[601] | 1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library. |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2009 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | #ifndef LEMON_NETWORK_SIMPLEX_H |
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| 20 | #define LEMON_NETWORK_SIMPLEX_H |
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| 21 | |
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| 22 | /// \ingroup min_cost_flow |
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| 23 | /// |
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| 24 | /// \file |
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| 25 | /// \brief Network simplex algorithm for finding a minimum cost flow. |
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| 26 | |
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| 27 | #include <vector> |
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| 28 | #include <limits> |
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| 29 | #include <algorithm> |
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| 30 | |
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[603] | 31 | #include <lemon/core.h> |
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[601] | 32 | #include <lemon/math.h> |
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| 33 | |
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| 34 | namespace lemon { |
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| 35 | |
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| 36 | /// \addtogroup min_cost_flow |
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| 37 | /// @{ |
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| 38 | |
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| 39 | /// \brief Implementation of the primal network simplex algorithm |
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| 40 | /// for finding a \ref min_cost_flow "minimum cost flow". |
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| 41 | /// |
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| 42 | /// \ref NetworkSimplex implements the primal network simplex algorithm |
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| 43 | /// for finding a \ref min_cost_flow "minimum cost flow". |
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| 44 | /// |
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| 45 | /// \tparam Digraph The digraph type the algorithm runs on. |
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| 46 | /// \tparam LowerMap The type of the lower bound map. |
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| 47 | /// \tparam CapacityMap The type of the capacity (upper bound) map. |
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| 48 | /// \tparam CostMap The type of the cost (length) map. |
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| 49 | /// \tparam SupplyMap The type of the supply map. |
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| 50 | /// |
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| 51 | /// \warning |
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| 52 | /// - Arc capacities and costs should be \e non-negative \e integers. |
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| 53 | /// - Supply values should be \e signed \e integers. |
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| 54 | /// - The value types of the maps should be convertible to each other. |
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| 55 | /// - \c CostMap::Value must be signed type. |
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| 56 | /// |
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| 57 | /// \note \ref NetworkSimplex provides five different pivot rule |
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| 58 | /// implementations that significantly affect the efficiency of the |
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| 59 | /// algorithm. |
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| 60 | /// By default "Block Search" pivot rule is used, which proved to be |
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| 61 | /// by far the most efficient according to our benchmark tests. |
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| 62 | /// However another pivot rule can be selected using \ref run() |
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| 63 | /// function with the proper parameter. |
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| 64 | #ifdef DOXYGEN |
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| 65 | template < typename Digraph, |
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| 66 | typename LowerMap, |
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| 67 | typename CapacityMap, |
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| 68 | typename CostMap, |
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| 69 | typename SupplyMap > |
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| 70 | |
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| 71 | #else |
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| 72 | template < typename Digraph, |
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| 73 | typename LowerMap = typename Digraph::template ArcMap<int>, |
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| 74 | typename CapacityMap = typename Digraph::template ArcMap<int>, |
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| 75 | typename CostMap = typename Digraph::template ArcMap<int>, |
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| 76 | typename SupplyMap = typename Digraph::template NodeMap<int> > |
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| 77 | #endif |
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| 78 | class NetworkSimplex |
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| 79 | { |
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| 80 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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| 81 | |
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| 82 | typedef typename CapacityMap::Value Capacity; |
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| 83 | typedef typename CostMap::Value Cost; |
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| 84 | typedef typename SupplyMap::Value Supply; |
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| 85 | |
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| 86 | typedef std::vector<Arc> ArcVector; |
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| 87 | typedef std::vector<Node> NodeVector; |
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| 88 | typedef std::vector<int> IntVector; |
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| 89 | typedef std::vector<bool> BoolVector; |
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| 90 | typedef std::vector<Capacity> CapacityVector; |
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| 91 | typedef std::vector<Cost> CostVector; |
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| 92 | typedef std::vector<Supply> SupplyVector; |
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| 93 | |
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| 94 | public: |
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| 95 | |
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| 96 | /// The type of the flow map |
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| 97 | typedef typename Digraph::template ArcMap<Capacity> FlowMap; |
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| 98 | /// The type of the potential map |
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| 99 | typedef typename Digraph::template NodeMap<Cost> PotentialMap; |
