _supply[s] = _excess[s] =  flow_value;
kpeter@805:       _supply[t] = _excess[t] = -flow_value;
kpeter@805:       _valid_supply = true;
kpeter@805:     }
kpeter@805: */
kpeter@805:     /// Destructor.
kpeter@805:     ~CapacityScaling() {
kpeter@805:       if (_local_flow) delete _flow;
kpeter@805:       if (_local_potential) delete _potential;
kpeter@805:       delete _dijkstra;
kpeter@805:     }
kpeter@805: 
kpeter@805:     /// \brief Set the flow map.
kpeter@805:     ///
kpeter@805:     /// Set the flow map.
kpeter@805:     ///
kpeter@805:     /// \return \c (*this)
kpeter@805:     CapacityScaling& flowMap(FlowMap &map) {
kpeter@805:       if (_local_flow) {
kpeter@805:         delete _flow;
kpeter@805:         _local_flow = false;
kpeter@805:       }
kpeter@805:       _flow = &map;
kpeter@805:       return *this;
kpeter@805:     }
kpeter@805: 
kpeter@805:     /// \brief Set the potential map.
kpeter@805:     ///
kpeter@805:     /// Set the potential map.
kpeter@805:     ///
kpeter@805:     /// \return \c (*this)
kpeter@805:     CapacityScaling& potentialMap(PotentialMap &map) {
kpeter@805:       if (_local_potential) {
kpeter@805:         delete _potential;
kpeter@805:         _local_potential = false;
kpeter@805:       }
kpeter@805:       _potential = &map;
kpeter@805:       return *this;
kpeter@805:     }
kpeter@805: 
kpeter@805:     /// \name Execution control
kpeter@805: 
kpeter@805:     /// @{
kpeter@805: 
kpeter@805:     /// \brief Run the algorithm.
kpeter@805:     ///
kpeter@805:     /// This function runs the algorithm.
kpeter@805:     ///
kpeter@805:     /// \param scaling Enable or disable capacity scaling.
kpeter@805:     /// If the maximum arc capacity and/or the amount of total supply
kpeter@805:     /// is rather small, the algorithm could be slightly faster without
kpeter@805:     /// scaling.
kpeter@805:     ///
kpeter@805:     /// \return \c true if a feasible flow can be found.
kpeter@805:     bool run(bool scaling = true) {
kpeter@805:       return init(scaling) && start();
kpeter@805:     }
kpeter@805: 
kpeter@805:     /// @}
kpeter@805: 
kpeter@805:     /// \name Query Functions
kpeter@805:     /// The results of the algorithm can be obtained using these
kpeter@805:     /// functions.\n
kpeter@805:     /// \ref lemon::CapacityScaling::run() "run()" must be called before
kpeter@805:     /// using them.
kpeter@805: 
kpeter@805:     /// @{
kpeter@805: 
kpeter@805:     /// \brief Return a const reference to the arc map storing the
kpeter@805:     /// found flow.
kpeter@805:     ///
kpeter@805:     /// Return a const reference to the arc map storing the found flow.
kpeter@805:     ///
kpeter@805:     /// \pre \ref run() must be called before using this function.
kpeter@805:     const FlowMap& flowMap() const {
kpeter@805:       return *_flow;
kpeter@805:     }
kpeter@805: 
kpeter@805:     /// \brief Return a const reference to the node map storing the
kpeter@805:     /// found potentials (the dual solution).
kpeter@805:     ///
kpeter@805:     /// Return a const reference to the node map storing the found
kpeter@805:     /// potentials (the dual solution).
kpeter@805:     ///
kpeter@805:     /// \pre \ref run() must be called before using this function.
kpeter@805:     const PotentialMap& potentialMap() const {
kpeter@805:       return *_potential;
kpeter@805:     }
kpeter@805: 
kpeter@805:     /// \brief Return the flow on the given arc.
kpeter@805:     ///
kpeter@805:     /// Return the flow on the given arc.
kpeter@805:     ///
kpeter@805:     /// \pre \ref run() must be called before using this function.
