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diff --git a/extern/quadriflow/3rd/lemon-1.3.1/lemon/cycle_canceling.h b/extern/quadriflow/3rd/lemon-1.3.1/lemon/cycle_canceling.h new file mode 100644 index 00000000000..646d299e3ec --- /dev/null +++ b/extern/quadriflow/3rd/lemon-1.3.1/lemon/cycle_canceling.h @@ -0,0 +1,1230 @@ +/* -*- mode: C++; indent-tabs-mode: nil; -*- + * + * This file is a part of LEMON, a generic C++ optimization library. + * + * Copyright (C) 2003-2013 + * 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_algs +/// \file +/// \brief Cycle-canceling algorithms for finding a minimum cost flow. + +#include <vector> +#include <limits> + +#include <lemon/core.h> +#include <lemon/maps.h> +#include <lemon/path.h> +#include <lemon/math.h> +#include <lemon/static_graph.h> +#include <lemon/adaptors.h> +#include <lemon/circulation.h> +#include <lemon/bellman_ford.h> +#include <lemon/howard_mmc.h> +#include <lemon/hartmann_orlin_mmc.h> + +namespace lemon { + + /// \addtogroup min_cost_flow_algs + /// @{ + + /// \brief Implementation of cycle-canceling algorithms for + /// finding a \ref min_cost_flow "minimum cost flow". + /// + /// \ref CycleCanceling implements three different cycle-canceling + /// algorithms for finding a \ref min_cost_flow "minimum cost flow" + /// \cite amo93networkflows, \cite klein67primal, + /// \cite goldberg89cyclecanceling. + /// The most efficent one is the \ref CANCEL_AND_TIGHTEN + /// "Cancel-and-Tighten" algorithm, thus it is the default method. + /// It runs in strongly polynomial time \f$O(n^2 m^2 \log n)\f$, + /// but in practice, it is typically orders of magnitude slower than + /// the scaling algorithms and \ref NetworkSimplex. + /// (For more information, see \ref min_cost_flow_algs "the module page".) + /// + /// Most of the parameters of the problem (except for the digraph) + /// can be given using separate functions, and the algorithm can be + /// executed using the \ref run() function. If some parameters are not + /// specified, then default values will be used. + /// + /// \tparam GR The digraph type the algorithm runs on. + /// \tparam V The number type used for flow amounts, capacity bounds + /// and supply values in the algorithm. By default, it is \c int. + /// \tparam C The number type used for costs and potentials in the + /// algorithm. By default, it is the same as \c V. + /// + /// \warning Both \c V and \c C must be signed number types. + /// \warning All input data (capacities, supply values, and costs) must + /// be integer. + /// \warning This algorithm does not support negative costs for + /// arcs having infinite upper bound. + /// + /// \note For more information about the three available methods, + /// see \ref Method. +#ifdef DOXYGEN + template <typename GR, typename V, typename C> +#else + template <typename GR, typename V = int, typename C = V> +#endif + class CycleCanceling + { + public: + + /// The type of the digraph + typedef GR Digraph; + /// The type of the flow amounts, capacity bounds and supply values + typedef V Value; + /// The type of the arc costs + typedef C Cost; + + public: + + /// \brief Problem type constants for the \c run() function. + /// + /// Enum type containing the problem type constants that can be + /// returned by the \ref run() function of the algorithm. + enum ProblemType { + /// The problem has no feasible solution (flow). + INFEASIBLE, + /// The problem has optimal solution (i.e. it is feasible and + /// bounded), and the algorithm has found optimal flow and node + /// potentials (primal and dual solutions). + OPTIMAL, + /// The digraph contains an arc of negative cost and infinite + /// upper bound. It means that the objective function is unbounded + /// on that arc, however, note that it could actually be bounded + /// over the feasible flows, but this algroithm cannot handle + /// these cases. + UNBOUNDED + }; + + /// \brief Constants for selecting the used method. + /// + /// Enum type containing constants for selecting the used method + /// for the \ref run() function. + /// + /// \ref CycleCanceling provides three different cycle-canceling + /// methods. By default, \ref CANCEL_AND_TIGHTEN "Cancel-and-Tighten" + /// is used, which is by far the most efficient and the most robust. + /// However, the other methods can be selected using the \ref run() + /// function with the proper parameter. + enum Method { + /// A simple cycle-canceling