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diff --git a/extern/quadriflow/3rd/lemon-1.3.1/lemon/network_simplex.h b/extern/quadriflow/3rd/lemon-1.3.1/lemon/network_simplex.h new file mode 100644 index 00000000000..6ccad33e68e --- /dev/null +++ b/extern/quadriflow/3rd/lemon-1.3.1/lemon/network_simplex.h @@ -0,0 +1,1659 @@ +/* -*- 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_NETWORK_SIMPLEX_H +#define LEMON_NETWORK_SIMPLEX_H + +/// \ingroup min_cost_flow_algs +/// +/// \file +/// \brief Network Simplex algorithm for finding a minimum cost flow. + +#include <vector> +#include <limits> +#include <algorithm> + +#include <lemon/core.h> +#include <lemon/math.h> + +namespace lemon { + + /// \addtogroup min_cost_flow_algs + /// @{ + + /// \brief Implementation of the primal Network Simplex algorithm + /// for finding a \ref min_cost_flow "minimum cost flow". + /// + /// \ref NetworkSimplex implements the primal Network Simplex algorithm + /// for finding a \ref min_cost_flow "minimum cost flow" + /// \cite amo93networkflows, \cite dantzig63linearprog, + /// \cite kellyoneill91netsimplex. + /// This algorithm is a highly efficient specialized version of the + /// linear programming simplex method directly for the minimum cost + /// flow problem. + /// + /// In general, \ref NetworkSimplex and \ref CostScaling are the fastest + /// implementations available in LEMON for solving this problem. + /// (For more information, see \ref min_cost_flow_algs "the module page".) + /// Furthermore, this class supports both directions of the supply/demand + /// inequality constraints. For more information, see \ref SupplyType. + /// + /// 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. + /// + /// \note %NetworkSimplex provides five different pivot rule + /// implementations, from which the most efficient one is used + /// by default. For more information, see \ref PivotRule. + template <typename GR, typename V = int, typename C = V> + class NetworkSimplex + { + public: + + /// 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 objective function of the problem is unbounded, i.e. + /// there is a directed cycle having negative total cost and + /// infinite upper bound. + UNBOUNDED + }; + + /// \brief Constants for selecting the type of the supply constraints. + /// + /// Enum type containing constants for selecting the supply type, + /// i.e. the direction of the inequalities in the supply/demand + /// constraints of the \ref min_cost_flow "minimum cost flow problem". + /// + /// The default supply type is \c GEQ, the \c LEQ type can be + /// selected using \ref supplyType(). + /// The equality form is a special case of both supply types. + enum SupplyType { + /// This option means that there are <em>"greater or equal"</em> + /// supply/demand constraints in the definition of the problem. + GEQ, + /// This option means that there are <em>"less or equal"</em> + /// supply/demand constraints in the definition of the problem. + LEQ + }; + + /// \brief Constants for selecting the pivot rule. + /// + /// Enum type containing constants for selecting the pivot rule for + /// the \ref run() function. + /// + /// \ref NetworkSimplex provides five different implementations for + /// the pivot strategy that significantly affects the running time + /// of the algorithm. + /// According to experimental tests conducted on various problem + /// instances, \ref BLOCK_SEARCH "Block Search" and + /// \ref ALTERING_LIST "Altering Candidate List" rules turned out + /// to be the most efficient. + /// Since \ref BLOCK_SEARCH "Block Search" is a simpler strategy that + /// seemed to be slightly more robust, it is used by default. + /// However, another pivot rule can easily be selected using the + /// \ref run() function with the proper parameter. + enum PivotRule { + + /// The \e First \e Eligible pivot rule. + /// The next eligible arc is selected in a wraparound fashion + /// in every iteration. + FIRST_ELIGIBLE, + + /// The \e Best \e Eligible pivot rule. + /// The best eligible arc is selected in every iteration. + BEST_ELIGIBLE, + + /// The \e Block \e Search pivot rule. + /// A specified number of arcs are examined in every iteration + /// in a wraparound fashion and the best eligible arc is selected + /// from this block. + BLOCK_SEARCH, + + /// The \e Candidate \e List pivot rule. + /// In a major iteration a candidate list is built from eligible arcs + /// in a wraparound fashion and in the following minor iterations + /// the best eligible arc is selected from this