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| 100 | |
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| 101 | public: |
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| 102 | |
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| 103 | /// Enum type for selecting the pivot rule used by \ref run() |
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| 104 | enum PivotRuleEnum { |
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| 105 | FIRST_ELIGIBLE_PIVOT, |
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| 106 | BEST_ELIGIBLE_PIVOT, |
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| 107 | BLOCK_SEARCH_PIVOT, |
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| 108 | CANDIDATE_LIST_PIVOT, |
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| 109 | ALTERING_LIST_PIVOT |
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| 110 | }; |
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| 111 | |
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| 112 | private: |
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| 113 | |
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| 114 | // State constants for arcs |
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| 115 | enum ArcStateEnum { |
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| 116 | STATE_UPPER = -1, |
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| 117 | STATE_TREE = 0, |
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| 118 | STATE_LOWER = 1 |
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| 119 | }; |
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| 120 | |
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| 121 | private: |
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| 122 | |
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| 123 | // References for the original data |
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[603] | 124 | const Digraph &_graph; |
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[601] | 125 | const LowerMap *_orig_lower; |
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| 126 | const CapacityMap &_orig_cap; |
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| 127 | const CostMap &_orig_cost; |
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| 128 | const SupplyMap *_orig_supply; |
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| 129 | Node _orig_source; |
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| 130 | Node _orig_target; |
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| 131 | Capacity _orig_flow_value; |
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| 132 | |
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| 133 | // Result maps |
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[603] | 134 | FlowMap *_flow_map; |
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| 135 | PotentialMap *_potential_map; |
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[601] | 136 | bool _local_flow; |
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| 137 | bool _local_potential; |
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| 138 | |
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| 139 | // The number of nodes and arcs in the original graph |
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| 140 | int _node_num; |
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| 141 | int _arc_num; |
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| 142 | |
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[603] | 143 | // Data structures for storing the graph |
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| 144 | IntNodeMap _node_id; |
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| 145 | ArcVector _arc_ref; |
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| 146 | IntVector _source; |
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| 147 | IntVector _target; |
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| 148 | |
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[601] | 149 | // Node and arc maps |
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| 150 | CapacityVector _cap; |
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| 151 | CostVector _cost; |
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| 152 | CostVector _supply; |
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| 153 | CapacityVector _flow; |
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| 154 | CostVector _pi; |
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| 155 | |
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[603] | 156 | // Data for storing the spanning tree structure |
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[601] | 157 | IntVector _parent; |
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| 158 | IntVector _pred; |
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| 159 | IntVector _thread; |
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[604] | 160 | IntVector _rev_thread; |
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| 161 | IntVector _succ_num; |
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| 162 | IntVector _last_succ; |
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| 163 | IntVector _dirty_revs; |
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[601] | 164 | BoolVector _forward; |
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| 165 | IntVector _state; |
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| 166 | int _root; |
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| 167 | |
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| 168 | // Temporary data used in the current pivot iteration |
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[603] | 169 | int in_arc, join, u_in, v_in, u_out, v_out; |
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| 170 | int first, second, right, last; |
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[601] | 171 | int stem, par_stem, new_stem; |
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| 172 | Capacity delta; |
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| 173 | |
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| 174 | private: |
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| 175 | |
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| 176 | /// \brief Implementation of the "First Eligible" pivot rule for the |
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| 177 | /// \ref NetworkSimplex "network simplex" algorithm. |
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| 178 | /// |
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| 179 | /// This class implements the "First Eligible" pivot rule |
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| 180 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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| 181 | /// |
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| 182 | /// For more information see \ref NetworkSimplex::run(). |
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| 183 | class FirstEligiblePivotRule |
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| 184 | { |
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| 185 | private: |
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| 186 | |
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| 187 | // References to the NetworkSimplex class |
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| 188 | const IntVector &_source; |
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| 189 | const IntVector &_target; |
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| 190 | const CostVector &_cost; |