method, which uses the + /// \ref BellmanFord "Bellman-Ford" algorithm for detecting negative + /// cycles in the residual network. + /// The number of Bellman-Ford iterations is bounded by a successively + /// increased limit. + SIMPLE_CYCLE_CANCELING, + /// The "Minimum Mean Cycle-Canceling" algorithm, which is a + /// well-known strongly polynomial method + /// \cite goldberg89cyclecanceling. It improves along a + /// \ref min_mean_cycle "minimum mean cycle" in each iteration. + /// Its running time complexity is \f$O(n^2 m^3 \log n)\f$. + MINIMUM_MEAN_CYCLE_CANCELING, + /// The "Cancel-and-Tighten" algorithm, which can be viewed as an + /// improved version of the previous method + /// \cite goldberg89cyclecanceling. + /// It is faster both in theory and in practice, its running time + /// complexity is \f$O(n^2 m^2 \log n)\f$. + CANCEL_AND_TIGHTEN + }; + + private: + + TEMPLATE_DIGRAPH_TYPEDEFS(GR); + + typedef std::vector<int> IntVector; + typedef std::vector<double> DoubleVector; + typedef std::vector<Value> ValueVector; + typedef std::vector<Cost> CostVector; + typedef std::vector<char> BoolVector; + // Note: vector<char> is used instead of vector<bool> for efficiency reasons + + private: + + template <typename KT, typename VT> + class StaticVectorMap { + public: + typedef KT Key; + typedef VT Value; + + StaticVectorMap(std::vector<Value>& v) : _v(v) {} + + const Value& operator[](const Key& key) const { + return _v[StaticDigraph::id(key)]; + } + + Value& operator[](const Key& key) { + return _v[StaticDigraph::id(key)]; + } + + void set(const Key& key, const Value& val) { + _v[StaticDigraph::id(key)] = val; + } + + private: + std::vector<Value>& _v; + }; + + typedef StaticVectorMap<StaticDigraph::Node, Cost> CostNodeMap; + typedef StaticVectorMap<StaticDigraph::Arc, Cost> CostArcMap; + + private: + + + // Data related to the underlying digraph + const GR &_graph; + int _node_num; + int _arc_num; + int _res_node_num; + int _res_arc_num; + int _root; + + // Parameters of the problem + bool _has_lower; + Value _sum_supply; + + // Data structures for storing the digraph + IntNodeMap _node_id; + IntArcMap _arc_idf; + IntArcMap _arc_idb; + IntVector _first_out; + BoolVector _forward; + IntVector _source; + IntVector _target; + IntVector _reverse; + + // Node and arc data + ValueVector _lower; + ValueVector _upper; + CostVector _cost; + ValueVector _supply; + + ValueVector _res_cap; + CostVector _pi; + + // Data for a StaticDigraph structure + typedef std::pair<int, int> IntPair; + StaticDigraph _sgr; + std::vector<IntPair> _arc_vec; + std::vector<Cost> _cost_vec; + IntVector _id_vec; + CostArcMap _cost_map; + CostNodeMap _pi_map; + + public: + + /// \brief Constant for infinite upper bounds (capacities). + /// + /// Constant for infinite upper bounds (capacities). + /// It is \c std::numeric_limits<Value>::infinity() if available, + /// \c std::numeric_limits<Value>::max() otherwise. + const Value INF; + + public: + + /// \brief Constructor. + /// + /// The constructor of the class. + /// + /// \param graph The digraph the algorithm runs on. + CycleCanceling(const GR& graph) : + _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph), + _cost_map(_cost_vec), _pi_map(_pi), + INF(std::numeric_limits<Value>::has_infinity ? + std::numeric_limits<Value>::infinity() : + std::numeric_limits<Value>::max()) + { + // Check the number types + LEMON_ASSERT(std::numeric_limits<Value>::is_signed, + "The flow type of CycleCanceling must be signed"); + LEMON_ASSERT(std::numeric_limits<Cost>::is_signed, + "The cost type of CycleCanceling must be signed"); + + // Reset data structures + reset(); + } + + /// \name Parameters + /// The parameters of the algorithm can be specified using these + /// functions. + + /// @{ + + /// \brief Set the lower bounds on the arcs. + /// + /// This function sets the lower bounds on the arcs. + /// If it is not used before calling \ref run(), the lower bounds + /// will be set to zero on all arcs. + /// + /// \param map An arc map storing the lower bounds. + /// Its \c Value type must be convertible to the \c Value type + /// of the algorithm. + /// + /// \return <tt>(*this)</tt> + template <typename LowerMap> + CycleCanceling& lowerMap(const LowerMap& map) { + _has_lower = true; + for (ArcIt a(_graph); a != INVALID; ++a) { + _lower[_arc_idf[a]] = map[a]; + } + return *this; + } + + /// \brief Set the upper bounds (capacities) on the