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@806: /// \ingroup min_cost_flow_algs
kpeter@805: ///
kpeter@805: /// \file
kpeter@806: /// \brief Capacity Scaling algorithm for finding a minimum cost flow.
kpeter@805: 
kpeter@805: #include <vector>
kpeter@806: #include <limits>
kpeter@806: #include <lemon/core.h>
kpeter@805: #include <lemon/bin_heap.h>
kpeter@805: 
kpeter@805: namespace lemon {
kpeter@805: 
kpeter@807:   /// \brief Default traits class of CapacityScaling algorithm.
kpeter@807:   ///
kpeter@807:   /// Default traits class of CapacityScaling algorithm.
kpeter@807:   /// \tparam GR Digraph type.
kpeter@812:   /// \tparam V The number type used for flow amounts, capacity bounds
kpeter@807:   /// and supply values. By default it is \c int.
kpeter@812:   /// \tparam C The number type used for costs and potentials.
kpeter@807:   /// By default it is the same as \c V.
kpeter@807:   template <typename GR, typename V = int, typename C = V>
kpeter@807:   struct CapacityScalingDefaultTraits
kpeter@807:   {
kpeter@807:     /// The type of the digraph
kpeter@807:     typedef GR Digraph;
kpeter@807:     /// The type of the flow amounts, capacity bounds and supply values
kpeter@807:     typedef V Value;
kpeter@807:     /// The type of the arc costs
kpeter@807:     typedef C Cost;
kpeter@807: 
kpeter@807:     /// \brief The type of the heap used for internal Dijkstra computations.
kpeter@807:     ///
kpeter@807:     /// The type of the heap used for internal Dijkstra computations.
kpeter@807:     /// It must conform to the \ref lemon::concepts::Heap "Heap" concept,
kpeter@807:     /// its priority type must be \c Cost and its cross reference type
kpeter@807:     /// must be \ref RangeMap "RangeMap<int>".
kpeter@807:     typedef BinHeap<Cost, RangeMap<int> > Heap;
kpeter@807:   };
kpeter@807: 
kpeter@806:   /// \addtogroup min_cost_flow_algs
kpeter@805:   /// @{
kpeter@805: 
kpeter@806:   /// \brief Implementation of the Capacity Scaling algorithm for
kpeter@806:   /// finding a \ref min_cost_flow "minimum cost flow".
kpeter@805:   ///
kpeter@805:   /// \ref CapacityScaling implements the capacity scaling version
kpeter@806:   /// of the successive shortest path algorithm for finding a
kpeter@813:   /// \ref min_cost_flow "minimum cost flow" \ref amo93networkflows,
kpeter@813:   /// \ref edmondskarp72theoretical. It is an efficient dual
kpeter@806:   /// solution method.
kpeter@805:   ///
kpeter@806:   /// Most of the parameters of the problem (except for the digraph)
kpeter@806:   /// can be given using separate functions, and the algorithm can be
kpeter@806:   /// executed using the \ref run() function. If some parameters are not
kpeter@806:   /// specified, then default values will be used.
kpeter@805:   ///
kpeter@806:   /// \tparam GR The digraph type the algorithm runs on.
kpeter@812:   /// \tparam V The number type used for flow amounts, capacity bounds
kpeter@806:   /// and supply values in the algorithm. By default it is \c int.
kpeter@812:   /// \tparam C The number type used for costs and potentials in the
kpeter@806:   /// algorithm. By default it is the same as \c V.
kpeter@805:   ///
kpeter@812:   /// \warning Both number types must be signed and all input data must
kpeter@806:   /// be integer.
kpeter@806:   /// \warning This algorithm does not support negative costs for such
kpeter@806:   /// arcs that have infinite upper bound.
kpeter@807: #ifdef DOXYGEN
kpeter@807:   template <typename GR, typename V, typename C, typename TR>
kpeter@807: #else
kpeter@807:   template < typename GR, typename V = int, typename C = V,
kpeter@807:              typename TR = CapacityScalingDefaultTraits<GR, V, C> >
kpeter@807: #endif
kpeter@805:   class CapacityScaling
kpeter@805:   {
kpeter@806:   public:
kpeter@805: 
kpeter@807:     /// The type of the digraph
kpeter@807:     typedef typename TR::Digraph Digraph;
kpeter@806:     /// The type of the flow amounts, capacity bounds and supply values
kpeter@807:     typedef typename TR::Value Value;
kpeter@806:     /// The type of the arc costs
kpeter@807:     typedef typename TR::Cost Cost;
kpeter@807: 
kpeter@807:     /// The type of the heap used for internal Dijkstra computations
kpeter@807:     typedef typename TR::Heap Heap;
kpeter@807: 
kpeter@807:     /// The \ref CapacityScalingDefaultTraits "traits class" of the algorithm
kpeter@807:     typedef TR Traits;
kpeter@805: 
kpeter@805:   public:
kpeter@805: 
kpeter@806:     /// \brief Problem type constants for the \c run() function.
kpeter@806:     ///
kpeter@806:     /// Enum type containing the problem type constants that can be
kpeter@806:     /// returned by the \ref run() function of the algorithm.
kpeter@806:     enum ProblemType {
kpeter@806:       /// The problem has no feasible solution (flow).
kpeter@806:       INFEASIBLE,
kpeter@806:       /// The problem has optimal solution (i.e. it is feasible and
kpeter@806:       /// bounded), and the algorithm has found optimal flow and node
kpeter@806:       /// potentials (primal and dual solutions).