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| 191 | const IntVector &_state; |
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| 192 | const CostVector &_pi; |
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| 193 | int &_in_arc; |
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| 194 | int _arc_num; |
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| 195 | |
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| 196 | // Pivot rule data |
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| 197 | int _next_arc; |
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| 198 | |
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| 199 | public: |
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| 200 | |
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| 201 | /// Constructor |
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| 202 | FirstEligiblePivotRule(NetworkSimplex &ns) : |
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[603] | 203 | _source(ns._source), _target(ns._target), |
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[601] | 204 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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[603] | 205 | _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0) |
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[601] | 206 | {} |
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| 207 | |
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| 208 | /// Find next entering arc |
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| 209 | bool findEnteringArc() { |
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| 210 | Cost c; |
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| 211 | for (int e = _next_arc; e < _arc_num; ++e) { |
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| 212 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 213 | if (c < 0) { |
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| 214 | _in_arc = e; |
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| 215 | _next_arc = e + 1; |
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| 216 | return true; |
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| 217 | } |
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| 218 | } |
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| 219 | for (int e = 0; e < _next_arc; ++e) { |
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| 220 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 221 | if (c < 0) { |
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| 222 | _in_arc = e; |
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| 223 | _next_arc = e + 1; |
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| 224 | return true; |
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| 225 | } |
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| 226 | } |
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| 227 | return false; |
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| 228 | } |
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| 229 | |
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| 230 | }; //class FirstEligiblePivotRule |
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| 231 | |
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| 232 | |
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| 233 | /// \brief Implementation of the "Best Eligible" pivot rule for the |
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| 234 | /// \ref NetworkSimplex "network simplex" algorithm. |
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| 235 | /// |
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| 236 | /// This class implements the "Best Eligible" pivot rule |
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| 237 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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| 238 | /// |
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| 239 | /// For more information see \ref NetworkSimplex::run(). |
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| 240 | class BestEligiblePivotRule |
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| 241 | { |
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| 242 | private: |
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| 243 | |
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| 244 | // References to the NetworkSimplex class |
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| 245 | const IntVector &_source; |
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| 246 | const IntVector &_target; |
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| 247 | const CostVector &_cost; |
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| 248 | const IntVector &_state; |
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| 249 | const CostVector &_pi; |
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| 250 | int &_in_arc; |
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| 251 | int _arc_num; |
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| 252 | |
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| 253 | public: |
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| 254 | |
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| 255 | /// Constructor |
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| 256 | BestEligiblePivotRule(NetworkSimplex &ns) : |
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[603] | 257 | _source(ns._source), _target(ns._target), |
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[601] | 258 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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[603] | 259 | _in_arc(ns.in_arc), _arc_num(ns._arc_num) |
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[601] | 260 | {} |
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| 261 | |
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| 262 | /// Find next entering arc |
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| 263 | bool findEnteringArc() { |
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| 264 | Cost c, min = 0; |
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| 265 | for (int e = 0; e < _arc_num; ++e) { |
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| 266 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 267 | if (c < min) { |
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| 268 | min = c; |
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| 269 | _in_arc = e; |
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| 270 | } |
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| 271 | } |
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| 272 | return min < 0; |
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| 273 | } |
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| 274 | |
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| 275 | }; //class BestEligiblePivotRule |
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| 276 | |
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| 277 | |
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| 278 | /// \brief Implementation of the "Block Search" pivot rule for the |
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| 279 | /// \ref NetworkSimplex "network simplex" algorithm. |
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| 280 | /// |
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| 281 | /// This class implements the "Block Search" pivot rule |
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| 282 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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| 283 | /// |
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| 284 | /// For more information see \ref NetworkSimplex::run(). |