arcs. + /// + /// This function sets the upper bounds (capacities) on the arcs. + /// If it is not used before calling \ref run(), the upper bounds + /// will be set to \ref INF on all arcs (i.e. the flow value will be + /// unbounded from above). + /// + /// \param map An arc map storing the upper bounds. + /// Its \c Value type must be convertible to the \c Value type + /// of the algorithm. + /// + /// \return <tt>(*this)</tt> + template<typename UpperMap> + CycleCanceling& upperMap(const UpperMap& map) { + for (ArcIt a(_graph); a != INVALID; ++a) { + _upper[_arc_idf[a]] = map[a]; + } + return *this; + } + + /// \brief Set the costs of the arcs. + /// + /// This function sets the costs of the arcs. + /// If it is not used before calling \ref run(), the costs + /// will be set to \c 1 on all arcs. + /// + /// \param map An arc map storing the costs. + /// Its \c Value type must be convertible to the \c Cost type + /// of the algorithm. + /// + /// \return <tt>(*this)</tt> + template<typename CostMap> + CycleCanceling& costMap(const CostMap& map) { + for (ArcIt a(_graph); a != INVALID; ++a) { + _cost[_arc_idf[a]] = map[a]; + _cost[_arc_idb[a]] = -map[a]; + } + return *this; + } + + /// \brief Set the supply values of the nodes. + /// + /// This function sets the supply values of the nodes. + /// If neither this function nor \ref stSupply() is used before + /// calling \ref run(), the supply of each node will be set to zero. + /// + /// \param map A node map storing the supply values. + /// Its \c Value type must be convertible to the \c Value type + /// of the algorithm. + /// + /// \return <tt>(*this)</tt> + template<typename SupplyMap> + CycleCanceling& supplyMap(const SupplyMap& map) { + for (NodeIt n(_graph); n != INVALID; ++n) { + _supply[_node_id[n]] = map[n]; + } + return *this; + } + + /// \brief Set single source and target nodes and a supply value. + /// + /// This function sets a single source node and a single target node + /// and the required flow value. + /// If neither this function nor \ref supplyMap() is used before + /// calling \ref run(), the supply of each node will be set to zero. + /// + /// Using this function has the same effect as using \ref supplyMap() + /// with a map in which \c k is assigned to \c s, \c -k is + /// assigned to \c t and all other nodes have zero supply value. + /// + /// \param s The source node. + /// \param t The target node. + /// \param k 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). + /// + /// \return <tt>(*this)</tt> + CycleCanceling& stSupply(const Node& s, const Node& t, Value k) { + for (int i = 0; i != _res_node_num; ++i) { + _supply[i] = 0; + } + _supply[_node_id[s]] = k; + _supply[_node_id[t]] = -k; + return *this; + } + + /// @} + + /// \name Execution control + /// The algorithm can be executed using \ref run(). + + /// @{ + + /// \brief Run the algorithm. + /// + /// This function runs the algorithm. + /// The paramters can be specified using functions \ref lowerMap(), + /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(). + /// For example, + /// \code + /// CycleCanceling<ListDigraph> cc(graph); + /// cc.lowerMap(lower).upperMap(upper).costMap(cost) + /// .supplyMap(sup).run(); + /// \endcode + /// + /// This function can be called more than once. All the given parameters + /// are kept for the next call, unless \ref resetParams() or \ref reset() + /// is used, thus only the modified parameters have to be set again. + /// If the underlying digraph was also modified after the construction + /// of the class (or the last \ref reset() call), then the \ref reset() + /// function must be called. + /// + /// \param method The cycle-canceling method that will be used. + /// For more information, see \ref Method. + /// + /// \return \c INFEASIBLE if no feasible flow exists, + /// \n \c OPTIMAL if the problem has optimal solution + /// (i.e. it is feasible and bounded), and the algorithm has found + /// optimal flow and node potentials (primal and dual solutions), + /// \n \c UNBOUNDED if the digraph contains an arc of negative cost + /// and infinite upper bound. It means that the objective function + /// is unbounded on that arc, however, note that it could actually be + /// bounded over the feasible flows, but this algroithm cannot handle + /// these cases. + /// + /// \see ProblemType, Method + /// \see resetParams(), reset() + ProblemType run(Method method = CANCEL_AND_TIGHTEN) { + ProblemType