kpeter@806:       OPTIMAL,
kpeter@806:       /// The digraph contains an arc of negative cost and infinite
kpeter@806:       /// upper bound. It means that the objective function is unbounded
kpeter@812:       /// on that arc, however, note that it could actually be bounded
kpeter@806:       /// over the feasible flows, but this algroithm cannot handle
kpeter@806:       /// these cases.
kpeter@806:       UNBOUNDED
kpeter@806:     };
kpeter@806:   
kpeter@806:   private:
kpeter@806: 
kpeter@806:     TEMPLATE_DIGRAPH_TYPEDEFS(GR);
kpeter@806: 
kpeter@806:     typedef std::vector<int> IntVector;
kpeter@811:     typedef std::vector<char> BoolVector;
kpeter@806:     typedef std::vector<Value> ValueVector;
kpeter@806:     typedef std::vector<Cost> CostVector;
kpeter@805: 
kpeter@805:   private:
kpeter@805: 
kpeter@806:     // Data related to the underlying digraph
kpeter@806:     const GR &_graph;
kpeter@806:     int _node_num;
kpeter@806:     int _arc_num;
kpeter@806:     int _res_arc_num;
kpeter@806:     int _root;
kpeter@806: 
kpeter@806:     // Parameters of the problem
kpeter@806:     bool _have_lower;
kpeter@806:     Value _sum_supply;
kpeter@806: 
kpeter@806:     // Data structures for storing the digraph
kpeter@806:     IntNodeMap _node_id;
kpeter@806:     IntArcMap _arc_idf;
kpeter@806:     IntArcMap _arc_idb;
kpeter@806:     IntVector _first_out;
kpeter@806:     BoolVector _forward;
kpeter@806:     IntVector _source;
kpeter@806:     IntVector _target;
kpeter@806:     IntVector _reverse;
kpeter@806: 
kpeter@806:     // Node and arc data
kpeter@806:     ValueVector _lower;
kpeter@806:     ValueVector _upper;
kpeter@806:     CostVector _cost;
kpeter@806:     ValueVector _supply;
kpeter@806: 
kpeter@806:     ValueVector _res_cap;
kpeter@806:     CostVector _pi;
kpeter@806:     ValueVector _excess;
kpeter@806:     IntVector _excess_nodes;
kpeter@806:     IntVector _deficit_nodes;
kpeter@806: 
kpeter@806:     Value _delta;
kpeter@810:     int _factor;
kpeter@806:     IntVector _pred;
kpeter@806: 
kpeter@806:   public:
kpeter@806:   
kpeter@806:     /// \brief Constant for infinite upper bounds (capacities).
kpeter@805:     ///
kpeter@806:     /// Constant for infinite upper bounds (capacities).
kpeter@806:     /// It is \c std::numeric_limits<Value>::infinity() if available,
kpeter@806:     /// \c std::numeric_limits<Value>::max() otherwise.
kpeter@806:     const Value INF;
kpeter@806: 
kpeter@806:   private:
kpeter@806: 
kpeter@806:     // Special implementation of the Dijkstra algorithm for finding
kpeter@806:     // shortest paths in the residual network of the digraph with
kpeter@806:     // respect to the reduced arc costs and modifying the node
kpeter@806:     // potentials according to the found distance labels.
kpeter@805:     class ResidualDijkstra
kpeter@805:     {
kpeter@805:     private:
kpeter@805: 
kpeter@806:       int _node_num;
kpeter@811:       bool _geq;
kpeter@806:       const IntVector &_first_out;
kpeter@806:       const IntVector &_target;
kpeter@806:       const CostVector &_cost;
kpeter@806:       const ValueVector &_res_cap;
kpeter@806:       const ValueVector &_excess;
kpeter@806:       CostVector &_pi;
kpeter@806:       IntVector &_pred;
kpeter@806:       
kpeter@806:       IntVector _proc_nodes;
kpeter@806:       CostVector _dist;
kpeter@806:       
kpeter@805:     public:
kpeter@805: 
kpeter@806:       ResidualDijkstra(CapacityScaling& cs) :
kpeter@811:         _node_num(cs._node_num), _geq(cs._sum_supply < 0),
kpeter@811:         _first_out(cs._first_out), _target(cs._target), _cost(cs._cost),
kpeter@811:         _res_cap(cs._res_cap), _excess(cs._excess), _pi(cs._pi),
kpeter@811:         _pred(cs._pred), _dist(cs._node_num)
kpeter@805:       {}
kpeter@805: 
kpeter@806:       int run(int s, Value delta = 1) {
kpeter@807:         RangeMap<int> heap_cross_ref(_node_num, Heap::PRE_HEAP);
kpeter@805:         Heap heap(heap_cross_ref);
kpeter@805:         heap.push(s, 0);
kpeter@806:         _pred[s] = -1;
kpeter@805:         _proc_nodes.clear();
kpeter@805: 
kpeter@806:         // Process nodes
kpeter@805:         while (!heap.empty() && _excess[heap.top()] > -delta) {
kpeter@806:           int u = heap.top(), v;
kpeter@806:           Cost d = heap.prio() + _pi[u], dn;
kpeter@805:           _dist[u] = heap.prio();
kpeter@806:           _proc_nodes.push_back(u);
kpeter@805:           heap.pop();
kpeter@805: 
kpeter@806:           // Traverse outgoing residual arcs
kpeter@811:           int last_out = _geq ? _first_out[u+1] : _first_out[u+1] - 1;
kpeter@811:           for (int a = _first_out[u]; a != last_out; ++a) {
kpeter@806:             if (_res_cap[a] < delta) continue;
kpeter@806:             v = _target[a];
kpeter@806:             switch (heap.state(v)) {
kpeter@805:               case Heap::PRE_HEAP:
kpeter@806:                 heap.push(v, d + _cost[a] - _pi[v]);
kpeter@806:                 _pred[v] = a;
kpeter@805:                 break;
kpeter@805:               case Heap::IN_HEAP:
kpeter@806:                 dn = d + _cost[a] - _pi[v];
kpeter@806:                 if (dn < heap[v]) {
kpeter@806:                   heap.decrease(v, dn);
kpeter@806:                   _pred[v] = a;
kpeter@805:                 }
kpeter@805:                 break;
kpeter@805:               case Heap::POST_HEAP:
kpeter@805:                 break;
kpeter@805:             }