list. + CANDIDATE_LIST, + + /// The \e Altering \e Candidate \e List pivot rule. + /// It is a modified version of the Candidate List method. + /// It keeps only a few of the best eligible arcs from the former + /// candidate list and extends this list in every iteration. + ALTERING_LIST + }; + + private: + + TEMPLATE_DIGRAPH_TYPEDEFS(GR); + + typedef std::vector<int> IntVector; + typedef std::vector<Value> ValueVector; + typedef std::vector<Cost> CostVector; + typedef std::vector<signed char> CharVector; + // Note: vector<signed char> is used instead of vector<ArcState> and + // vector<ArcDirection> for efficiency reasons + + // State constants for arcs + enum ArcState { + STATE_UPPER = -1, + STATE_TREE = 0, + STATE_LOWER = 1 + }; + + // Direction constants for tree arcs + enum ArcDirection { + DIR_DOWN = -1, + DIR_UP = 1 + }; + + private: + + // Data related to the underlying digraph + const GR &_graph; + int _node_num; + int _arc_num; + int _all_arc_num; + int _search_arc_num; + + // Parameters of the problem + bool _has_lower; + SupplyType _stype; + Value _sum_supply; + + // Data structures for storing the digraph + IntNodeMap _node_id; + IntArcMap _arc_id; + IntVector _source; + IntVector _target; + bool _arc_mixing; + + // Node and arc data + ValueVector _lower; + ValueVector _upper; + ValueVector _cap; + CostVector _cost; + ValueVector _supply; + ValueVector _flow; + CostVector _pi; + + // Data for storing the spanning tree structure + IntVector _parent; + IntVector _pred; + IntVector _thread; + IntVector _rev_thread; + IntVector _succ_num; + IntVector _last_succ; + CharVector _pred_dir; + CharVector _state; + IntVector _dirty_revs; + int _root; + + // Temporary data used in the current pivot iteration + int in_arc, join, u_in, v_in, u_out, v_out; + Value delta; + + const Value MAX; + + 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; + + private: + + // Implementation of the First Eligible pivot rule + class FirstEligiblePivotRule + { + private: + + // References to the NetworkSimplex class + const IntVector &_source; + const IntVector &_target; + const CostVector &_cost; + const CharVector &_state; + const CostVector &_pi; + int &_in_arc; + int _search_arc_num; + + // Pivot rule data + int _next_arc; + + public: + + // Constructor + FirstEligiblePivotRule(NetworkSimplex &ns) : + _source(ns._source), _target(ns._target), + _cost(ns._cost), _state(ns._state), _pi(ns._pi), + _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), + _next_arc(0) + {} + + // Find next entering arc + bool findEnteringArc() { + Cost c; + for (int e = _next_arc; e != _search_arc_num; ++e) { + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); + if (c < 0) { + _in_arc = e; + _next_arc = e + 1; + return true; + } + } + for (int e = 0; e != _next_arc; ++e) { + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); + if (c < 0) { + _in_arc = e; + _next_arc = e + 1; + return true; + } + } + return false; + } + + }; //class FirstEligiblePivotRule + + + // Implementation of the Best Eligible pivot rule + class BestEligiblePivotRule + { + private: + + // References to the NetworkSimplex class + const IntVector &_source; + const IntVector &_target; + const CostVector &_cost; + const CharVector &_state; + const CostVector &_pi; + int &_in_arc; + int _search_arc_num; + + public: + + // Constructor + BestEligiblePivotRule(NetworkSimplex &ns) : + _source(ns._source), _target(ns._target), + _cost(ns._cost), _state(ns._state), _pi(ns._pi), + _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num) + {} + + // Find next entering arc + bool findEnteringArc() { + Cost c, min = 0; + for (int e = 0; e != _search_arc_num; ++e) { + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); + if (c < min) { + min = c; + _in_arc = e; + } + } + return min < 0; + } + + }; //class BestEligiblePivotRule + + + // Implementation of the Block Search pivot rule + class BlockSearchPivotRule + { + private: + + // References to the NetworkSimplex class + const IntVector &_source; + const IntVector &_target; + const CostVector &_cost; + const CharVector &_state; + const CostVector &_pi; + int &_in_arc; + int _search_arc_num; + + // Pivot rule data + int _block_size; + int _next_arc; + + public: + + // Constructor + BlockSearchPivotRule(NetworkSimplex &ns) : + _source(ns._source), _target(ns._target), + _cost(ns._cost), _state(ns._state), _pi(ns._pi), + _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), + _next_arc(0) + { + // The main parameters of the pivot rule + const double BLOCK_SIZE_FACTOR = 