alpar@877: /* -*- mode: C++; indent-tabs-mode: nil; -*-
kpeter@805: *
alpar@877: * This file is a part of LEMON, a generic C++ optimization library.
kpeter@805: *
alpar@877: * Copyright (C) 2003-2010
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@825: /// 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@825: /// algorithm. By default, it is the same as \c V.
kpeter@825: /// \tparam TR The traits class that defines various types used by the
kpeter@825: /// algorithm. By default, it is \ref CapacityScalingDefaultTraits
kpeter@825: /// "CapacityScalingDefaultTraits<GR, V, C>".
kpeter@825: /// In most cases, this parameter should not be set directly,
kpeter@825: /// consider to use the named template parameters instead.
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: };
alpar@877:
kpeter@806: private:
kpeter@806:
kpeter@806: TEMPLATE_DIGRAPH_TYPEDEFS(GR);
kpeter@806:
kpeter@806: typedef std::vector<int> IntVector;
kpeter@806: typedef std::vector<Value> ValueVector;
kpeter@806: typedef std::vector<Cost> CostVector;
kpeter@839: typedef std::vector<char> BoolVector;
kpeter@839: // Note: vector<char> is used instead of vector<bool> for efficiency reasons
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:
alpar@877:
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;
alpar@877:
kpeter@806: IntVector _proc_nodes;
kpeter@806: CostVector _dist;
alpar@877:
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@863: protected:
kpeter@863:
kpeter@863: CapacityScaling() {}
kpeter@863:
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@830: // Reset data structures
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: }
alpar@877:
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@830: /// This function can be called more than once. All the given parameters
kpeter@830: /// are kept for the next call, unless \ref resetParams() or \ref reset()
kpeter@830: /// is used, thus only the modified parameters have to be set again.
kpeter@830: /// If the underlying digraph was also modified after the construction
kpeter@830: /// of the class (or the last \ref reset() call), then the \ref reset()
kpeter@830: /// function must be called.
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@830: /// \see resetParams(), reset()
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@830: /// It is useful for multiple \ref run() calls. Basically, all the given
kpeter@830: /// parameters are kept for the next \ref run() call, unless
kpeter@830: /// \ref resetParams() or \ref reset() is used.
kpeter@830: /// If the underlying digraph was also modified after the construction
kpeter@830: /// of the class or the last \ref reset() call, then the \ref reset()
kpeter@830: /// function must be used, otherwise \ref resetParams() is sufficient.
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@830: /// // Run again with modified cost map (resetParams() 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@830: /// // Run again from scratch using resetParams()
kpeter@806: /// // (the lower bounds will be set to zero on all arcs)
kpeter@830: /// cs.resetParams();
kpeter@806: /// cs.upperMap(capacity).costMap(cost)
kpeter@806: /// .supplyMap(sup).run();
kpeter@806: /// \endcode
kpeter@806: ///
kpeter@806: /// \return <tt>(*this)</tt>
kpeter@830: ///
kpeter@830: /// \see reset(), run()
kpeter@830: CapacityScaling& resetParams() {
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@830: /// \brief Reset the internal data structures and all the parameters
kpeter@830: /// that have been given before.
kpeter@830: ///
kpeter@830: /// This function resets the internal data structures and all the
kpeter@830: /// paramaters that have been given before using functions \ref lowerMap(),
kpeter@830: /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
kpeter@830: ///
kpeter@830: /// It is useful for multiple \ref run() calls. Basically, all the given
kpeter@830: /// parameters are kept for the next \ref run() call, unless
kpeter@830: /// \ref resetParams() or \ref reset() is used.
kpeter@830: /// If the underlying digraph was also modified after the construction
kpeter@830: /// of the class or the last \ref reset() call, then the \ref reset()
kpeter@830: /// function must be used, otherwise \ref resetParams() is sufficient.
kpeter@830: ///
kpeter@830: /// See \ref resetParams() for examples.
kpeter@830: ///
kpeter@830: /// \return <tt>(*this)</tt>
kpeter@830: ///
kpeter@830: /// \see resetParams(), run()
kpeter@830: CapacityScaling& reset() {
kpeter@830: // Resize vectors
kpeter@830: _node_num = countNodes(_graph);
kpeter@830: _arc_num = countArcs(_graph);
kpeter@830: _res_arc_num = 2 * (_arc_num + _node_num);
kpeter@830: _root = _node_num;
kpeter@830: ++_node_num;
kpeter@830:
kpeter@830: _first_out.resize(_node_num + 1);
kpeter@830: _forward.resize(_res_arc_num);
kpeter@830: _source.resize(_res_arc_num);
kpeter@830: _target.resize(_res_arc_num);
kpeter@830: _reverse.resize(_res_arc_num);
kpeter@830:
kpeter@830: _lower.resize(_res_arc_num);
kpeter@830: _upper.resize(_res_arc_num);
kpeter@830: _cost.resize(_res_arc_num);
kpeter@830: _supply.resize(_node_num);
alpar@877:
kpeter@830: _res_cap.resize(_res_arc_num);
kpeter@830: _pi.resize(_node_num);
kpeter@830: _excess.resize(_node_num);
kpeter@830: _pred.resize(_node_num);
kpeter@830:
kpeter@830: // Copy the graph
kpeter@830: int i = 0, j = 0, k = 2 * _arc_num + _node_num - 1;
kpeter@830: for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@830: _node_id[n] = i;
kpeter@830: }
kpeter@830: i = 0;
kpeter@830: for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
kpeter@830: _first_out[i] = j;
kpeter@830: for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) {
kpeter@830: _arc_idf[a] = j;
kpeter@830: _forward[j] = true;
kpeter@830: _source[j] = i;
kpeter@830: _target[j] = _node_id[_graph.runningNode(a)];
kpeter@830: }
kpeter@830: for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) {
kpeter@830: _arc_idb[a] = j;
kpeter@830: _forward[j] = false;
kpeter@830: _source[j] = i;
kpeter@830: _target[j] = _node_id[_graph.runningNode(a)];
kpeter@830: }
kpeter@830: _forward[j] = false;
kpeter@830: _source[j] = i;
kpeter@830: _target[j] = _root;
kpeter@830: _reverse[j] = k;
kpeter@830: _forward[k] = true;
kpeter@830: _source[k] = _root;
kpeter@830: _target[k] = i;
kpeter@830: _reverse[k] = j;
kpeter@830: ++j; ++k;
kpeter@830: }
kpeter@830: _first_out[i] = j;
kpeter@830: _first_out[_node_num] = k;
kpeter@830: for (ArcIt a(_graph); a != INVALID; ++a) {
kpeter@830: int fi = _arc_idf[a];
kpeter@830: int bi = _arc_idb[a];
kpeter@830: _reverse[fi] = bi;
kpeter@830: _reverse[bi] = fi;
kpeter@830: }
alpar@877:
kpeter@830: // Reset parameters
kpeter@830: resetParams();
kpeter@830: return *this;
kpeter@830: }
kpeter@830:
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;
alpar@877:
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: }
alpar@877:
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@839: Value max_sup = 0, max_dem = 0, max_cap = 0;
kpeter@839: for (int i = 0; i != _root; ++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@839: int last_out = _first_out[i+1] - 1;
kpeter@839: for (int j = _first_out[i]; j != last_out; ++j) {
kpeter@839: if (_res_cap[j] > max_cap) max_cap = _res_cap[j];
kpeter@839: }
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;
alpar@877: }
kpeter@806: }
alpar@877:
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