kpeter@805:           }
kpeter@805:         }
kpeter@806:         if (heap.empty()) return -1;
kpeter@805: 
kpeter@806:         // Update potentials of processed nodes
kpeter@806:         int t = heap.top();
kpeter@806:         Cost dt = heap.prio();
kpeter@806:         for (int i = 0; i < int(_proc_nodes.size()); ++i) {
kpeter@806:           _pi[_proc_nodes[i]] += _dist[_proc_nodes[i]] - dt;
kpeter@806:         }
kpeter@805: 
kpeter@805:         return t;
kpeter@805:       }
kpeter@805: 
kpeter@805:     }; //class ResidualDijkstra
kpeter@805: 
kpeter@805:   public:
kpeter@805: 
kpeter@807:     /// \name Named Template Parameters
kpeter@807:     /// @{
kpeter@807: 
kpeter@807:     template <typename T>
kpeter@807:     struct SetHeapTraits : public Traits {
kpeter@807:       typedef T Heap;
kpeter@807:     };
kpeter@807: 
kpeter@807:     /// \brief \ref named-templ-param "Named parameter" for setting
kpeter@807:     /// \c Heap type.
kpeter@807:     ///
kpeter@807:     /// \ref named-templ-param "Named parameter" for setting \c Heap
kpeter@807:     /// type, which is used for internal Dijkstra computations.
kpeter@807:     /// It must conform to the \ref lemon::concepts::Heap "Heap" concept,
kpeter@807:     /// its priority type must be \c Cost and its cross reference type
kpeter@807:     /// must be \ref RangeMap "RangeMap<int>".
kpeter@807:     template <typename T>
kpeter@807:     struct SetHeap
kpeter@807:       : public CapacityScaling<GR, V, C, SetHeapTraits<T> > {
kpeter@807:       typedef  CapacityScaling<GR, V, C, SetHeapTraits<T> > Create;
kpeter@807:     };
kpeter@807: 
kpeter@807:     /// @}
kpeter@807: 
kpeter@807:   public:
kpeter@807: 
kpeter@806:     /// \brief Constructor.
kpeter@805:     ///
kpeter@806:     /// The constructor of the class.
kpeter@805:     ///
kpeter@806:     /// \param graph The digraph the algorithm runs on.
kpeter@806:     CapacityScaling(const GR& graph) :
kpeter@806:       _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph),
kpeter@806:       INF(std::numeric_limits<Value>::has_infinity ?
kpeter@806:           std::numeric_limits<Value>::infinity() :
kpeter@806:           std::numeric_limits<Value>::max())
kpeter@805:     {
kpeter@812:       // Check the number types
kpeter@806:       LEMON_ASSERT(std::numeric_limits<Value>::is_signed,
kpeter@806:         "The flow type of CapacityScaling must be signed");
kpeter@806:       LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
kpeter@806:         "The cost type of CapacityScaling must be signed");
kpeter@806: 
kpeter@806:       // Resize vectors
kpeter@806:       _node_num = countNodes(_graph);
kpeter@806:       _arc_num = countArcs(_graph);
kpeter@806:       _res_arc_num = 2 * (_arc_num + _node_num);
kpeter@806:       _root = _node_num;
kpeter@806:       ++_node_num;
kpeter@806: 
kpeter@806:       _first_out.resize(_node_num + 1);
kpeter@806:       _forward.resize(_res_arc_num);
kpeter@806:       _source.resize(_res_arc_num);
kpeter@806:       _target.resize(_res_arc_num);
kpeter@806:       _reverse.resize(_res_arc_num);
kpeter@806: 
kpeter@806:       _lower.resize(_res_arc_num);
kpeter@806:       _upper.resize(_res_arc_num);
kpeter@806:       _cost.resize(_res_arc_num);
kpeter@806:       _supply.resize(_node_num);
kpeter@806:       
kpeter@806:       _res_cap.resize(_res_arc_num);
kpeter@806:       _pi.resize(_node_num);
kpeter@806:       _excess.resize(_node_num);
kpeter@806:       _pred.resize(_node_num);
kpeter@806: 
kpeter@806:       // Copy the graph
kpeter@806:       int i = 0, j = 0, k = 2 * _arc_num + _node_num - 1;
kpeter@806:       for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@806:         _node_id[n] = i;
kpeter@805:       }
kpeter@806:       i = 0;
kpeter@806:       for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@806:         _first_out[i] = j;
kpeter@806:         for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) {
kpeter@806:           _arc_idf[a] = j;
kpeter@806:           _forward[j] = true;
kpeter@806:           _source[j] = i;
kpeter@806:           _target[j] = _node_id[_graph.runningNode(a)];
kpeter@806:         }
kpeter@806:         for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) {
kpeter@806:           _arc_idb[a] = j;
kpeter@806:           _forward[j] = false;
kpeter@806:           _source[j] = i;
kpeter@806:           _target[j] = _node_id[_graph.runningNode(a)];
kpeter@806:         }
kpeter@806:         _forward[j] = false;
kpeter@806:         _source[j] = i;
kpeter@806:         _target[j] = _root;
kpeter@806:         _reverse[j] = k;
kpeter@806:         _forward[k] = true;
kpeter@806:         _source[k] = _root;
kpeter@806:         _target[k] = i;
kpeter@806:         _reverse[k] = j;
kpeter@806:         ++j; ++k;
kpeter@806:       }
kpeter@806:       _first_out[i] = j;
kpeter@806:       _first_out[_node_num] = k;
kpeter@805:       for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@806:         int fi = _arc_idf[a];
kpeter@806:         int bi = _arc_idb[a];
kpeter@806:         _reverse[fi] = bi;
kpeter@806:         _reverse[bi] = fi;
kpeter@805:       }
kpeter@806:       
kpeter@806:       // Reset parameters
kpeter@806:       reset();
kpeter@805:     }
kpeter@805: 
kpeter@806:     /// \name Parameters
kpeter@806:     /// The parameters of the algorithm can be specified using these
kpeter@806:     /// functions.