1.0; + const int MIN_BLOCK_SIZE = 10; + + _block_size = std::max( int(BLOCK_SIZE_FACTOR * + std::sqrt(double(_search_arc_num))), + MIN_BLOCK_SIZE ); + } + + // Find next entering arc + bool findEnteringArc() { + Cost c, min = 0; + int cnt = _block_size; + int e; + for (e = _next_arc; e != _search_arc_num; ++e) { + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); + if (c < min) { + min = c; + _in_arc = e; + } + if (--cnt == 0) { + if (min < 0) goto search_end; + cnt = _block_size; + } + } + for (e = 0; e != _next_arc; ++e) { + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); + if (c < min) { + min = c; + _in_arc = e; + } + if (--cnt == 0) { + if (min < 0) goto search_end; + cnt = _block_size; + } + } + if (min >= 0) return false; + + search_end: + _next_arc = e; + return true; + } + + }; //class BlockSearchPivotRule + + + // Implementation of the Candidate List pivot rule + class CandidateListPivotRule + { + private: + + // References to the NetworkSimplex class + const IntVector &_source; + const IntVector &_target; + const CostVector &_cost; + const CharVector &_state; + const CostVector &_pi; + int &_in_arc; + int _search_arc_num; + + // Pivot rule data + IntVector _candidates; + int _list_length, _minor_limit; + int _curr_length, _minor_count; + int _next_arc; + + public: + + /// Constructor + CandidateListPivotRule(NetworkSimplex &ns) : + _source(ns._source), _target(ns._target), + _cost(ns._cost), _state(ns._state), _pi(ns._pi), + _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), + _next_arc(0) + { + // The main parameters of the pivot rule + const double LIST_LENGTH_FACTOR = 0.25; + const int MIN_LIST_LENGTH = 10; + const double MINOR_LIMIT_FACTOR = 0.1; + const int MIN_MINOR_LIMIT = 3; + + _list_length = std::max( int(LIST_LENGTH_FACTOR * + std::sqrt(double(_search_arc_num))), + MIN_LIST_LENGTH ); + _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length), + MIN_MINOR_LIMIT ); + _curr_length = _minor_count = 0; + _candidates.resize(_list_length); + } + + /// Find next entering arc + bool findEnteringArc() { + Cost min, c; + int e; + if (_curr_length > 0 && _minor_count < _minor_limit) { + // Minor iteration: select the best eligible arc from the + // current candidate list + ++_minor_count; + min = 0; + for (int i = 0; i < _curr_length; ++i) { + e = _candidates[i]; + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); + if (c < min) { + min = c; + _in_arc = e; + } + else if (c >= 0) { + _candidates[i--] = _candidates[--_curr_length]; + } + } + if (min < 0) return true; + } + + // Major iteration: build a new candidate list + min = 0; + _curr_length = 0; + for (e = _next_arc; e != _search_arc_num; ++e) { + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); + if (c < 0) { + _candidates[_curr_length++] = e; + if (c < min) { + min = c; + _in_arc = e; + } + if (_curr_length == _list_length) goto search_end; + } + } + for (e = 0; e != _next_arc; ++e) { + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); + if (c < 0) { + _candidates[_curr_length++] = e; + if (c < min) { + min = c; + _in_arc = e; + } + if (_curr_length == _list_length) goto search_end; + } + } + if (_curr_length == 0) return false; + + search_end: + _minor_count = 1; + _next_arc = e; + return true; + } + + }; //class CandidateListPivotRule + + + // Implementation of the Altering Candidate List pivot rule + class AlteringListPivotRule + { + private: + + // References to the NetworkSimplex class + const IntVector &_source; + const IntVector &_target; + const CostVector &_cost; + const CharVector &_state; + const CostVector &_pi; + int &_in_arc; + int _search_arc_num; + + // Pivot rule data + int _block_size, _head_length, _curr_length; + int _next_arc; + IntVector _candidates; + CostVector _cand_cost; + + // Functor class to compare arcs during sort of the candidate list + class SortFunc + { + private: + const CostVector &_map; + public: + SortFunc(const CostVector &map) : _map(map) {} + bool operator()(int left, int right) { + return _map[left] < _map[right]; + } + }; + + SortFunc _sort_func; + + public: + + // Constructor + AlteringListPivotRule(NetworkSimplex &ns) : + _source(ns._source), _target(ns._target), + _cost(ns._cost), _state(ns._state), _pi(ns._pi), + _in_arc(ns.in_arc), _search_arc_num(ns._search_arc_num), + _next_arc(0), _cand_cost(ns._search_arc_num), _sort_func(_cand_cost) + { + // The main parameters of the pivot rule + const double BLOCK_SIZE_FACTOR = 1.0; + const int MIN_BLOCK_SIZE = 10; + const double HEAD_LENGTH_FACTOR = 0.01; + const int MIN_HEAD_LENGTH = 3; + + _block_size = std::max( int(BLOCK_SIZE_FACTOR * + std::sqrt(double(_search_arc_num))), + MIN_BLOCK_SIZE ); + _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size), + MIN_HEAD_LENGTH ); + _candidates.resize(_head_length + _block_size); + _curr_length = 0; + } + + // Find next entering arc + bool findEnteringArc() { + // Check the current candidate list + int e; + Cost c; + for (int i = 0; i != _curr_length; ++i) { + e = _candidates[i]; + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); + if (c < 0) { + _cand_cost[e] = c; + } else { + _candidates[i--] = _candidates[--_curr_length]; + } + } + + // Extend the list + int cnt = _block_size; + int limit = _head_length; + + for (e = _next_arc; e != _search_arc_num; ++e) { + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); + if (c < 0) { + _cand_cost[e] = c; + _candidates[_curr_length++] = e; + } + if (--cnt == 0) { + if (_curr_length > limit) goto search_end; + limit = 0; + cnt = _block_size; + } + } + for (e = 0; e != _next_arc; ++e) { + c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); + if (c < 0) { + _cand_cost[e] = c; + _candidates[_curr_length++] = e; + } + if (--cnt == 0) { + if (_curr_length > limit) goto search_end; + limit = 0; + cnt = _block_size; + } + } + if (_curr_length == 0) return false; + + search_end: + + // Perform partial sort operation on the candidate list + int new_length = std::min(_head_length + 1, _curr_length); + std::partial_sort(_candidates.begin(), _candidates.begin() + new_length, + _candidates.begin() + _curr_length, _sort_func); + + // Select the entering arc and remove it from the list + _in_arc = _candidates[0]; + _next_arc = e; + _candidates[0] = _candidates[new_length - 1]; + _curr_length = new_length - 1; + return true; + } + + }; //class AlteringListPivotRule + + public: + + /// \brief Constructor. + /// + /// The constructor of the class. + /// + /// \param graph The digraph the algorithm runs on. + /// \param arc_mixing Indicate if the arcs will be stored in a + /// mixed order in the internal data structure. + /// In general, it leads to similar performance as using the original + /// arc order, but it makes the algorithm more robust and in special + /// cases, even significantly faster. Therefore, it is enabled by default. + NetworkSimplex(const GR& graph, bool arc_mixing = true) : + _graph(graph), _node_id(graph), _arc_id(graph), + _arc_mixing(arc_mixing), + MAX(std::numeric_limits<Value>::max()), + INF(std::numeric_limits<Value>::has_infinity ? + std::numeric_limits<Value>::infinity() : MAX) + { + // Check the number types + LEMON_ASSERT(std::numeric_limits<Value>::is_signed, + "The flow type of NetworkSimplex must be signed"); + LEMON_ASSERT(std::numeric_limits<Cost>::is_signed, + "The cost type of NetworkSimplex 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> + NetworkSimplex& lowerMap(const LowerMap& map) { + _has_lower = true; + for (ArcIt a(_graph); a != INVALID; ++a) { + _lower[_arc_id[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> + NetworkSimplex& upperMap(const UpperMap& map) { + for (ArcIt a(_graph); a != INVALID; ++a) { + _upper[_arc_id[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> + NetworkSimplex& costMap(const CostMap& map) { + for (ArcIt a(_graph); a != INVALID; ++a) { + _cost[_arc_id[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> + /// + /// \sa supplyType() + template<typename SupplyMap> + NetworkSimplex& 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> + NetworkSimplex& stSupply(const Node& s, const Node& t, Value k) { + for (int i = 0; i != _node_num; ++i) { + _supply[i] = 0; + } + _supply[_node_id[s]] = k; + _supply[_node_id[t]] = -k; + return *this; + } + + /// \brief Set the type of the supply constraints. + /// + /// This function sets the type of the supply/demand constraints. + /// If it is not used before calling \ref run(), the \ref GEQ supply + /// type will be used. + /// + /// For more information, see \ref SupplyType. + /// + /// \return <tt>(*this)</tt> + NetworkSimplex& supplyType(SupplyType supply_type) { + _stype = supply_type; + 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(), + /// \ref supplyType(). + /// For example, + /// \code + /// NetworkSimplex<ListDigraph> ns(graph); + /// ns.