kpeter@805:     Capacity flow(const Arc& arc) const {
kpeter@805:       return (*_flow)[arc];
kpeter@805:     }
kpeter@805: 
kpeter@805:     /// \brief Return the potential of the given node.
kpeter@805:     ///
kpeter@805:     /// Return the potential of the given node.
kpeter@805:     ///
kpeter@805:     /// \pre \ref run() must be called before using this function.
kpeter@805:     Cost potential(const Node& node) const {
kpeter@805:       return (*_potential)[node];
kpeter@805:     }
kpeter@805: 
kpeter@805:     /// \brief Return the total cost of the found flow.
kpeter@805:     ///
kpeter@805:     /// Return the total cost of the found flow. The complexity of the
kpeter@805:     /// function is \f$ O(e) \f$.
kpeter@805:     ///
kpeter@805:     /// \pre \ref run() must be called before using this function.
kpeter@805:     Cost totalCost() const {
kpeter@805:       Cost c = 0;
kpeter@805:       for (ArcIt e(_graph); e != INVALID; ++e)
kpeter@805:         c += (*_flow)[e] * _cost[e];
kpeter@805:       return c;
kpeter@805:     }
kpeter@805: 
kpeter@805:     /// @}
kpeter@805: 
kpeter@805:   private:
kpeter@805: 
kpeter@805:     /// Initialize the algorithm.
kpeter@805:     bool init(bool scaling) {
kpeter@805:       if (!_valid_supply) return false;
kpeter@805: 
kpeter@805:       // Initializing maps
kpeter@805:       if (!_flow) {
kpeter@805:         _flow = new FlowMap(_graph);
kpeter@805:         _local_flow = true;
kpeter@805:       }
kpeter@805:       if (!_potential) {
kpeter@805:         _potential = new PotentialMap(_graph);
kpeter@805:         _local_potential = true;
kpeter@805:       }
kpeter@805:       for (ArcIt e(_graph); e != INVALID; ++e) (*_flow)[e] = 0;
kpeter@805:       for (NodeIt n(_graph); n != INVALID; ++n) (*_potential)[n] = 0;
kpeter@805: 
kpeter@805:       _dijkstra = new ResidualDijkstra( _graph, *_flow, _res_cap, _cost,
kpeter@805:                                         _excess, *_potential, _pred );
kpeter@805: 
kpeter@805:       // Initializing delta value
kpeter@805:       if (scaling) {
kpeter@805:         // With scaling
kpeter@805:         Supply max_sup = 0, max_dem = 0;
kpeter@805:         for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@805:           if ( _supply[n] > max_sup) max_sup =  _supply[n];
kpeter@805:           if (-_supply[n] > max_dem) max_dem = -_supply[n];
kpeter@805:         }
kpeter@805:         Capacity max_cap = 0;
kpeter@805:         for (ArcIt e(_graph); e != INVALID; ++e) {
kpeter@805:           if (_capacity[e] > max_cap) max_cap = _capacity[e];
kpeter@805:         }
kpeter@805:         max_sup = std::min(std::min(max_sup, max_dem), max_cap);
kpeter@805:         _phase_num = 0;
kpeter@805:         for (_delta = 1; 2 * _delta <= max_sup; _delta *= 2)
kpeter@805:           ++_phase_num;
kpeter@805:       } else {
kpeter@805:         // Without scaling
kpeter@805:         _delta = 1;
kpeter@805:       }
kpeter@805: 
kpeter@805:       return true;
kpeter@805:     }
kpeter@805: 
kpeter@805:     bool start() {
kpeter@805:       if (_delta > 1)
kpeter@805:         return startWithScaling();
kpeter@805:       else
kpeter@805:         return startWithoutScaling();
kpeter@805:     }
kpeter@805: 
kpeter@805:     /// Execute the capacity scaling algorithm.