kpeter@806: 
kpeter@806:     /// @{
kpeter@806: 
kpeter@806:     /// \brief Set the lower bounds on the arcs.
kpeter@805:     ///
kpeter@806:     /// This function sets the lower bounds on the arcs.
kpeter@806:     /// If it is not used before calling \ref run(), the lower bounds
kpeter@806:     /// will be set to zero on all arcs.
kpeter@805:     ///
kpeter@806:     /// \param map An arc map storing the lower bounds.
kpeter@806:     /// Its \c Value type must be convertible to the \c Value type
kpeter@806:     /// of the algorithm.
kpeter@806:     ///
kpeter@806:     /// \return <tt>(*this)</tt>
kpeter@806:     template <typename LowerMap>
kpeter@806:     CapacityScaling& lowerMap(const LowerMap& map) {
kpeter@806:       _have_lower = true;
kpeter@806:       for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@806:         _lower[_arc_idf[a]] = map[a];
kpeter@806:         _lower[_arc_idb[a]] = map[a];
kpeter@805:       }
kpeter@805:       return *this;
kpeter@805:     }
kpeter@805: 
kpeter@806:     /// \brief Set the upper bounds (capacities) on the arcs.
kpeter@805:     ///
kpeter@806:     /// This function sets the upper bounds (capacities) on the arcs.
kpeter@806:     /// If it is not used before calling \ref run(), the upper bounds
kpeter@806:     /// will be set to \ref INF on all arcs (i.e. the flow value will be
kpeter@812:     /// unbounded from above).
kpeter@805:     ///
kpeter@806:     /// \param map An arc map storing the upper bounds.
kpeter@806:     /// Its \c Value type must be convertible to the \c Value type
kpeter@806:     /// of the algorithm.
kpeter@806:     ///
kpeter@806:     /// \return <tt>(*this)</tt>
kpeter@806:     template<typename UpperMap>
kpeter@806:     CapacityScaling& upperMap(const UpperMap& map) {
kpeter@806:       for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@806:         _upper[_arc_idf[a]] = map[a];
kpeter@805:       }
kpeter@805:       return *this;
kpeter@805:     }
kpeter@805: 
kpeter@806:     /// \brief Set the costs of the arcs.
kpeter@806:     ///
kpeter@806:     /// This function sets the costs of the arcs.
kpeter@806:     /// If it is not used before calling \ref run(), the costs
kpeter@806:     /// will be set to \c 1 on all arcs.
kpeter@806:     ///
kpeter@806:     /// \param map An arc map storing the costs.
kpeter@806:     /// Its \c Value type must be convertible to the \c Cost type
kpeter@806:     /// of the algorithm.
kpeter@806:     ///
kpeter@806:     /// \return <tt>(*this)</tt>
kpeter@806:     template<typename CostMap>
kpeter@806:     CapacityScaling& costMap(const CostMap& map) {
kpeter@806:       for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@806:         _cost[_arc_idf[a]] =  map[a];
kpeter@806:         _cost[_arc_idb[a]] = -map[a];
kpeter@806:       }
kpeter@806:       return *this;
kpeter@806:     }
kpeter@806: 
kpeter@806:     /// \brief Set the supply values of the nodes.
kpeter@806:     ///
kpeter@806:     /// This function sets the supply values of the nodes.
kpeter@806:     /// If neither this function nor \ref stSupply() is used before
kpeter@806:     /// calling \ref run(), the supply of each node will be set to zero.
kpeter@806:     ///
kpeter@806:     /// \param map A node map storing the supply values.
kpeter@806:     /// Its \c Value type must be convertible to the \c Value type
kpeter@806:     /// of the algorithm.
kpeter@806:     ///
kpeter@806:     /// \return <tt>(*this)</tt>
kpeter@806:     template<typename SupplyMap>
kpeter@806:     CapacityScaling& supplyMap(const SupplyMap& map) {
kpeter@806:       for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@806:         _supply[_node_id[n]] = map[n];
kpeter@806:       }
kpeter@806:       return *this;
kpeter@806:     }
kpeter@806: 
kpeter@806:     /// \brief Set single source and target nodes and a supply value.