pt = init(); + if (pt != OPTIMAL) return pt; + start(method); + return OPTIMAL; + } + + /// \brief Reset all the parameters that have been given before. + /// + /// This function resets all the paramaters that have been given + /// before using functions \ref lowerMap(), \ref upperMap(), + /// \ref costMap(), \ref supplyMap(), \ref stSupply(). + /// + /// It is useful for multiple \ref run() calls. Basically, all the given + /// parameters are kept for the next \ref run() call, unless + /// \ref resetParams() or \ref reset() is used. + /// If the underlying digraph was also modified after the construction + /// of the class or the last \ref reset() call, then the \ref reset() + /// function must be used, otherwise \ref resetParams() is sufficient. + /// + /// For example, + /// \code + /// CycleCanceling<ListDigraph> cs(graph); + /// + /// // First run + /// cc.lowerMap(lower).upperMap(upper).costMap(cost) + /// .supplyMap(sup).run(); + /// + /// // Run again with modified cost map (resetParams() is not called, + /// // so only the cost map have to be set again) + /// cost[e] += 100; + /// cc.costMap(cost).run(); + /// + /// // Run again from scratch using resetParams() + /// // (the lower bounds will be set to zero on all arcs) + /// cc.resetParams(); + /// cc.upperMap(capacity).costMap(cost) + /// .supplyMap(sup).run(); + /// \endcode + /// + /// \return <tt>(*this)</tt> + /// + /// \see reset(), run() + CycleCanceling& resetParams() { + for (int i = 0; i != _res_node_num; ++i) { + _supply[i] = 0; + } + int limit = _first_out[_root]; + for (int j = 0; j != limit; ++j) { + _lower[j] = 0; + _upper[j] = INF; + _cost[j] = _forward[j] ? 1 : -1; + } + for (int j = limit; j != _res_arc_num; ++j) { + _lower[j] = 0; + _upper[j] = INF; + _cost[j] = 0; + _cost[_reverse[j]] = 0; + } + _has_lower = false; + return *this; + } + + /// \brief Reset the internal data structures and all the parameters + /// that have been given before. + /// + /// This function resets the internal data structures and all the + /// paramaters that have been given before using functions \ref lowerMap(), + /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(). + /// + /// It is useful for multiple \ref run() calls. Basically, all the given + /// parameters are kept for the next \ref run() call, unless + /// \ref resetParams() or \ref reset() is used. + /// If the underlying digraph was also modified after the construction + /// of the class or the last \ref reset() call, then the \ref reset() + /// function must be used, otherwise \ref resetParams() is sufficient. + /// + /// See \ref resetParams() for examples. + /// + /// \return <tt>(*this)</tt> + /// + /// \see resetParams(), run() + CycleCanceling& reset() { + // Resize vectors + _node_num = countNodes(_graph); + _arc_num = countArcs(_graph); + _res_node_num = _node_num + 1; + _res_arc_num = 2 * (_arc_num + _node_num); + _root = _node_num; + + _first_out.resize(_res_node_num + 1); + _forward.resize(_res_arc_num); + _source.resize(_res_arc_num); + _target.resize(_res_arc_num); + _reverse.resize(_res_arc_num); + + _lower.resize(_res_arc_num); + _upper.resize(_res_arc_num); + _cost.resize(_res_arc_num); + _supply.resize(_res_node_num); + + _res_cap.resize(_res_arc_num); + _pi.resize(_res_node_num); + + _arc_vec.reserve(_res_arc_num); + _cost_vec.reserve(_res_arc_num); + _id_vec.reserve(_res_arc_num); + + // Copy the graph + int i = 0, j = 0, k = 2 * _arc_num + _node_num; + for (NodeIt n(_graph); n != INVALID; ++n, ++i) { + _node_id[n] = i; + } + i = 0; + for (NodeIt n(_graph); n != INVALID; ++n, ++i) { + _first_out[i] = j; + for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) { + _arc_idf[a] = j; + _forward[j] = true; + _source[j] = i; + _target[j] = _node_id[_graph.runningNode(a)]; + } + for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) { + _arc_idb[a] = j; + _forward[j] = false; + _source[j] = i; + _target[j] = _node_id[_graph.runningNode(a)]; + } + _forward[j] = false; + _source[j] = i; + _target[j] = _root; + _reverse[j] = k; + _forward[k] = true; + _source[k] = _root; + _target[k] = i; + _reverse[k] = j; + ++j; ++k; + } + _first_out[i] = j; + _first_out[_res_node_num] = k; + for (ArcIt a(_graph); a != INVALID; ++a) { + int fi = _arc_idf[a]; + int bi = _arc_idb[a]; + _reverse[fi] = bi; + _reverse[bi] = fi; + } + + // Reset parameters + resetParams(); + return *this; + } + + /// @} + + /// \name Query Functions + /// The results of the algorithm can be obtained using these + /// functions.