diff --git a/lemon/cycle_canceling.h b/lemon/cycle_canceling.h new file mode 100644 --- /dev/null +++ b/lemon/cycle_canceling.h @@ -0,0 +1,559 @@ +/* -*- C++ -*- + * + * This file is a part of LEMON, a generic C++ optimization library + * + * Copyright (C) 2003-2008 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport + * (Egervary Research Group on Combinatorial Optimization, EGRES). + * + * Permission to use, modify and distribute this software is granted + * provided that this copyright notice appears in all copies. For + * precise terms see the accompanying LICENSE file. + * + * This software is provided "AS IS" with no warranty of any kind, + * express or implied, and with no claim as to its suitability for any + * purpose. + * + */ + +#ifndef LEMON_CYCLE_CANCELING_H +#define LEMON_CYCLE_CANCELING_H + +/// \ingroup min_cost_flow +/// +/// \file +/// \brief Cycle-canceling algorithm for finding a minimum cost flow. + +#include +#include +#include + +#include +#include +#include + +namespace lemon { + + /// \addtogroup min_cost_flow + /// @{ + + /// \brief Implementation of a cycle-canceling algorithm for + /// finding a minimum cost flow. + /// + /// \ref CycleCanceling implements a cycle-canceling algorithm for + /// finding a minimum cost flow. + /// + /// \tparam Digraph The digraph type the algorithm runs on. + /// \tparam LowerMap The type of the lower bound map. + /// \tparam CapacityMap The type of the capacity (upper bound) map. + /// \tparam CostMap The type of the cost (length) map. + /// \tparam SupplyMap The type of the supply map. + /// + /// \warning + /// - Arc capacities and costs should be \e non-negative \e integers. + /// - Supply values should be \e signed \e integers. + /// - The value types of the maps should be convertible to each other. + /// - \c CostMap::Value must be signed type. + /// + /// \note By default the \ref BellmanFord "Bellman-Ford" algorithm is + /// used for negative cycle detection with limited iteration number. + /// However \ref CycleCanceling also provides the "Minimum Mean + /// Cycle-Canceling" algorithm, which is \e strongly \e polynomial, + /// but rather slower in practice. + /// To use this version of the algorithm, call \ref run() with \c true + /// parameter. + /// + /// \author Peter Kovacs + template < typename Digraph, + typename LowerMap = typename Digraph::template ArcMap, + typename CapacityMap = typename Digraph::template ArcMap, + typename CostMap = typename Digraph::template ArcMap, + typename SupplyMap = typename Digraph::template NodeMap > + class CycleCanceling + { + TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); + + typedef typename CapacityMap::Value Capacity; + typedef typename CostMap::Value Cost; + typedef typename SupplyMap::Value Supply; + typedef typename Digraph::template ArcMap CapacityArcMap; + typedef typename Digraph::template NodeMap SupplyNodeMap; + + typedef ResidualDigraph< const Digraph, + CapacityArcMap, CapacityArcMap > ResDigraph; + typedef typename ResDigraph::Node ResNode; + typedef typename ResDigraph::NodeIt ResNodeIt; + typedef typename ResDigraph::Arc ResArc; + typedef typename ResDigraph::ArcIt ResArcIt; + + public: + + /// The type of the flow map. + typedef typename Digraph::template ArcMap FlowMap; + /// The type of the potential map. + typedef typename Digraph::template NodeMap PotentialMap; + + private: + + /// \brief Map adaptor class for handling residual arc costs. + /// + /// Map adaptor class for handling residual arc costs. + class ResidualCostMap : public MapBase + { + private: + + const CostMap &_cost_map; + + public: + + ///\e + ResidualCostMap(const CostMap &cost_map) : _cost_map(cost_map) {} + + ///\e + Cost operator[](const ResArc &e) const { + return ResDigraph::forward(e) ? _cost_map[e] : -_cost_map[e]; + } + + }; //class ResidualCostMap + + private: + + // The maximum number of iterations for the first execution of the + // Bellman-Ford algorithm. It should be at least 2. + static const int