kpeter@806:     ///
kpeter@806:     /// This function sets a single source node and a single target node
kpeter@806:     /// and the required flow value.
kpeter@806:     /// If neither this function nor \ref supplyMap() is used before
kpeter@806:     /// calling \ref run(), the supply of each node will be set to zero.
kpeter@806:     ///
kpeter@806:     /// Using this function has the same effect as using \ref supplyMap()
kpeter@806:     /// with such a map in which \c k is assigned to \c s, \c -k is
kpeter@806:     /// assigned to \c t and all other nodes have zero supply value.
kpeter@806:     ///
kpeter@806:     /// \param s The source node.
kpeter@806:     /// \param t The target node.
kpeter@806:     /// \param k The required amount of flow from node \c s to node \c t
kpeter@806:     /// (i.e. the supply of \c s and the demand of \c t).
kpeter@806:     ///
kpeter@806:     /// \return <tt>(*this)</tt>
kpeter@806:     CapacityScaling& stSupply(const Node& s, const Node& t, Value k) {
kpeter@806:       for (int i = 0; i != _node_num; ++i) {
kpeter@806:         _supply[i] = 0;
kpeter@806:       }
kpeter@806:       _supply[_node_id[s]] =  k;
kpeter@806:       _supply[_node_id[t]] = -k;
kpeter@806:       return *this;
kpeter@806:     }
kpeter@806:     
kpeter@806:     /// @}
kpeter@806: 
kpeter@805:     /// \name Execution control
kpeter@807:     /// The algorithm can be executed using \ref run().
kpeter@805: 
kpeter@805:     /// @{
kpeter@805: 
kpeter@805:     /// \brief Run the algorithm.
kpeter@805:     ///
kpeter@805:     /// This function runs the algorithm.
kpeter@806:     /// The paramters can be specified using functions \ref lowerMap(),
kpeter@806:     /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@806:     /// For example,
kpeter@806:     /// \code
kpeter@806:     ///   CapacityScaling<ListDigraph> cs(graph);
kpeter@806:     ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@806:     ///     .supplyMap(sup).run();
kpeter@806:     /// \endcode
kpeter@806:     ///
kpeter@806:     /// This function can be called more than once. All the parameters
kpeter@806:     /// that have been given are kept for the next call, unless
kpeter@806:     /// \ref reset() is called, thus only the modified parameters
kpeter@806:     /// have to be set again. See \ref reset() for examples.
kpeter@812:     /// However, the underlying digraph must not be modified after this
kpeter@810:     /// class have been constructed, since it copies and extends the graph.
kpeter@805:     ///
kpeter@810:     /// \param factor The capacity scaling factor. It must be larger than
kpeter@810:     /// one to use scaling. If it is less or equal to one, then scaling
kpeter@810:     /// will be disabled.
kpeter@805:     ///
kpeter@806:     /// \return \c INFEASIBLE if no feasible flow exists,
kpeter@806:     /// \n \c OPTIMAL if the problem has optimal solution
kpeter@806:     /// (i.e. it is feasible and bounded), and the algorithm has found
kpeter@806:     /// optimal flow and node potentials (primal and dual solutions),
kpeter@806:     /// \n \c UNBOUNDED if the digraph contains an arc of negative cost
kpeter@806:     /// and infinite upper bound. It means that the objective function
kpeter@812:     /// is unbounded on that arc, however, note that it could actually be
kpeter@806:     /// bounded over the feasible flows, but this algroithm cannot handle
kpeter@806:     /// these cases.
kpeter@806:     ///
kpeter@806:     /// \see ProblemType
kpeter@810:     ProblemType run(int factor = 4) {
kpeter@810:       _factor = factor;
kpeter@810:       ProblemType pt = init();
kpeter@806:       if (pt != OPTIMAL) return pt;
kpeter@806:       return start();
kpeter@806:     }
kpeter@806: 
kpeter@806:     /// \brief Reset all the parameters that have been given before.
kpeter@806:     ///
kpeter@806:     /// This function resets all the paramaters that have been given
kpeter@806:     /// before using functions \ref lowerMap(), \ref upperMap(),
kpeter@806:     /// \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@806:     ///
kpeter@806:     /// It is useful for multiple run() calls. If this function is not
kpeter@806:     /// used, all the parameters given before are kept for the next
kpeter@806:     /// \ref run() call.
kpeter@810:     /// However, the underlying digraph must not be modified after this
kpeter@806:     /// class have been constructed, since it copies and extends the graph.