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| 285 | class BlockSearchPivotRule |
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| 286 | { |
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| 287 | private: |
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| 288 | |
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| 289 | // References to the NetworkSimplex class |
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| 290 | const IntVector &_source; |
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| 291 | const IntVector &_target; |
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| 292 | const CostVector &_cost; |
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| 293 | const IntVector &_state; |
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| 294 | const CostVector &_pi; |
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| 295 | int &_in_arc; |
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| 296 | int _arc_num; |
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| 297 | |
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| 298 | // Pivot rule data |
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| 299 | int _block_size; |
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| 300 | int _next_arc; |
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| 301 | |
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| 302 | public: |
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| 303 | |
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| 304 | /// Constructor |
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| 305 | BlockSearchPivotRule(NetworkSimplex &ns) : |
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[603] | 306 | _source(ns._source), _target(ns._target), |
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[601] | 307 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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[603] | 308 | _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0) |
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[601] | 309 | { |
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| 310 | // The main parameters of the pivot rule |
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| 311 | const double BLOCK_SIZE_FACTOR = 2.0; |
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| 312 | const int MIN_BLOCK_SIZE = 10; |
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| 313 | |
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| 314 | _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_arc_num)), |
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| 315 | MIN_BLOCK_SIZE ); |
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| 316 | } |
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| 317 | |
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| 318 | /// Find next entering arc |
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| 319 | bool findEnteringArc() { |
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| 320 | Cost c, min = 0; |
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| 321 | int cnt = _block_size; |
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| 322 | int e, min_arc = _next_arc; |
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| 323 | for (e = _next_arc; e < _arc_num; ++e) { |
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| 324 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 325 | if (c < min) { |
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| 326 | min = c; |
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| 327 | min_arc = e; |
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| 328 | } |
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| 329 | if (--cnt == 0) { |
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| 330 | if (min < 0) break; |
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| 331 | cnt = _block_size; |
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| 332 | } |
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| 333 | } |
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| 334 | if (min == 0 || cnt > 0) { |
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| 335 | for (e = 0; e < _next_arc; ++e) { |
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| 336 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 337 | if (c < min) { |
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| 338 | min = c; |
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| 339 | min_arc = e; |
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| 340 | } |
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| 341 | if (--cnt == 0) { |
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| 342 | if (min < 0) break; |
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| 343 | cnt = _block_size; |
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| 344 | } |
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| 345 | } |
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| 346 | } |
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| 347 | if (min >= 0) return false; |
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| 348 | _in_arc = min_arc; |
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| 349 | _next_arc = e; |
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| 350 | return true; |
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| 351 | } |
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| 352 | |
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| 353 | }; //class BlockSearchPivotRule |
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| 354 | |
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| 355 | |
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| 356 | /// \brief Implementation of the "Candidate List" pivot rule for the |
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| 357 | /// \ref NetworkSimplex "network simplex" algorithm. |
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| 358 | /// |
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| 359 | /// This class implements the "Candidate List" pivot rule |
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| 360 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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| 361 | /// |
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| 362 | /// For more information see \ref NetworkSimplex::run(). |
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| 363 | class CandidateListPivotRule |
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| 364 | { |
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| 365 | private: |
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| 366 | |
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| 367 | // References to the NetworkSimplex class |
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| 368 | const IntVector &_source; |
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| 369 | const IntVector &_target; |
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| 370 | const CostVector &_cost; |
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| 371 | const IntVector &_state; |
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| 372 | const CostVector &_pi; |
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| 373 | int &_in_arc; |
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| 374 | int _arc_num; |
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| 375 | |
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| 376 | // Pivot rule data |
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| 377 | IntVector _candidates; |