BF_FIRST_LIMIT = 2; + // The iteration limit for the Bellman-Ford algorithm is multiplied + // by BF_LIMIT_FACTOR/100 in every round. + static const int BF_LIMIT_FACTOR = 150; + + private: + + // The digraph the algorithm runs on + const Digraph &_graph; + // The original lower bound map + const LowerMap *_lower; + // The modified capacity map + CapacityArcMap _capacity; + // The original cost map + const CostMap &_cost; + // The modified supply map + SupplyNodeMap _supply; + bool _valid_supply; + + // Arc map of the current flow + FlowMap *_flow; + bool _local_flow; + // Node map of the current potentials + PotentialMap *_potential; + bool _local_potential; + + // The residual digraph + ResDigraph *_res_graph; + // The residual cost map + ResidualCostMap _res_cost; + + public: + + /// \brief General constructor (with lower bounds). + /// + /// General constructor (with lower bounds). + /// + /// \param digraph The digraph the algorithm runs on. + /// \param lower The lower bounds of the arcs. + /// \param capacity The capacities (upper bounds) of the arcs. + /// \param cost The cost (length) values of the arcs. + /// \param supply The supply values of the nodes (signed). + CycleCanceling( const Digraph &digraph, + const LowerMap &lower, + const CapacityMap &capacity, + const CostMap &cost, + const SupplyMap &supply ) : + _graph(digraph), _lower(&lower), _capacity(digraph), _cost(cost), + _supply(digraph), _flow(NULL), _local_flow(false), + _potential(NULL), _local_potential(false), + _res_graph(NULL), _res_cost(_cost) + { + // Check the sum of supply values + Supply sum = 0; + for (NodeIt n(_graph); n != INVALID; ++n) { + _supply[n] = supply[n]; + sum += _supply[n]; + } + _valid_supply = sum == 0; + + // Remove non-zero lower bounds + for (ArcIt e(_graph); e != INVALID; ++e) { + _capacity[e] = capacity[e]; + if (lower[e] != 0) { + _capacity[e] -= lower[e]; + _supply[_graph.source(e)] -= lower[e]; + _supply[_graph.target(e)] += lower[e]; + } + } + } +/* + /// \brief General constructor (without lower bounds). + /// + /// General constructor (without lower bounds). + /// + /// \param digraph The digraph the algorithm runs on. + /// \param capacity The capacities (upper bounds) of the arcs. + /// \param cost The cost (length) values of the arcs. + /// \param supply The supply values of the nodes (signed). + CycleCanceling( const Digraph &digraph, + const CapacityMap &capacity, + const CostMap &cost, + const SupplyMap &supply ) : + _graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost), + _supply(supply), _flow(NULL), _local_flow(false), + _potential(NULL), _local_potential(false), _res_graph(NULL), + _res_cost(_cost) + { + // Check the sum of supply values + Supply sum = 0; + for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n]; + _valid_supply = sum == 0; + } + + /// \brief Simple constructor (with lower bounds). + /// + /// Simple constructor (with lower bounds). + /// + /// \param digraph The digraph the algorithm runs on. + /// \param lower The lower bounds of the arcs. + /// \param capacity The capacities (upper bounds) of the arcs. + /// \param cost The cost (length) values of the arcs. + /// \param s The source node. + /// \param t The target node. + /// \param flow_value The required amount of flow from node \c s + /// to node \c t (i.e. the supply of \c s and the demand of \c t). + CycleCanceling( const Digraph &digraph, + const LowerMap &lower, + const CapacityMap &capacity, + const CostMap &cost, + Node s, Node t, + Supply flow_value ) : + _graph(digraph), _lower(&lower), _capacity(capacity), _cost(cost), + _supply(digraph, 0), _flow(NULL), _local_flow(false), + _potential(NULL), _local_potential(false), _res_graph(NULL), + _res_cost(_cost) + { + // Remove non-zero lower bounds + _supply[s] = flow_value; + _supply[t] = -flow_value; + for (ArcIt e(_graph); e != INVALID; ++e) { + if (lower[e] != 0) { + _capacity[e] -= lower[e]; + _supply[_graph.source(e)] -= lower[e]; + _supply[_graph.target(e)] += lower[e]; + } + } + _valid_supply = true; + } + + /// \brief Simple constructor (without lower bounds). + /// + /// Simple constructor (without lower bounds). + /// + /// \param digraph The digraph the algorithm runs on. + /// \param capacity The capacities (upper bounds) of the arcs. + /// \param cost The cost (length) values of the arcs. + /// \param s The source node. + /// \param t The target node. + /// \param flow_value The required amount of flow from node \c s + /// to node \c t (i.e. the supply of \c s and the demand of \c t). + CycleCanceling( const Digraph &digraph, + const CapacityMap &capacity, + const CostMap &cost, + Node s, Node t, + Supply flow_value ) : + _graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost), + _supply(digraph, 0), _flow(NULL), _local_flow(false), + _potential(NULL), _local_potential(false), _res_graph(NULL), + _res_cost(_cost) + { + _supply[s] = flow_value; + _supply[t] = -flow_value; + _valid_supply = true; + } +*/ + /// Destructor. + ~CycleCanceling() { + if (_local_flow) delete _flow; + if (_local_potential) delete _potential; + delete _res_graph; + } + + /// \brief Set the flow map. + /// + /// Set the flow map. + /// + /// \return \c (*this) + CycleCanceling& flowMap(FlowMap &map) { + if (_local_flow) { + delete _flow; + _local_flow = false; + } + _flow = ↦ + return *this; + } + + /// \brief Set the potential map. + /// + /// Set the potential map. + /// + /// \return \c (*this) + CycleCanceling& potentialMap(PotentialMap &map) { + if (_local_potential) { + delete _potential; + _local_potential = false; + } + _potential = ↦ + return *this; + } + + /// \name Execution control + + /// @{ + + /// \brief Run the algorithm. + /// + /// Run the algorithm. + /// + /// \param min_mean_cc Set this parameter to \c true to run the + /// "Minimum Mean Cycle-Canceling" algorithm, which is strongly + /// polynomial, but rather slower in practice. + /// + /// \return \c true if a feasible flow can be found. + bool run(bool min_mean_cc = false) { + return init() && start(min_mean_cc); + } + + /// @} + + /// \name Query Functions + /// The result of the algorithm can be obtained using these + /// functions.\n + /// \ref lemon::CycleCanceling::run() "run()" must be called before + /// using them. + + /// @{ + + /// \brief Return a const reference to the arc map storing the + /// found flow. + /// + /// Return a const reference to the arc map storing the found flow. + /// + /// \pre \ref run() must be called before using this function. + const FlowMap& flowMap() const { + return *_flow; + } + + /// \brief Return a const reference to the node map storing the + /// found potentials (the dual solution). + /// + /// Return a const reference to the node map storing the found + /// potentials (the dual solution). + /// + /// \pre \ref run() must be called before using this function. + const PotentialMap& potentialMap() const { + return *_potential; + } + + /// \brief Return the flow on the given arc. + /// + /// Return the flow on the given arc. + /// + /// \pre \ref run() must be called before using this function. + Capacity flow(const Arc& arc) const { + return (*_flow)[arc]; + } + + /// \brief Return the potential of the given node. + /// + /// Return the potential of the given node. + /// + /// \pre \ref run() must be called before using this function. + Cost potential(const Node& node) const { + return (*_potential)[node]; + } + + /// \brief Return the total cost of the found flow. + /// + /// Return the total cost of the found flow. The complexity of the + /// function is \f$ O(e) \f$. + /// + /// \pre \ref run() must be called before using this function. + Cost totalCost() const { + Cost c = 0; + for (ArcIt e(_graph); e != INVALID; ++e) + c += (*_flow)[e] * _cost[e]; + return c; + } + + /// @} + + private: + + /// Initialize the algorithm. + bool init() { + if (!_valid_supply) return false; + + // Initializing flow and potential maps + if (!_flow) { + _flow = new FlowMap(_graph); + _local_flow = true; + } + if (!