kpeter@806:     ///
kpeter@806:     /// For example,
kpeter@806:     /// \code
kpeter@806:     ///   CapacityScaling<ListDigraph> cs(graph);
kpeter@806:     ///
kpeter@806:     ///   // First run
kpeter@806:     ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
kpeter@806:     ///     .supplyMap(sup).run();
kpeter@806:     ///
kpeter@806:     ///   // Run again with modified cost map (reset() is not called,
kpeter@806:     ///   // so only the cost map have to be set again)
kpeter@806:     ///   cost[e] += 100;
kpeter@806:     ///   cs.costMap(cost).run();
kpeter@806:     ///
kpeter@806:     ///   // Run again from scratch using reset()
kpeter@806:     ///   // (the lower bounds will be set to zero on all arcs)
kpeter@806:     ///   cs.reset();
kpeter@806:     ///   cs.upperMap(capacity).costMap(cost)
kpeter@806:     ///     .supplyMap(sup).run();
kpeter@806:     /// \endcode
kpeter@806:     ///
kpeter@806:     /// \return <tt>(*this)</tt>
kpeter@806:     CapacityScaling& reset() {
kpeter@806:       for (int i = 0; i != _node_num; ++i) {
kpeter@806:         _supply[i] = 0;
kpeter@806:       }
kpeter@806:       for (int j = 0; j != _res_arc_num; ++j) {
kpeter@806:         _lower[j] = 0;
kpeter@806:         _upper[j] = INF;
kpeter@806:         _cost[j] = _forward[j] ? 1 : -1;
kpeter@806:       }
kpeter@806:       _have_lower = false;
kpeter@806:       return *this;
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@806:     /// The \ref run() function must be called before using them.
kpeter@805: 
kpeter@805:     /// @{
kpeter@805: 
kpeter@806:     /// \brief Return the total cost of the found flow.
kpeter@805:     ///
kpeter@806:     /// This function returns the total cost of the found flow.
kpeter@806:     /// Its complexity is O(e).
kpeter@806:     ///
kpeter@806:     /// \note The return type of the function can be specified as a
kpeter@806:     /// template parameter. For example,
kpeter@806:     /// \code
kpeter@806:     ///   cs.totalCost<double>();
kpeter@806:     /// \endcode
kpeter@806:     /// It is useful if the total cost cannot be stored in the \c Cost
kpeter@806:     /// type of the algorithm, which is the default return type of the
kpeter@806:     /// function.
kpeter@805:     ///
kpeter@805:     /// \pre \ref run() must be called before using this function.
kpeter@806:     template <typename Number>
kpeter@806:     Number totalCost() const {
kpeter@806:       Number c = 0;
kpeter@806:       for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@806:         int i = _arc_idb[a];
kpeter@806:         c += static_cast<Number>(_res_cap[i]) *
kpeter@806:              (-static_cast<Number>(_cost[i]));
kpeter@806:       }
kpeter@806:       return c;
kpeter@805:     }
kpeter@805: 
kpeter@806: #ifndef DOXYGEN
kpeter@806:     Cost totalCost() const {
kpeter@806:       return totalCost<Cost>();
kpeter@805:     }
kpeter@806: #endif
kpeter@805: 
kpeter@805:     /// \brief Return the flow on the given arc.
kpeter@805:     ///
kpeter@806:     /// This function returns the flow on the given arc.
kpeter@805:     ///
kpeter@805:     /// \pre \ref run() must be called before using this function.
kpeter@806:     Value flow(const Arc& a) const {
kpeter@806:       return _res_cap[_arc_idb[a]];
kpeter@805:     }
kpeter@805: 
kpeter@806:     /// \brief Return the flow map (the primal solution).
kpeter@805:     ///
kpeter@806:     /// This function copies the flow value on each arc into the given
kpeter@806:     /// map. The \c Value type of the algorithm must be convertible to
kpeter@806:     /// the \c Value type of the map.
kpeter@805:     ///
kpeter@805:     /// \pre \ref run() must be called before using this function.
kpeter@806:     template <typename FlowMap>
kpeter@806:     void flowMap(FlowMap &map) const {
kpeter@806:       for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@806:         map.set(a, _res_cap[_arc_idb[a]]);
kpeter@806:       }
kpeter@805:     }
kpeter@805: 
kpeter@806:     /// \brief Return the potential (dual value) of the given node.
kpeter@805:     ///
kpeter@806:     /// This function returns the potential (dual value) of the
kpeter@806:     /// given node.
kpeter@805:     ///
kpeter@805:     /// \pre \ref run() must be called before using this function.
kpeter@806:     Cost potential(const Node& n) const {
kpeter@806:       return _pi[_node_id[n]];
kpeter@806:     }
kpeter@806: 
kpeter@806:     /// \brief Return the potential map (the dual solution).
kpeter@806:     ///
kpeter@806:     /// This function copies the potential (dual value) of each node
kpeter@806:     /// into the given map.
kpeter@806:     /// The \c Cost type of the algorithm must be convertible to the
kpeter@806:     /// \c Value type of the map.
kpeter@806:     ///
kpeter@806:     /// \pre \ref run() must be called before using this function.