\n + /// The \ref run() function must be called before using them. + + /// @{ + + /// \brief Return the total cost of the found flow. + /// + /// This function returns the total cost of the found flow. + /// Its complexity is O(m). + /// + /// \note The return type of the function can be specified as a + /// template parameter. For example, + /// \code + /// cc.totalCost<double>(); + /// \endcode + /// It is useful if the total cost cannot be stored in the \c Cost + /// type of the algorithm, which is the default return type of the + /// function. + /// + /// \pre \ref run() must be called before using this function. + template <typename Number> + Number totalCost() const { + Number c = 0; + for (ArcIt a(_graph); a != INVALID; ++a) { + int i = _arc_idb[a]; + c += static_cast<Number>(_res_cap[i]) * + (-static_cast<Number>(_cost[i])); + } + return c; + } + +#ifndef DOXYGEN + Cost totalCost() const { + return totalCost<Cost>(); + } +#endif + + /// \brief Return the flow on the given arc. + /// + /// This function returns the flow on the given arc. + /// + /// \pre \ref run() must be called before using this function. + Value flow(const Arc& a) const { + return _res_cap[_arc_idb[a]]; + } + + /// \brief Copy the flow values (the primal solution) into the + /// given map. + /// + /// This function copies the flow value on each arc into the given + /// map. The \c Value type of the algorithm must be convertible to + /// the \c Value type of the map. + /// + /// \pre \ref run() must be called before using this function. + template <typename FlowMap> + void flowMap(FlowMap &map) const { + for (ArcIt a(_graph); a != INVALID; ++a) { + map.set(a, _res_cap[_arc_idb[a]]); + } + } + + /// \brief Return the potential (dual value) of the given node. + /// + /// This function returns the potential (dual value) of the + /// given node. + /// + /// \pre \ref run() must be called before using this function. + Cost potential(const Node& n) const { + return static_cast<Cost>(_pi[_node_id[n]]); + } + + /// \brief Copy the potential values (the dual solution) into the + /// given map. + /// + /// This function copies the potential (dual value) of each node + /// into the given map. + /// The \c Cost type of the algorithm must be convertible to the + /// \c Value type of the map. + /// + /// \pre \ref run() must be called before using this function. + template <typename PotentialMap> + void potentialMap(PotentialMap &map) const { + for (NodeIt n(_graph); n != INVALID; ++n) { + map.set(n, static_cast<Cost>(_pi[_node_id[n]])); + } + } + + /// @} + + private: + + // Initialize the algorithm + ProblemType init() { + if (_res_node_num <= 1) return INFEASIBLE; + + // Check the sum of supply values + _sum_supply = 0; + for (int i = 0; i != _root; ++i) { + _sum_supply += _supply[i]; + } + if (_sum_supply > 0) return INFEASIBLE; + + // Check lower and upper bounds + LEMON_DEBUG(checkBoundMaps(), + "Upper bounds must be greater or equal to the lower bounds"); + + + // Initialize vectors + for (int i = 0; i != _res_node_num; ++i) { + _pi[i] = 0; + } + ValueVector excess(_supply); + + // Remove infinite upper bounds and check negative arcs + const Value MAX = std::numeric_limits<Value>::max(); + int last_out; + if (_has_lower) { + for (int i = 0; i != _root; ++i) { + last_out = _first_out[i+1]; + for (int j = _first_out[i]; j != last_out; ++j) { + if (_forward[j]) { + Value c = _cost[j] < 0 ? _upper[j] : _lower[j]; + if (c >= MAX) return UNBOUNDED; + excess[i] -= c; + excess[_target[j]] += c; + } + } + } + } else { + for (int i = 0; i != _root; ++i) { + last_out = _first_out[i+1]; + for (int j = _first_out[i]; j != last_out; ++j) { + if (_forward[j] && _cost[j] < 0) { + Value c = _upper[j]; + if (c >= MAX) return UNBOUNDED; + excess[i] -= c; + excess[_target[j]] += c; + } + } + } + } + Value ex, max_cap = 0; + for (int i = 0; i != _res_node_num; ++i) { + ex = excess[i]; + if (ex < 0) max_cap -= ex; + } + for (int j = 0; j != _res_arc_num; ++j) { + if (_upper[j] >= MAX) _upper[j] = max_cap; + } + + // Initialize maps for Circulation and remove non-zero lower bounds + ConstMap<Arc, Value> low(0); + typedef typename Digraph::template ArcMap<Value> ValueArcMap; + typedef typename Digraph::template NodeMap<Value> ValueNodeMap; + ValueArcMap cap(_graph), flow(_graph); + ValueNodeMap sup(_graph); + for (NodeIt n(_graph); n != INVALID; ++n) { + sup[n] = _supply[_node_id[n]]; + } + if (_has_lower) { + for (ArcIt a(_graph); a != INVALID; ++a) { + int j = _arc_idf[a]; + Value c = _lower[j]; + cap[a] = _upper[j] - c; + sup[_graph.source(a)] -= c; + sup[_graph.target(a)] += c; + } + } else { + for (ArcIt a(_graph); a != INVALID; ++a) { + cap[a] = _upper[_arc_idf[a]]; + } + } + + // Find a feasible flow using Circulation + Circulation<Digraph, ConstMap<Arc, Value>, ValueArcMap, ValueNodeMap> + circ(_graph, low, cap, sup); + if (!circ.flowMap(flow).run()) return INFEASIBLE; + + // Set residual capacities and handle GEQ supply type + if (_sum_supply < 0) { + for (ArcIt a(_graph); a != INVALID; ++a) { + Value fa = flow[a]; + _res_cap[_arc_idf[a]] = cap[a] - fa; + _res_cap[_arc_idb[a]] = fa; + sup[_graph.source(a)] -= fa; + sup[_graph.target(a)] += fa; + } + for (NodeIt n(_graph); n != INVALID; ++n) { + excess[_node_id[n]] = sup[n]; + } + for (int a = _first_out[_root]; a != _res_arc_num; ++a) { + int u = _target[a]; + int ra = _reverse[a]; + _res_cap[a] = -_sum_supply + 1; + _res_cap[ra] = -excess[u]; + _cost[a] = 0; + _cost[ra] = 0; + } + } else { + for (ArcIt a(_graph); a != INVALID; ++a) { + Value fa = flow[a]; + _res_cap[_arc_idf[a]] = cap[a] - fa; + _res_cap[_arc_idb[a]] = fa; + } + for (int a = _first_out[_root]; a != _res_arc_num; ++a) { + int ra = _reverse[a]; + _res_cap[a] = 1; + _res_cap[ra] = 0; + _cost[a] = 0; + _cost[ra] = 0; + } + } + + return OPTIMAL; + } + + // Check if the upper bound is greater than or equal to the lower bound + // on each forward arc. + bool checkBoundMaps() { + for (int j = 0; j != _res_arc_num; ++j) { + if (_forward[j] && _upper[j] < _lower[j]) return false; + } + return true; + } + + // Build a StaticDigraph structure containing the current + // residual network + void buildResidualNetwork() { + _arc_vec.clear(); + _cost_vec.clear(); + _id_vec.clear(); + for (int j = 0; j != _res_arc_num; ++j) { + if (_res_cap[j] > 0) { + _arc_vec.push_back(IntPair(_source[j], _target[j])); + _cost_vec.push_back(_cost[j]); + _id_vec.push_back(j); + } + } + _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end()); + } + + // Execute the algorithm and transform the results + void start(Method method) { + // Execute the algorithm + switch (method) { + case SIMPLE_CYCLE_CANCELING: + startSimpleCycleCanceling(); + break; + case MINIMUM_MEAN_CYCLE_CANCELING: + startMinMeanCycleCanceling(); + break; + case CANCEL_AND_TIGHTEN: + startCancelAndTighten(); + break; + } + + // Compute node potentials + if (method != SIMPLE_CYCLE_CANCELING) { + buildResidualNetwork(); + typename BellmanFord<StaticDigraph, CostArcMap> + ::template SetDistMap<CostNodeMap>::Create bf(_sgr, _cost_map); + bf.distMap(_pi_map); + bf.init(0); + bf.start(); + } + + // Handle non-zero lower bounds + if (_has_lower) { + int limit = _first_out[_root]; + for (int j = 0; j != limit; ++j) { + if (_forward[j]) _res_cap[_reverse[j]] += _lower[j]; + } + } + } + + // Execute the "Simple Cycle Canceling" method + void startSimpleCycleCanceling() { + // Constants for computing the iteration limits + const int BF_FIRST_LIMIT = 2; + const double BF_LIMIT_FACTOR = 1.5; + + typedef StaticVectorMap<StaticDigraph::Arc, Value> FilterMap; + typedef FilterArcs<StaticDigraph, FilterMap> ResDigraph; + typedef StaticVectorMap<StaticDigraph::Node, StaticDigraph::Arc> PredMap; + typedef typename BellmanFord<ResDigraph, CostArcMap> + ::template SetDistMap<CostNodeMap> + ::template SetPredMap<PredMap>::Create BF; + + // Build the residual network + _arc_vec.clear(); + _cost_vec.clear(); + for (int j = 0; j != _res_arc_num; ++j) { + _arc_vec.push_back(IntPair(_source[j], _target[j])); + _cost_vec.push_back(_cost[j]); + } + _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end()); + + FilterMap filter_map(_res_cap); + ResDigraph rgr(_sgr, filter_map); + std::vector<int> cycle; + std::vector<StaticDigraph::Arc> pred(_res_arc_num); + PredMap pred_map(pred); + BF bf(rgr, _cost_map); + bf.distMap(_pi_map).predMap(pred_map); + + int length_bound = BF_FIRST_LIMIT; + bool optimal = false; + while (!optimal) { + bf.init(0); + int iter_num = 0; + bool cycle_found = false; + while (!cycle_found) { + // Perform some iterations of the Bellman-Ford algorithm + 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; + break; + } else { + // Search for node disjoint negative cycles + std::vector<int> state(_res_node_num, 0); + int