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| 378 | int _list_length, _minor_limit; |
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| 379 | int _curr_length, _minor_count; |
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| 380 | int _next_arc; |
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| 381 | |
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| 382 | public: |
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| 383 | |
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| 384 | /// Constructor |
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| 385 | CandidateListPivotRule(NetworkSimplex &ns) : |
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[603] | 386 | _source(ns._source), _target(ns._target), |
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[601] | 387 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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[603] | 388 | _in_arc(ns.in_arc), _arc_num(ns._arc_num), _next_arc(0) |
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[601] | 389 | { |
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| 390 | // The main parameters of the pivot rule |
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| 391 | const double LIST_LENGTH_FACTOR = 1.0; |
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| 392 | const int MIN_LIST_LENGTH = 10; |
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| 393 | const double MINOR_LIMIT_FACTOR = 0.1; |
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| 394 | const int MIN_MINOR_LIMIT = 3; |
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| 395 | |
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| 396 | _list_length = std::max( int(LIST_LENGTH_FACTOR * sqrt(_arc_num)), |
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| 397 | MIN_LIST_LENGTH ); |
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| 398 | _minor_limit = std::max( int(MINOR_LIMIT_FACTOR * _list_length), |
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| 399 | MIN_MINOR_LIMIT ); |
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| 400 | _curr_length = _minor_count = 0; |
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| 401 | _candidates.resize(_list_length); |
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| 402 | } |
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| 403 | |
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| 404 | /// Find next entering arc |
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| 405 | bool findEnteringArc() { |
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| 406 | Cost min, c; |
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| 407 | int e, min_arc = _next_arc; |
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| 408 | if (_curr_length > 0 && _minor_count < _minor_limit) { |
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| 409 | // Minor iteration: select the best eligible arc from the |
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| 410 | // current candidate list |
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| 411 | ++_minor_count; |
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| 412 | min = 0; |
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| 413 | for (int i = 0; i < _curr_length; ++i) { |
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| 414 | e = _candidates[i]; |
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| 415 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 416 | if (c < min) { |
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| 417 | min = c; |
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| 418 | min_arc = e; |
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| 419 | } |
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| 420 | if (c >= 0) { |
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| 421 | _candidates[i--] = _candidates[--_curr_length]; |
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| 422 | } |
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| 423 | } |
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| 424 | if (min < 0) { |
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| 425 | _in_arc = min_arc; |
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| 426 | return true; |
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| 427 | } |
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| 428 | } |
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| 429 | |
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| 430 | // Major iteration: build a new candidate list |
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| 431 | min = 0; |
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| 432 | _curr_length = 0; |
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| 433 | for (e = _next_arc; e < _arc_num; ++e) { |
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| 434 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 435 | if (c < 0) { |
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| 436 | _candidates[_curr_length++] = e; |
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| 437 | if (c < min) { |
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| 438 | min = c; |
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| 439 | min_arc = e; |
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| 440 | } |
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| 441 | if (_curr_length == _list_length) break; |
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| 442 | } |
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| 443 | } |
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| 444 | if (_curr_length < _list_length) { |
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| 445 | for (e = 0; e < _next_arc; ++e) { |
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| 446 | c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 447 | if (c < 0) { |
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| 448 | _candidates[_curr_length++] = e; |
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| 449 | if (c < min) { |
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| 450 | min = c; |
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| 451 | min_arc = e; |
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| 452 | } |
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| 453 | if (_curr_length == _list_length) break; |
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| 454 | } |
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| 455 | } |
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| 456 | } |
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| 457 | if (_curr_length == 0) return false; |
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| 458 | _minor_count = 1; |
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| 459 | _in_arc = min_arc; |
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| 460 | _next_arc = e; |
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| 461 | return true; |
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| 462 | } |
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| 463 | |
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| 464 | }; //class CandidateListPivotRule |
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| 465 | |
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| 466 | |
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| 467 | /// \brief Implementation of the "Altering Candidate List" pivot rule |
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| 468 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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| 469 | /// |