kpeter@806:     template <typename PotentialMap>
kpeter@806:     void potentialMap(PotentialMap &map) const {
kpeter@806:       for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@806:         map.set(n, _pi[_node_id[n]]);
kpeter@806:       }
kpeter@805:     }
kpeter@805: 
kpeter@805:     /// @}
kpeter@805: 
kpeter@805:   private:
kpeter@805: 
kpeter@806:     // Initialize the algorithm
kpeter@810:     ProblemType init() {
kpeter@821:       if (_node_num <= 1) return INFEASIBLE;
kpeter@805: 
kpeter@806:       // Check the sum of supply values
kpeter@806:       _sum_supply = 0;
kpeter@806:       for (int i = 0; i != _root; ++i) {
kpeter@806:         _sum_supply += _supply[i];
kpeter@805:       }
kpeter@806:       if (_sum_supply > 0) return INFEASIBLE;
kpeter@806:       
kpeter@811:       // Initialize vectors
kpeter@806:       for (int i = 0; i != _root; ++i) {
kpeter@806:         _pi[i] = 0;
kpeter@806:         _excess[i] = _supply[i];
kpeter@805:       }
kpeter@805: 
kpeter@806:       // Remove non-zero lower bounds
kpeter@811:       const Value MAX = std::numeric_limits<Value>::max();
kpeter@811:       int last_out;
kpeter@806:       if (_have_lower) {
kpeter@806:         for (int i = 0; i != _root; ++i) {
kpeter@811:           last_out = _first_out[i+1];
kpeter@811:           for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@806:             if (_forward[j]) {
kpeter@806:               Value c = _lower[j];
kpeter@806:               if (c >= 0) {
kpeter@811:                 _res_cap[j] = _upper[j] < MAX ? _upper[j] - c : INF;
kpeter@806:               } else {
kpeter@811:                 _res_cap[j] = _upper[j] < MAX + c ? _upper[j] - c : INF;
kpeter@806:               }
kpeter@806:               _excess[i] -= c;
kpeter@806:               _excess[_target[j]] += c;
kpeter@806:             } else {
kpeter@806:               _res_cap[j] = 0;
kpeter@806:             }
kpeter@806:           }
kpeter@806:         }
kpeter@806:       } else {
kpeter@806:         for (int j = 0; j != _res_arc_num; ++j) {
kpeter@806:           _res_cap[j] = _forward[j] ? _upper[j] : 0;
kpeter@806:         }
kpeter@806:       }
kpeter@805: 
kpeter@806:       // Handle negative costs
kpeter@811:       for (int i = 0; i != _root; ++i) {
kpeter@811:         last_out = _first_out[i+1] - 1;
kpeter@811:         for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@811:           Value rc = _res_cap[j];
kpeter@811:           if (_cost[j] < 0 && rc > 0) {
kpeter@811:             if (rc >= MAX) return UNBOUNDED;
kpeter@811:             _excess[i] -= rc;
kpeter@811:             _excess[_target[j]] += rc;
kpeter@811:             _res_cap[j] = 0;
kpeter@811:             _res_cap[_reverse[j]] += rc;
kpeter@806:           }
kpeter@806:         }
kpeter@806:       }
kpeter@806:       
kpeter@806:       // Handle GEQ supply type
kpeter@806:       if (_sum_supply < 0) {
kpeter@806:         _pi[_root] = 0;
kpeter@806:         _excess[_root] = -_sum_supply;
kpeter@806:         for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
kpeter@811:           int ra = _reverse[a];
kpeter@811:           _res_cap[a] = -_sum_supply + 1;
kpeter@811:           _res_cap[ra] = 0;
kpeter@806:           _cost[a] = 0;
kpeter@811:           _cost[ra] = 0;
kpeter@806:         }
kpeter@806:       } else {
kpeter@806:         _pi[_root] = 0;
kpeter@806:         _excess[_root] = 0;
kpeter@806:         for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
kpeter@811:           int ra = _reverse[a];
kpeter@806:           _res_cap[a] = 1;
kpeter@811:           _res_cap[ra] = 0;
kpeter@806:           _cost[a] = 0;
kpeter@811:           _cost[ra] = 0;
kpeter@806:         }
kpeter@806:       }
kpeter@806: 
kpeter@806:       // Initialize delta value
kpeter@810:       if (_factor > 1) {
kpeter@805:         // With scaling
kpeter@806:         Value max_sup = 0, max_dem = 0;
kpeter@806:         for (int i = 0; i != _node_num; ++i) {
kpeter@811:           Value ex = _excess[i];
kpeter@811:           if ( ex > max_sup) max_sup =  ex;
kpeter@811:           if (-ex > max_dem) max_dem = -ex;
kpeter@805:         }
kpeter@806:         Value max_cap = 0;
kpeter@806:         for (int j = 0; j != _res_arc_num; ++j) {
kpeter@806:           if (_res_cap[j] > max_cap) max_cap = _res_cap[j];
kpeter@805:         }
kpeter@805:         max_sup = std::min(std::min(max_sup, max_dem), max_cap);
kpeter@810:         for (_delta = 1; 2 * _delta <= max_sup; _delta *= 2) ;
kpeter@805:       } else {
kpeter@805:         // Without scaling
kpeter@805:         _delta = 1;
kpeter@805:       }
kpeter@805: 
kpeter@806:       return OPTIMAL;
kpeter@805:     }
kpeter@805: 
kpeter@806:     ProblemType start() {
kpeter@806:       // Execute the algorithm
kpeter@806:       ProblemType pt;
kpeter@805:       if (_delta > 1)
kpeter@806:         pt = startWithScaling();
kpeter@805:       else
kpeter@806:         pt = startWithoutScaling();
kpeter@806: 
kpeter@806:       // Handle non-zero lower bounds
kpeter@806:       if (_have_lower) {
kpeter@811:         int limit = _first_out[_root];
kpeter@811:         for (int j = 0; j != limit; ++j) {
kpeter@806:           if (!_forward[j]) _res_cap[j] += _lower[j];
kpeter@806:         }
kpeter@806:       }
kpeter@806: 
kpeter@806:       // Shift potentials if necessary
kpeter@806:       Cost pr = _pi[_root];
kpeter@806:       if (_sum_supply < 0 || pr > 0) {
kpeter@806:         for (int i = 0; i != _node_num; ++i) {
kpeter@806:           _pi[i] -= pr;
kpeter@806:         }        
kpeter@806:       }
kpeter@806:       
kpeter@806:       return pt;
kpeter@805:     }
kpeter@805: 
kpeter@806:     // Execute the capacity scaling algorithm
kpeter@806:     ProblemType startWithScaling() {
kpeter@807:       // Perform capacity scaling phases
kpeter@806:       int s, t;
kpeter@806:       ResidualDijkstra _dijkstra(*this);
kpeter@805:       while (true) {
kpeter@806:         // Saturate all arcs not satisfying the optimality condition
kpeter@811:         int last_out;
kpeter@806:         for (int u = 0; u != _node_num; ++u) {
kpeter@811:           last_out = _sum_supply < 0 ?