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 pivot_rule The pivot rule that will be used during the + /// algorithm. For more information, see \ref PivotRule. + /// + /// \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 objective function of the problem is + /// unbounded, i.e. there is a directed cycle having negative total + /// cost and infinite upper bound. + /// + /// \see ProblemType, PivotRule + /// \see resetParams(), reset() + ProblemType run(PivotRule pivot_rule = BLOCK_SEARCH) { + if (!init()) return INFEASIBLE; + return start(pivot_rule); + } + + /// \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(), \ref supplyType(). + /// + /// 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 + /// NetworkSimplex<ListDigraph> ns(graph); + /// + /// // First run + /// ns.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; + /// ns.costMap(cost).run(); + /// + /// // Run again from scratch using resetParams() + /// // (the lower bounds will be set to zero on all arcs) + /// ns.resetParams(); + /// ns.upperMap(capacity).costMap(cost) + /// .supplyMap(sup).run(); + /// \endcode + /// + /// \return <tt>(*this)</tt> + /// + /// \see reset(), run() + NetworkSimplex& resetParams() { + for (int i = 0; i != _node_num; ++i) { + _supply[i] = 0; + } + for (int i = 0; i != _arc_num; ++i) { + _lower[i] = 0; + _upper[i] = INF; + _cost[i] = 1; + } + _has_lower = false; + _stype = GEQ; + 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(), + /// \ref supplyType(). + /// + /// 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() + NetworkSimplex& reset() { + // Resize vectors + _node_num = countNodes(_graph); + _arc_num = countArcs(_graph); + int all_node_num = _node_num + 1; + int max_arc_num = _arc_num + 2 * _node_num; + + _source.resize(max_arc_num); + _target.resize(max_arc_num); + + _lower.resize(_arc_num); + _upper.resize(_arc_num); + _cap.resize(max_arc_num); + _cost.resize(max_arc_num); + _supply.resize(all_node_num); + _flow.resize(max_arc_num); + _pi.resize(all_node_num); + + _parent.resize(all_node_num); + _pred.resize(all_node_num); + _pred_dir.resize(all_node_num); + _thread.resize(all_node_num); + _rev_thread.resize(all_node_num); + _succ_num.resize(all_node_num); + _last_succ.resize(all_node_num); + _state.resize(max_arc_num); + + // Copy the graph + int i = 0; + for (NodeIt n(_graph); n != INVALID; ++n, ++i) { + _node_id[n] = i; + } + if (_arc_mixing && _node_num > 1) { + // Store the arcs in a mixed order + const int skip = std::max(_arc_num / _node_num, 3); + int i = 0, j = 0; + for (ArcIt a(_graph); a != INVALID; ++a) { + _arc_id[a] = i; + _source[i] = _node_id[_graph.source(a)]; + _target[i] = _node_id[_graph.target(a)]; + if ((i += skip) >= _arc_num) i = ++j; + } + } else { + // Store the arcs in the original order + int i = 0; + for (ArcIt a(_graph); a != INVALID; ++a, ++i) { + _arc_id[a] = i; + _source[i] = _node_id[_graph.source(a)]; + _target[i] = _node_id[_graph.target(a)]; + } + } + + // 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 + /// ns.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_id[a]; + c += Number(_flow[i]) * 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 _flow[_arc_id[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, _flow[_arc_id[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 _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, _pi[_node_id[n]]); + } + } + + /// @} + + private: + + // Initialize internal data structures + bool init() { + if (_node_num == 0) return false; + + // Check the sum of supply values + _sum_supply = 0; + for (int i = 0; i != _node_num; ++i) { + _sum_supply += _supply[i]; + } + if ( !((_stype == GEQ && _sum_supply <= 0) || + (_stype == LEQ && _sum_supply >= 0)) ) return false; + + // Check lower and upper bounds + LEMON_DEBUG(checkBoundMaps(), + "Upper bounds must be greater or equal to the lower bounds"); + + // Remove non-zero lower bounds + if (_has_lower) { + for (int i = 0; i != _arc_num; ++i) { + Value c = _lower[i]; + if (c >= 0) { + _cap[i] = _upper[i] < MAX ? _upper[i] - c : INF; + } else { + _cap[i] = _upper[i] < MAX + c ? _upper[i] - c : INF; + } + _supply[_source[i]] -= c; + _supply[_target[i]] += c; + } + } else { + for (int i = 0; i != _arc_num; ++i) { + _cap[i] = _upper[i]; + } + } + + // Initialize artifical cost + Cost ART_COST; + if (std::numeric_limits<Cost>::is_exact) { + ART_COST = std::numeric_limits<Cost>::max() / 2 + 1; + } else { + ART_COST = 0; + for (int i = 0; i != _arc_num; ++i) { + if (_cost[i] > ART_COST) ART_COST = _cost[i]; + } + ART_COST = (ART_COST + 1) * _node_num; + } + + // Initialize arc maps + for (int i = 0; i != _arc_num; ++i) { + _flow[i] = 0; + _state[i] = STATE_LOWER; + } + + // Set data for the artificial root node + _root = _node_num; + _parent[_root] = -1; + _pred[_root] = -1; + _thread[_root] = 