kpeter@805:     bool startWithScaling() {
kpeter@805:       // Processing capacity scaling phases
kpeter@805:       Node s, t;
kpeter@805:       int phase_cnt = 0;
kpeter@805:       int factor = 4;
kpeter@805:       while (true) {
kpeter@805:         // Saturating all arcs not satisfying the optimality condition
kpeter@805:         for (ArcIt e(_graph); e != INVALID; ++e) {
kpeter@805:           Node u = _graph.source(e), v = _graph.target(e);
kpeter@805:           Cost c = _cost[e] + (*_potential)[u] - (*_potential)[v];
kpeter@805:           if (c < 0 && _res_cap[e] >= _delta) {
kpeter@805:             _excess[u] -= _res_cap[e];
kpeter@805:             _excess[v] += _res_cap[e];
kpeter@805:             (*_flow)[e] = _capacity[e];
kpeter@805:             _res_cap[e] = 0;
kpeter@805:           }
kpeter@805:           else if (c > 0 && (*_flow)[e] >= _delta) {
kpeter@805:             _excess[u] += (*_flow)[e];
kpeter@805:             _excess[v] -= (*_flow)[e];
kpeter@805:             (*_flow)[e] = 0;
kpeter@805:             _res_cap[e] = _capacity[e];
kpeter@805:           }
kpeter@805:         }
kpeter@805: 
kpeter@805:         // Finding excess nodes and deficit nodes
kpeter@805:         _excess_nodes.clear();
kpeter@805:         _deficit_nodes.clear();
kpeter@805:         for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@805:           if (_excess[n] >=  _delta) _excess_nodes.push_back(n);
kpeter@805:           if (_excess[n] <= -_delta) _deficit_nodes.push_back(n);
kpeter@805:         }
kpeter@805:         int next_node = 0, next_def_node = 0;
kpeter@805: 
kpeter@805:         // Finding augmenting shortest paths
kpeter@805:         while (next_node < int(_excess_nodes.size())) {
kpeter@805:           // Checking deficit nodes
kpeter@805:           if (_delta > 1) {
kpeter@805:             bool delta_deficit = false;
kpeter@805:             for ( ; next_def_node < int(_deficit_nodes.size());
kpeter@805:                     ++next_def_node ) {
kpeter@805:               if (_excess[_deficit_nodes[next_def_node]] <= -_delta) {
kpeter@805:                 delta_deficit = true;
kpeter@805:                 break;
kpeter@805:               }
kpeter@805:             }
kpeter@805:             if (!delta_deficit) break;
kpeter@805:           }
kpeter@805: 
kpeter@805:           // Running Dijkstra
kpeter@805:           s = _excess_nodes[next_node];
kpeter@805:           if ((t = _dijkstra->run(s, _delta)) == INVALID) {
kpeter@805:             if (_delta > 1) {
kpeter@805:               ++next_node;
kpeter@805:               continue;
kpeter@805:             }
kpeter@805:             return false;
kpeter@805:           }
kpeter@805: 
kpeter@805:           // Augmenting along a shortest path from s to t.
kpeter@805:           Capacity d = std::min(_excess[s], -_excess[t]);
kpeter@805:           Node u = t;
kpeter@805:           Arc e;
kpeter@805:           if (d > _delta) {
kpeter@805:             while ((e = _pred[u]) != INVALID) {
kpeter@805:               Capacity rc;
kpeter@805:               if (u == _graph.target(e)) {
kpeter@805:                 rc = _res_cap[e];
kpeter@805:                 u = _graph.source(e);
kpeter@805:               } else {
kpeter@805:                 rc = (*_flow)[e];
kpeter@805:                 u = _graph.target(e);
kpeter@805:               }
kpeter@805:               if (rc < d) d = rc;
kpeter@805:             }
kpeter@805:           }
kpeter@805:           u = t;
kpeter@805:           while ((e = _pred[u]) != INVALID) {
kpeter@805:             if (u == _graph.target(e)) {
kpeter@805:               (*_flow)[e] += d;
kpeter@805:               _res_cap[e] -= d;
kpeter@805:               u = _graph.source(e);
kpeter@805:             } else {
kpeter@805:               (*_flow)[e] -= d;
kpeter@805:               _res_cap[e] += d;
kpeter@805:               u = _graph.target(e);
kpeter@805:             }
kpeter@805:           }
kpeter@805:           _excess[s] -= d;
kpeter@805:           _excess[t] += d;
kpeter@805: 
kpeter@805:           if (_excess[s] < _delta) ++next_node;
kpeter@805:         }
kpeter@805: 
kpeter@805:         if (_delta == 1) break;
kpeter@805:         if (++phase_cnt > _phase_num / 4) factor = 2;
kpeter@805:         _delta = _delta <= factor ? 1 : _delta / factor;
kpeter@805:       }
kpeter@805: 
kpeter@805:       // Handling non-zero lower bounds
kpeter@805:       if (_lower) {
kpeter@805:         for (ArcIt e(_graph); e != INVALID; ++e)
kpeter@805:           (*_flow)[e] += (*_lower)[e];
kpeter@805:       }
kpeter@805:       return true;
kpeter@805:     }
kpeter@805: 
kpeter@805:     /// Execute the successive shortest path algorithm.