kpeter@811:             _first_out[u+1] : _first_out[u+1] - 1;
kpeter@811:           for (int a = _first_out[u]; a != last_out; ++a) {
kpeter@806:             int v = _target[a];
kpeter@806:             Cost c = _cost[a] + _pi[u] - _pi[v];
kpeter@806:             Value rc = _res_cap[a];
kpeter@806:             if (c < 0 && rc >= _delta) {
kpeter@806:               _excess[u] -= rc;
kpeter@806:               _excess[v] += rc;
kpeter@806:               _res_cap[a] = 0;
kpeter@806:               _res_cap[_reverse[a]] += rc;
kpeter@806:             }
kpeter@805:           }
kpeter@805:         }
kpeter@805: 
kpeter@806:         // Find excess nodes and deficit nodes
kpeter@805:         _excess_nodes.clear();
kpeter@805:         _deficit_nodes.clear();
kpeter@806:         for (int u = 0; u != _node_num; ++u) {
kpeter@811:           Value ex = _excess[u];
kpeter@811:           if (ex >=  _delta) _excess_nodes.push_back(u);
kpeter@811:           if (ex <= -_delta) _deficit_nodes.push_back(u);
kpeter@805:         }
kpeter@805:         int next_node = 0, next_def_node = 0;
kpeter@805: 
kpeter@806:         // Find augmenting shortest paths
kpeter@805:         while (next_node < int(_excess_nodes.size())) {
kpeter@806:           // Check 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@806:           // Run Dijkstra in the residual network
kpeter@805:           s = _excess_nodes[next_node];
kpeter@806:           if ((t = _dijkstra.run(s, _delta)) == -1) {
kpeter@805:             if (_delta > 1) {
kpeter@805:               ++next_node;
kpeter@805:               continue;
kpeter@805:             }
kpeter@806:             return INFEASIBLE;
kpeter@805:           }
kpeter@805: 
kpeter@806:           // Augment along a shortest path from s to t
kpeter@806:           Value d = std::min(_excess[s], -_excess[t]);
kpeter@806:           int u = t;
kpeter@806:           int a;
kpeter@805:           if (d > _delta) {
kpeter@806:             while ((a = _pred[u]) != -1) {
kpeter@806:               if (_res_cap[a] < d) d = _res_cap[a];
kpeter@806:               u = _source[a];
kpeter@805:             }
kpeter@805:           }
kpeter@805:           u = t;
kpeter@806:           while ((a = _pred[u]) != -1) {
kpeter@806:             _res_cap[a] -= d;
kpeter@806:             _res_cap[_reverse[a]] += d;
kpeter@806:             u = _source[a];
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@810:         _delta = _delta <= _factor ? 1 : _delta / _factor;
kpeter@805:       }
kpeter@805: 
kpeter@806:       return OPTIMAL;
kpeter@805:     }
kpeter@805: 
kpeter@806:     // Execute the successive shortest path algorithm
kpeter@806:     ProblemType startWithoutScaling() {
kpeter@806:       // Find excess nodes
kpeter@806:       _excess_nodes.clear();
kpeter@806:       for (int i = 0; i != _node_num; ++i) {
kpeter@806:         if (_excess[i] > 0) _excess_nodes.push_back(i);
kpeter@806:       }
kpeter@806:       if (_excess_nodes.size() == 0) return OPTIMAL;
kpeter@805:       int next_node = 0;
kpeter@805: 
kpeter@806:       // Find shortest paths
kpeter@806:       int s, t;
kpeter@806:       ResidualDijkstra _dijkstra(*this);
kpeter@805:       while ( _excess[_excess_nodes[next_node]] > 0 ||
kpeter@805:               ++next_node < int(_excess_nodes.size()) )
kpeter@805:       {
kpeter@806:         // Run Dijkstra in the residual network
kpeter@805:         s = _excess_nodes[next_node];
kpeter@806:         if ((t = _dijkstra.run(s)) == -1) return INFEASIBLE;
kpeter@805: 
kpeter@806:         // Augment along a shortest path from s to t
kpeter@806:         Value d = std::min(_excess[s], -_excess[t]);
kpeter@806:         int u = t;
kpeter@806:         int a;
kpeter@805:         if (d > 1) {
kpeter@806:           while ((a = _pred[u]) != -1) {
kpeter@806:             if (_res_cap[a] < d) d = _res_cap[a];
kpeter@806:             u = _source[a];
kpeter@805:           }
kpeter@805:         }
kpeter@805:         u = t;
kpeter@806:         while ((a = _pred[u]) != -1) {
kpeter@806:           _res_cap[a] -= d;
kpeter@806:           _res_cap[_reverse[a]] += d;
kpeter@806:           u = _source[a];
kpeter@805:         }
kpeter@805:         _excess[s] -= d;
kpeter@805:         _excess[t] += d;
kpeter@805:       }
kpeter@805: 
kpeter@806:       return OPTIMAL;
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