_potential) { + _potential = new PotentialMap(_graph); + _local_potential = true; + } + + _res_graph = new ResDigraph(_graph, _capacity, *_flow); + + // Finding a feasible flow using Circulation + Circulation< Digraph, ConstMap, CapacityArcMap, + SupplyMap > + circulation( _graph, constMap(Capacity(0)), _capacity, + _supply ); + return circulation.flowMap(*_flow).run(); + } + + bool start(bool min_mean_cc) { + if (min_mean_cc) + startMinMean(); + else + start(); + + // Handling non-zero lower bounds + if (_lower) { + for (ArcIt e(_graph); e != INVALID; ++e) + (*_flow)[e] += (*_lower)[e]; + } + return true; + } + + /// \brief Execute the algorithm using \ref BellmanFord. + /// + /// Execute the algorithm using the \ref BellmanFord + /// "Bellman-Ford" algorithm for negative cycle detection with + /// successively larger limit for the number of iterations. + void start() { + typename BellmanFord::PredMap pred(*_res_graph); + typename ResDigraph::template NodeMap visited(*_res_graph); + std::vector cycle; + int node_num = countNodes(_graph); + + int length_bound = BF_FIRST_LIMIT; + bool optimal = false; + while (!optimal) { + BellmanFord bf(*_res_graph, _res_cost); + bf.predMap(pred); + bf.init(0); + int iter_num = 0; + bool cycle_found = false; + while (!cycle_found) { + int curr_iter_num = iter_num + length_bound <= node_num ? + length_bound : node_num - iter_num; + iter_num += curr_iter_num; + int real_iter_num = curr_iter_num; + for (int i = 0; i < curr_iter_num; ++i) { + if (bf.processNextWeakRound()) { + real_iter_num = i; + break; + } + } + if (real_iter_num < curr_iter_num) { + // Optimal flow is found + optimal = true; + // Setting node potentials + for (NodeIt n(_graph); n != INVALID; ++n) + (*_potential)[n] = bf.dist(n); + break; + } else { + // Searching for node disjoint negative cycles + for (ResNodeIt n(*_res_graph); n != INVALID; ++n) + visited[n] = 0; + int id = 0; + for (ResNodeIt n(*_res_graph); n != INVALID; ++n) { + if (visited[n] > 0) continue; + visited[n] = ++id; + ResNode u = pred[n] == INVALID ? + INVALID : _res_graph->source(pred[n]); + while (u != INVALID && visited[u] == 0) { + visited[u] = id; + u = pred[u] == INVALID ? + INVALID : _res_graph->source(pred[u]); + } + if (u != INVALID && visited[u] == id) { + // Finding the negative cycle + cycle_found = true; + cycle.clear(); + ResArc e = pred[u]; + cycle.push_back(e); + Capacity d = _res_graph->residualCapacity(e); + while (_res_graph->source(e) != u) { + cycle.push_back(e = pred[_res_graph->source(e)]); + if (_res_graph->residualCapacity(e) < d) + d = _res_graph->residualCapacity(e); + } + + // Augmenting along the cycle + for (int i = 0; i < int(cycle.size()); ++i) + _res_graph->augment(cycle[i], d); + } + } + } + + if (!cycle_found) + length_bound = length_bound * BF_LIMIT_FACTOR / 100; + } + } + } + + /// \brief Execute the algorithm using \ref Howard. + /// + /// Execute the algorithm using \ref Howard for negative + /// cycle detection. + void startMinMean() { + typedef Path ResPath; + Howard mmc(*_res_graph, _res_cost); + ResPath cycle; + + mmc.cycle(cycle); + if (mmc.findMinMean()) { + while (mmc.cycleLength() < 0) { + // Finding the cycle + mmc.findCycle(); + + // Finding the largest flow amount that can be augmented + // along the cycle + Capacity delta = 0; + for (typename ResPath::ArcIt e(cycle); e != INVALID; ++e) { + if (delta == 0 || _res_graph->residualCapacity(e) < delta) + delta = _res_graph->residualCapacity(e); + } + + // Augmenting along the cycle + for (typename ResPath::ArcIt e(cycle); e != INVALID; ++e) + _res_graph->augment(e, delta); + + // Finding the minimum cycle mean for the modified residual + // digraph + if (!mmc.findMinMean()) break; + } + } + + // Computing node potentials + BellmanFord bf(*_res_graph, _res_cost); + bf.init(0); bf.start(); + for (NodeIt n(_graph); n != INVALID; ++n) + (*_potential)[n] = bf.dist(n); + } + + }; //class CycleCanceling + + ///@} + +} //namespace lemon + +#endif //LEMON_CYCLE_CANCELING_H