id = 0; + for (int u = 0; u != _res_node_num; ++u) { + if (state[u] != 0) continue; + ++id; + int v = u; + for (; v != -1 && state[v] == 0; v = pred[v] == INVALID ? + -1 : rgr.id(rgr.source(pred[v]))) { + state[v] = id; + } + if (v != -1 && state[v] == id) { + // A negative cycle is found + cycle_found = true; + cycle.clear(); + StaticDigraph::Arc a = pred[v]; + Value d, delta = _res_cap[rgr.id(a)]; + cycle.push_back(rgr.id(a)); + while (rgr.id(rgr.source(a)) != v) { + a = pred_map[rgr.source(a)]; + d = _res_cap[rgr.id(a)]; + if (d < delta) delta = d; + cycle.push_back(rgr.id(a)); + } + + // Augment along the cycle + for (int i = 0; i < int(cycle.size()); ++i) { + int j = cycle[i]; + _res_cap[j] -= delta; + _res_cap[_reverse[j]] += delta; + } + } + } + } + + // Increase iteration limit if no cycle is found + if (!cycle_found) { + length_bound = static_cast<int>(length_bound * BF_LIMIT_FACTOR); + } + } + } + } + + // Execute the "Minimum Mean Cycle Canceling" method + void startMinMeanCycleCanceling() { + typedef Path<StaticDigraph> SPath; + typedef typename SPath::ArcIt SPathArcIt; + typedef typename HowardMmc<StaticDigraph, CostArcMap> + ::template SetPath<SPath>::Create HwMmc; + typedef typename HartmannOrlinMmc<StaticDigraph, CostArcMap> + ::template SetPath<SPath>::Create HoMmc; + + const double HW_ITER_LIMIT_FACTOR = 1.0; + const int HW_ITER_LIMIT_MIN_VALUE = 5; + + const int hw_iter_limit = + std::max(static_cast<int>(HW_ITER_LIMIT_FACTOR * _node_num), + HW_ITER_LIMIT_MIN_VALUE); + + SPath cycle; + HwMmc hw_mmc(_sgr, _cost_map); + hw_mmc.cycle(cycle); + buildResidualNetwork(); + while (true) { + + typename HwMmc::TerminationCause hw_tc = + hw_mmc.findCycleMean(hw_iter_limit); + if (hw_tc == HwMmc::ITERATION_LIMIT) { + // Howard's algorithm reached the iteration limit, start a + // strongly polynomial algorithm instead + HoMmc ho_mmc(_sgr, _cost_map); + ho_mmc.cycle(cycle); + // Find a minimum mean cycle (Hartmann-Orlin algorithm) + if (!(ho_mmc.findCycleMean() && ho_mmc.cycleCost() < 0)) break; + ho_mmc.findCycle(); + } else { + // Find a minimum mean cycle (Howard algorithm) + if (!(hw_tc == HwMmc::OPTIMAL && hw_mmc.cycleCost() < 0)) break; + hw_mmc.findCycle(); + } + + // Compute delta value + Value delta = INF; + for (SPathArcIt a(cycle); a != INVALID; ++a) { + Value d = _res_cap[_id_vec[_sgr.id(a)]]; + if (d < delta) delta = d; + } + + // Augment along the cycle + for (SPathArcIt a(cycle); a != INVALID; ++a) { + int j = _id_vec[_sgr.id(a)]; + _res_cap[j] -= delta; + _res_cap[_reverse[j]] += delta; + } + + // Rebuild the residual network + buildResidualNetwork(); + } + } + + // Execute the "Cancel-and-Tighten" method + void startCancelAndTighten() { + // Constants for the min mean cycle computations + const double LIMIT_FACTOR = 1.0; + const int MIN_LIMIT = 5; + const double HW_ITER_LIMIT_FACTOR = 1.0; + const int HW_ITER_LIMIT_MIN_VALUE = 5; + + const int hw_iter_limit = + std::max(static_cast<int>(HW_ITER_LIMIT_FACTOR * _node_num), + HW_ITER_LIMIT_MIN_VALUE); + + // Contruct auxiliary data vectors + DoubleVector pi(_res_node_num, 0.0); + IntVector level(_res_node_num); + BoolVector reached(_res_node_num); + BoolVector processed(_res_node_num); + IntVector pred_node(_res_node_num); + IntVector pred_arc(_res_node_num); + std::vector<int> stack(_res_node_num); + std::vector<int> proc_vector(_res_node_num); + + // Initialize epsilon + double epsilon = 0; + for (int a = 0; a != _res_arc_num; ++a) { + if (_res_cap[a] > 0 && -_cost[a] > epsilon) + epsilon = -_cost[a]; + } + + // Start phases + Tolerance<double> tol; + tol.epsilon(1e-6); + int limit = int(LIMIT_FACTOR * std::sqrt(double(_res_node_num))); + if (limit < MIN_LIMIT) limit = MIN_LIMIT; + int iter = limit; + while (epsilon * _res_node_num >= 1) { + // Find and cancel cycles in the admissible network using DFS + for (int u = 0; u != _res_node_num; ++u) { + reached[u] = false; + processed[u] = false; + } + int stack_head = -1; + int proc_head = -1; + for (int start = 0; start != _res_node_num; ++start) { + if (reached[start]) continue; + + // New start node + reached[start] = true; + pred_arc[start] = -1; + pred_node[start] = -1; + + // Find the first admissible outgoing arc + double p = pi[start]; + int a = _first_out[start]; + int last_out = _first_out[start+1]; + for (; a != last_out && (_res_cap[a] == 0 || + !tol.negative(_cost[a] + p - pi[_target[a]])); ++a) ; + if (a == last_out) { + processed[start] = true; + proc_vector[++proc_head] = start; + continue; + } + stack[++stack_head] = a; + + while (stack_head >= 0) { + int sa = stack[stack_head]; + int u = _source[sa]; + int v = _target[sa]; + + if (!reached[v]) { + // A new node is reached + reached[v] = true; + pred_node[v] = u; + pred_arc[v] = sa; + p = pi[v]; + a = _first_out[v]; + last_out = _first_out[v+1]; + for (; a != last_out && (_res_cap[a] == 0 || + !tol.negative(_cost[a] + p - pi[_target[a]])); ++a) ; + stack[++stack_head] = a == last_out ? -1 : a; + } else { + if (!processed[v]) { + // A cycle is found + int n, w = u; + Value d, delta = _res_cap[sa]; + for (n = u; n != v; n = pred_node[n]) { + d = _res_cap[pred_arc[n]]; + if (d <= delta) { + delta = d; + w = pred_node[n]; + } + } + + // Augment along the cycle + _res_cap[sa] -= delta; + _res_cap[_reverse[sa]] += delta; + for (n = u; n != v; n = pred_node[n]) { + int pa = pred_arc[n]; + _res_cap[pa] -= delta; + _res_cap[_reverse[pa]] += delta; + } + for (n = u; stack_head > 0 && n != w; n = pred_node[n]) { + --stack_head; + reached[n] = false; + } + u = w; + } + v = u; + + // Find the next admissible outgoing arc + p = pi[v]; + a = stack[stack_head] + 1; + last_out = _first_out[v+1]; + for (; a != last_out && (_res_cap[a] == 0 || + !tol.negative(_cost[a] + p - pi[_target[a]])); ++a) ; + stack[stack_head] = a == last_out ? -1 : a; + } + + while (stack_head >= 0 && stack[stack_head] == -1) { + processed[v] = true; + proc_vector[++proc_head] = v; + if (--stack_head >= 0) { + // Find the next admissible outgoing arc + v = _source[stack[stack_head]]; + p = pi[v]; + a = stack[stack_head] + 1; + last_out = _first_out[v+1]; + for (; a != last_out && (_res_cap[a] == 0 || + !tol.negative(_cost[a] + p - pi[_target[a]])); ++a) ; + stack[stack_head] = a == last_out ? -1 : a; + } + } + } + } + + // Tighten potentials and epsilon + if (--iter > 0) { + for (int u = 0; u != _res_node_num; ++u) { + level[u] = 0; + } + for (int i = proc_head; i > 0; --i) { + int u = proc_vector[i]; + double p = pi[u]; + int l = level[u] + 1; + int last_out = _first_out[u+1]; + for (int a = _first_out[u]; a != last_out; ++a) { + int v = _target[a]; + if (_res_cap[a] > 0 && tol.negative(_cost[a] + p - pi[v]) && + l > level[v]) level[v] = l; + } + } + + // Modify potentials + double q = std::numeric_limits<double>::max(); + for (int u = 0; u != _res_node_num; ++u) { + int lu = level[u]; + double p, pu = pi[u]; + int last_out = _first_out[u+1]; + for (int a = _first_out[u]; a != last_out; ++a) { + if (_res_cap[a] == 0) continue; + int v = _target[a]; + int ld = lu - level[v]; + if (ld > 0) { + p = (_cost[a] + pu - pi[v] + epsilon) / (ld + 1); + if (p < q) q = p; + } + } + } + for (int u = 0; u != _res_node_num; ++u) { + pi[u] -= q * level[u]; + } + + // Modify epsilon + epsilon = 0; + for (int u = 0; u != _res_node_num; ++u) { + double curr, pu = pi[u]; + int last_out = _first_out[u+1]; + for (int a = _first_out[u]; a != last_out; ++a) { + if (_res_cap[a] == 0) continue; + curr = _cost[a] + pu - pi[_target[a]]; + if (-curr > epsilon) epsilon = -curr; + } + } + } else { + typedef HowardMmc<StaticDigraph, CostArcMap> HwMmc; + typedef HartmannOrlinMmc<StaticDigraph, CostArcMap> HoMmc; + typedef typename BellmanFord<StaticDigraph, CostArcMap> + ::template SetDistMap<CostNodeMap>::Create BF; + + // Set epsilon to the minimum cycle mean + Cost cycle_cost = 0; + int cycle_size = 1; + buildResidualNetwork(); + HwMmc hw_mmc(_sgr, _cost_map); + if (hw_mmc.findCycleMean(hw_iter_limit) == HwMmc::ITERATION_LIMIT) { + // Howard's algorithm reached the iteration limit, start a + // strongly polynomial algorithm instead + HoMmc ho_mmc(_sgr, _cost_map); + ho_mmc.findCycleMean(); + epsilon = -ho_mmc.cycleMean(); + cycle_cost = ho_mmc.cycleCost(); + cycle_size = ho_mmc.cycleSize(); + } else { + // Set epsilon + epsilon = -hw_mmc.cycleMean(); + cycle_cost = hw_mmc.cycleCost(); + cycle_size = hw_mmc.cycleSize(); + } + + // Compute feasible potentials for the current epsilon + for (int i = 0; i != int(_cost_vec.size()); ++i) { + _cost_vec[i] = cycle_size * _cost_vec[i] - cycle_cost; + } + BF bf(_sgr, _cost_map); + bf.distMap(_pi_map); + bf.init(0); + bf.start(); + for (int u = 0; u != _res_node_num; ++u) { + pi[u] = static_cast<double>(_pi[u]) / cycle_size; + } + + iter = limit; + } + } + } + + }; //class CycleCanceling + + ///@} + +} //namespace lemon + +#endif //LEMON_CYCLE_CANCELING_H |