0; + _rev_thread[0] = _root; + _succ_num[_root] = _node_num + 1; + _last_succ[_root] = _root - 1; + _supply[_root] = -_sum_supply; + _pi[_root] = 0; + + // Add artificial arcs and initialize the spanning tree data structure + if (_sum_supply == 0) { + // EQ supply constraints + _search_arc_num = _arc_num; + _all_arc_num = _arc_num + _node_num; + for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { + _parent[u] = _root; + _pred[u] = e; + _thread[u] = u + 1; + _rev_thread[u + 1] = u; + _succ_num[u] = 1; + _last_succ[u] = u; + _cap[e] = INF; + _state[e] = STATE_TREE; + if (_supply[u] >= 0) { + _pred_dir[u] = DIR_UP; + _pi[u] = 0; + _source[e] = u; + _target[e] = _root; + _flow[e] = _supply[u]; + _cost[e] = 0; + } else { + _pred_dir[u] = DIR_DOWN; + _pi[u] = ART_COST; + _source[e] = _root; + _target[e] = u; + _flow[e] = -_supply[u]; + _cost[e] = ART_COST; + } + } + } + else if (_sum_supply > 0) { + // LEQ supply constraints + _search_arc_num = _arc_num + _node_num; + int f = _arc_num + _node_num; + for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { + _parent[u] = _root; + _thread[u] = u + 1; + _rev_thread[u + 1] = u; + _succ_num[u] = 1; + _last_succ[u] = u; + if (_supply[u] >= 0) { + _pred_dir[u] = DIR_UP; + _pi[u] = 0; + _pred[u] = e; + _source[e] = u; + _target[e] = _root; + _cap[e] = INF; + _flow[e] = _supply[u]; + _cost[e] = 0; + _state[e] = STATE_TREE; + } else { + _pred_dir[u] = DIR_DOWN; + _pi[u] = ART_COST; + _pred[u] = f; + _source[f] = _root; + _target[f] = u; + _cap[f] = INF; + _flow[f] = -_supply[u]; + _cost[f] = ART_COST; + _state[f] = STATE_TREE; + _source[e] = u; + _target[e] = _root; + _cap[e] = INF; + _flow[e] = 0; + _cost[e] = 0; + _state[e] = STATE_LOWER; + ++f; + } + } + _all_arc_num = f; + } + else { + // GEQ supply constraints + _search_arc_num = _arc_num + _node_num; + int f = _arc_num + _node_num; + for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { + _parent[u] = _root; + _thread[u] = u + 1; + _rev_thread[u + 1] = u; + _succ_num[u] = 1; + _last_succ[u] = u; + if (_supply[u] <= 0) { + _pred_dir[u] = DIR_DOWN; + _pi[u] = 0; + _pred[u] = e; + _source[e] = _root; + _target[e] = u; + _cap[e] = INF; + _flow[e] = -_supply[u]; + _cost[e] = 0; + _state[e] = STATE_TREE; + } else { + _pred_dir[u] = DIR_UP; + _pi[u] = -ART_COST; + _pred[u] = f; + _source[f] = u; + _target[f] = _root; + _cap[f] = INF; + _flow[f] = _supply[u]; + _state[f] = STATE_TREE; + _cost[f] = ART_COST; + _source[e] = _root; + _target[e] = u; + _cap[e] = INF; + _flow[e] = 0; + _cost[e] = 0; + _state[e] = STATE_LOWER; + ++f; + } + } + _all_arc_num = f; + } + + return true; + } + + // Check if the upper bound is greater than or equal to the lower bound + // on each arc. + bool checkBoundMaps() { + for (int j = 0; j != _arc_num; ++j) { + if (_upper[j] < _lower[j]) return false; + } + return true; + } + + // Find the join node + void findJoinNode() { + int u = _source[in_arc]; + int v = _target[in_arc]; + while (u != v) { + if (_succ_num[u] < _succ_num[v]) { + u = _parent[u]; + } else { + v = _parent[v]; + } + } + join = u; + } + + // Find the leaving arc of the cycle and returns true if the + // leaving arc is not the same as the entering arc + bool findLeavingArc() { + // Initialize first and second nodes according to the direction + // of the cycle + int first, second; + if (_state[in_arc] == STATE_LOWER) { + first = _source[in_arc]; + second = _target[in_arc]; + } else { + first = _target[in_arc]; + second = _source[in_arc]; + } + delta = _cap[in_arc]; + int result = 0; + Value c, d; + int e; + + // Search the cycle form the first node to the join node + for (int u = first; u != join; u = _parent[u]) { + e = _pred[u]; + d = _flow[e]; + if (_pred_dir[u] == DIR_DOWN) { + c = _cap[e]; + d = c >= MAX ? INF : c - d; + } + if (d < delta) { + delta = d; + u_out = u; + result = 1; + } + } + + // Search the cycle form the second node to the join node + for (int u = second; u != join; u = _parent[u]) { + e = _pred[u]; + d = _flow[e]; + if (_pred_dir[u] == DIR_UP) { + c = _cap[e]; + d = c >= MAX ? INF : c - d; + } + if (d <= delta) { + delta = d; + u_out = u; + result = 2; + } + } + + if (result == 1) { + u_in = first; + v_in = second; + } else { + u_in = second; + v_in = first; + } + return result != 0; + } + + // Change _flow and _state vectors + void changeFlow(bool change) { + // Augment along the cycle + if (delta > 0) { + Value val = _state[in_arc] * delta; + _flow[in_arc] += val; + for (int u = _source[in_arc]; u != join; u = _parent[u]) { + _flow[_pred[u]] -= _pred_dir[u] * val; + } + for (int u = _target[in_arc]; u != join; u = _parent[u]) { + _flow[_pred[u]] += _pred_dir[u] * val; + } + } + // Update the state of the entering and leaving arcs + if (change) { + _state[in_arc] = STATE_TREE; + _state[_pred[u_out]] = + (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER; + } else { + _state[in_arc] = -_state[in_arc]; + } + } + + // Update the tree structure + void updateTreeStructure() { + int old_rev_thread = _rev_thread[u_out]; + int old_succ_num = _succ_num[u_out]; + int old_last_succ = _last_succ[u_out]; + v_out = _parent[u_out]; + + // Check if u_in and u_out coincide + if (u_in == u_out) { + // Update _parent, _pred, _pred_dir + _parent[u_in] = v_in; + _pred[u_in] = in_arc; + _pred_dir[u_in] = u_in == _source[in_arc] ? DIR_UP : DIR_DOWN; + + // Update _thread and _rev_thread + if (_thread[v_in] != u_out) { + int after = _thread[old_last_succ]; + _thread[old_rev_thread] = after; + _rev_thread[after] = old_rev_thread; + after = _thread[v_in]; + _thread[v_in] = u_out; + _rev_thread[u_out] = v_in; + _thread[old_last_succ] = after; + _rev_thread[after] = old_last_succ; + } + } else { + // Handle the case when old_rev_thread equals to v_in + // (it also means that join and v_out coincide) + int thread_continue = old_rev_thread == v_in ? + _thread[old_last_succ] : _thread[v_in]; + + // Update _thread and _parent along the stem nodes (i.e. the nodes + // between u_in and u_out, whose parent have to be changed) + int stem = u_in; // the current stem node + int par_stem = v_in; // the new parent of stem + int next_stem; // the next stem node + int last = _last_succ[u_in]; // the last successor of stem + int before, after = _thread[last]; + _thread[v_in] = u_in; + _dirty_revs.clear(); + _dirty_revs.push_back(v_in); + while (stem != u_out) { + // Insert the next stem node into the thread list + next_stem = _parent[stem]; + _thread[last] = next_stem; + _dirty_revs.push_back(last); + + // Remove the subtree of stem from the thread list + before = _rev_thread[stem]; + _thread[before] = after; + _rev_thread[after] = before; + + // Change the parent node and shift stem nodes + _parent[stem] = par_stem; + par_stem = stem; + stem = next_stem; + + // Update last and after + last = _last_succ[stem] == _last_succ[par_stem] ? + _rev_thread[par_stem] : _last_succ[stem]; + after = _thread[last]; + } + _parent[u_out] = par_stem; + _thread[last] = thread_continue; + _rev_thread[thread_continue] = last; + _last_succ[u_out] = last; + + // Remove the subtree of u_out from the thread list except for + // the case when old_rev_thread equals to v_in + if (old_rev_thread != v_in) { + _thread[old_rev_thread] = after; + _rev_thread[after] = old_rev_thread; + } + + // Update _rev_thread using the new _thread values + for (int i = 0; i != int(_dirty_revs.size()); ++i) { + int u = _dirty_revs[i]; + _rev_thread[_thread[u]] = u; + } + + // Update _pred, _pred_dir, _last_succ and _succ_num for the + // stem nodes from u_out to u_in + int tmp_sc = 0, tmp_ls = _last_succ[u_out]; + for (int u = u_out, p = _parent[u]; u != u_in; u = p, p = _parent[u]) { + _pred[u] = _pred[p]; + _pred_dir[u] = -_pred_dir[p]; + tmp_sc += _succ_num[u] - _succ_num[p]; + _succ_num[u] = tmp_sc; + _last_succ[p] = tmp_ls; + } + _pred[u_in] = in_arc; + _pred_dir[u_in] = u_in == _source[in_arc] ? DIR_UP : DIR_DOWN; + _succ_num[u_in] = old_succ_num; + } + + // Update _last_succ from v_in towards the root + int up_limit_out = _last_succ[join] == v_in ? join : -1; + int last_succ_out = _last_succ[u_out]; + for (int u = v_in; u != -1 && _last_succ[u] == v_in; u = _parent[u]) { + _last_succ[u] = last_succ_out; + } + + // Update _last_succ from v_out towards the root + if (join != old_rev_thread && v_in != old_rev_thread) { + for (int u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; + u = _parent[u]) { + _last_succ[u] = old_rev_thread; + } + } + else if (last_succ_out != old_last_succ) { + for (int u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; + u = _parent[u]) { + _last_succ[u] = last_succ_out; + } + } + + // Update _succ_num from v_in to join + for (int u = v_in; u != join; u = _parent[u]) { + _succ_num[u] += old_succ_num; + } + // Update _succ_num from v_out to join + for (int u = v_out; u != join; u = _parent[u]) { + _succ_num[u] -= old_succ_num; + } + } + + // Update potentials in the subtree that has been moved + void updatePotential() { + Cost sigma = _pi[v_in] - _pi[u_in] - + _pred_dir[u_in] * _cost[in_arc]; + int end = _thread[_last_succ[u_in]]; + for (int u = u_in; u != end; u = _thread[u]) { + _pi[u] += sigma; + } + } + + // Heuristic initial pivots + bool initialPivots() { + Value curr, total = 0; + std::vector<Node> supply_nodes, demand_nodes; + for (NodeIt u(_graph); u != INVALID; ++u) { + curr = _supply[_node_id[u]]; + if (curr > 0) { + total += curr; + supply_nodes.push_back(u); + } + else if (curr < 0) { + demand_nodes.push_back(u); + } + } + if (_sum_supply > 0) total -= _sum_supply; + if (total <= 0) return true; + + IntVector arc_vector; + if (_sum_supply >= 0) { + if (supply_nodes.size() == 1 && demand_nodes.size() == 1) { + // Perform a reverse graph search from the sink to the source + typename GR::template NodeMap<bool> reached(_graph, false); + Node s = supply_nodes[0], t = demand_nodes[0]; + std::vector<Node> stack; + reached[t] = true; + stack.push_back(t); + while (!stack.empty()) { + Node u, v = stack.back(); + stack.pop_back(); + if (v == s) break; + for (InArcIt a(_graph, v); a != INVALID; ++a) { + if (reached[u = _graph.source(a)]) continue; + int j = _arc_id[a]; + if (_cap[j] >= total) { + arc_vector.push_back(j); + reached[u] = true; + stack.push_back(u); + } + } + } + } else { + // Find the min. cost incoming arc for each demand node + for (int i = 0; i != int(demand_nodes.size()); ++i) { + Node v = demand_nodes[i]; + Cost c, min_cost = std::numeric_limits<Cost>::max(); + Arc min_arc = INVALID; + for (InArcIt a(_graph, v); a != INVALID; ++a) { + c = _cost[_arc_id[a]]; + if (c < min_cost) { + min_cost = c; + min_arc = a; + } + } + if (min_arc != INVALID) { + arc_vector.push_back(_arc_id[min_arc]); + } + } + } + } else { + // Find the min. cost outgoing arc for each supply node + for (int i = 0; i != int(supply_nodes.size()); ++i) { + Node u = supply_nodes[i]; + Cost c, min_cost = std::numeric_limits<Cost>::max(); + Arc min_arc = INVALID; + for (OutArcIt a(_graph, u); a != INVALID; ++a) { + c = _cost[_arc_id[a]]; + if (c < min_cost) { + min_cost = c; + min_arc = a; + } + } + if (min_arc != INVALID) { + arc_vector.push_back(_arc_id[min_arc]); + } + } + } + + // Perform heuristic initial pivots + for (int i = 0; i != int(arc_vector.size()); ++i) { + in_arc = arc_vector[i]; + if (_state[in_arc] * (_cost[in_arc] + _pi[_source[in_arc]] - + _pi[_target[in_arc]]) >= 0) continue; + findJoinNode(); + bool change = findLeavingArc(); + if (delta >= MAX) return false; + changeFlow(change); + if (change) { + updateTreeStructure(); + updatePotential(); + } + } + return true; + } + + // Execute the algorithm + ProblemType start(PivotRule pivot_rule) { + // Select the pivot rule implementation + switch (pivot_rule) { + case FIRST_ELIGIBLE: + return start<FirstEligiblePivotRule>(); + case BEST_ELIGIBLE: + return start<BestEligiblePivotRule>(); + case BLOCK_SEARCH: + return start<BlockSearchPivotRule>(); + case CANDIDATE_LIST: + return start<CandidateListPivotRule>(); + case ALTERING_LIST: + return start<AlteringListPivotRule>(); + } + return INFEASIBLE; // avoid warning + } + + template <typename PivotRuleImpl> + ProblemType start() { + PivotRuleImpl pivot(*this); + + // Perform heuristic initial pivots + if (!initialPivots()) return UNBOUNDED; + + // Execute the Network Simplex algorithm + while (pivot.findEnteringArc()) { + findJoinNode(); + bool change = findLeavingArc(); + if (delta >= MAX) return UNBOUNDED; + changeFlow(change); + if (change) { + updateTreeStructure(); + updatePotential(); + } + } + + // Check feasibility + for (int e = _search_arc_num; e != _all_arc_num; ++e) { + if (_flow[e] != 0) return INFEASIBLE; + } + + // Transform the solution and the supply map to the original form + if (_has_lower) { + for (int i = 0; i != _arc_num; ++i) { + Value c = _lower[i]; + if (c != 0) { + _flow[i] += c; + _supply[_source[i]] += c; + _supply[_target[i]] -= c; + } + } + } + + // Shift potentials to meet the requirements of the GEQ/LEQ type + // optimality conditions + if (_sum_supply == 0) { + if (_stype == GEQ) { + Cost max_pot = -std::numeric_limits<Cost>::max(); + for (int i = 0; i != _node_num; ++i) { + if (_pi[i] > max_pot) max_pot = _pi[i]; + } + if (max_pot > 0) { + for (int i = 0; i != _node_num; ++i) + _pi[i] -= max_pot; + } + } else { + Cost min_pot = std::numeric_limits<Cost>::max(); + for (int i = 0; i != _node_num; ++i) { + if (_pi[i] < min_pot) min_pot = _pi[i]; + } + if (min_pot < 0) { + for (int i = 0; i != _node_num; ++i) + _pi[i] -= min_pot; + } + } + } + + return OPTIMAL; + } + + }; //class NetworkSimplex + + ///@} + +} //namespace lemon + +#endif //LEMON_NETWORK_SIMPLEX_H |