kpeter@805:     bool startWithoutScaling() {
kpeter@805:       // Finding excess nodes
kpeter@805:       for (NodeIt n(_graph); n != INVALID; ++n)
kpeter@805:         if (_excess[n] > 0) _excess_nodes.push_back(n);
kpeter@805:       if (_excess_nodes.size() == 0) return true;
kpeter@805:       int next_node = 0;
kpeter@805: 
kpeter@805:       // Finding shortest paths
kpeter@805:       Node s, t;
kpeter@805:       while ( _excess[_excess_nodes[next_node]] > 0 ||
kpeter@805:               ++next_node < int(_excess_nodes.size()) )
kpeter@805:       {
kpeter@805:         // Running Dijkstra
kpeter@805:         s = _excess_nodes[next_node];
kpeter@805:         if ((t = _dijkstra->run(s)) == INVALID) return false;
kpeter@805: 
kpeter@805:         // Augmenting along a shortest path from s to t
kpeter@805:         Capacity d = std::min(_excess[s], -_excess[t]);
kpeter@805:         Node u = t;
kpeter@805:         Arc e;
kpeter@805:         if (d > 1) {
kpeter@805:           while ((e = _pred[u]) != INVALID) {
kpeter@805:             Capacity rc;
kpeter@805:             if (u == _graph.target(e)) {
kpeter@805:               rc = _res_cap[e];
kpeter@805:               u = _graph.source(e);
kpeter@805:             } else {
kpeter@805:               rc = (*_flow)[e];
kpeter@805:               u = _graph.target(e);
kpeter@805:             }
kpeter@805:             if (rc < d) d = rc;
kpeter@805:           }
kpeter@805:         }
kpeter@805:         u = t;
kpeter@805:         while ((e = _pred[u]) != INVALID) {
kpeter@805:           if (u == _graph.target(e)) {
kpeter@805:             (*_flow)[e] += d;
kpeter@805:             _res_cap[e] -= d;
kpeter@805:             u = _graph.source(e);
kpeter@805:           } else {
kpeter@805:             (*_flow)[e] -= d;
kpeter@805:             _res_cap[e] += d;
kpeter@805:             u = _graph.target(e);
kpeter@805:           }
kpeter@805:         }
kpeter@805:         _excess[s] -= d;
kpeter@805:         _excess[t] += d;
kpeter@805:       }
kpeter@805: 
kpeter@805:       // Handling non-zero lower bounds
kpeter@805:       if (_lower) {
kpeter@805:         for (ArcIt e(_graph); e != INVALID; ++e)
kpeter@805:           (*_flow)[e] += (*_lower)[e];
kpeter@805:       }
kpeter@805:       return true;
kpeter@805:     }
kpeter@805: 
kpeter@805:   }; //class CapacityScaling
kpeter@805: 
kpeter@805:   ///@}
kpeter@805: 
kpeter@805: } //namespace lemon
kpeter@805: 
kpeter@805: #endif //LEMON_CAPACITY_SCALING_H