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| 470 | /// This class implements the "Altering Candidate List" pivot rule |
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| 471 | /// for the \ref NetworkSimplex "network simplex" algorithm. |
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| 472 | /// |
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| 473 | /// For more information see \ref NetworkSimplex::run(). |
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| 474 | class AlteringListPivotRule |
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| 475 | { |
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| 476 | private: |
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| 477 | |
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| 478 | // References to the NetworkSimplex class |
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| 479 | const IntVector &_source; |
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| 480 | const IntVector &_target; |
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| 481 | const CostVector &_cost; |
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| 482 | const IntVector &_state; |
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| 483 | const CostVector &_pi; |
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| 484 | int &_in_arc; |
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| 485 | int _arc_num; |
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| 486 | |
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| 487 | // Pivot rule data |
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| 488 | int _block_size, _head_length, _curr_length; |
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| 489 | int _next_arc; |
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| 490 | IntVector _candidates; |
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| 491 | CostVector _cand_cost; |
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| 492 | |
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| 493 | // Functor class to compare arcs during sort of the candidate list |
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| 494 | class SortFunc |
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| 495 | { |
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| 496 | private: |
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| 497 | const CostVector &_map; |
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| 498 | public: |
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| 499 | SortFunc(const CostVector &map) : _map(map) {} |
---|
| 500 | bool operator()(int left, int right) { |
---|
| 501 | return _map[left] > _map[right]; |
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| 502 | } |
---|
| 503 | }; |
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| 504 | |
---|
| 505 | SortFunc _sort_func; |
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| 506 | |
---|
| 507 | public: |
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| 508 | |
---|
| 509 | /// Constructor |
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| 510 | AlteringListPivotRule(NetworkSimplex &ns) : |
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[603] | 511 | _source(ns._source), _target(ns._target), |
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[601] | 512 | _cost(ns._cost), _state(ns._state), _pi(ns._pi), |
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[603] | 513 | _in_arc(ns.in_arc), _arc_num(ns._arc_num), |
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[601] | 514 | _next_arc(0), _cand_cost(ns._arc_num), _sort_func(_cand_cost) |
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| 515 | { |
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| 516 | // The main parameters of the pivot rule |
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| 517 | const double BLOCK_SIZE_FACTOR = 1.5; |
---|
| 518 | const int MIN_BLOCK_SIZE = 10; |
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| 519 | const double HEAD_LENGTH_FACTOR = 0.1; |
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| 520 | const int MIN_HEAD_LENGTH = 3; |
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| 521 | |
---|
| 522 | _block_size = std::max( int(BLOCK_SIZE_FACTOR * sqrt(_arc_num)), |
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| 523 | MIN_BLOCK_SIZE ); |
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| 524 | _head_length = std::max( int(HEAD_LENGTH_FACTOR * _block_size), |
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| 525 | MIN_HEAD_LENGTH ); |
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| 526 | _candidates.resize(_head_length + _block_size); |
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| 527 | _curr_length = 0; |
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| 528 | } |
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| 529 | |
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| 530 | /// Find next entering arc |
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| 531 | bool findEnteringArc() { |
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| 532 | // Check the current candidate list |
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| 533 | int e; |
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| 534 | for (int i = 0; i < _curr_length; ++i) { |
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| 535 | e = _candidates[i]; |
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| 536 | _cand_cost[e] = _state[e] * |
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| 537 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 538 | if (_cand_cost[e] >= 0) { |
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| 539 | _candidates[i--] = _candidates[--_curr_length]; |
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| 540 | } |
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| 541 | } |
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| 542 | |
---|
| 543 | // Extend the list |
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| 544 | int cnt = _block_size; |
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[603] | 545 | int last_arc = 0; |
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[601] | 546 | int limit = _head_length; |
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| 547 | |
---|
| 548 | for (int e = _next_arc; e < _arc_num; ++e) { |
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| 549 | _cand_cost[e] = _state[e] * |
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| 550 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 551 | if (_cand_cost[e] < 0) { |
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| 552 | _candidates[_curr_length++] = e; |
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[603] | 553 | last_arc = e; |
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[601] | 554 | } |
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| 555 | if (--cnt == 0) { |
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| 556 | if (_curr_length > limit) break; |
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| 557 | limit = 0; |
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| 558 | cnt = _block_size; |
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| 559 | } |
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| 560 | } |
---|
| 561 | if (_curr_length <= limit) { |
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| 562 | for (int e = 0; e < _next_arc; ++e) { |
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| 563 | _cand_cost[e] = _state[e] * |
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| 564 | (_cost[e] + _pi[_source[e]] - _pi[_target[e]]); |
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| 565 | if (_cand_cost[e] < 0) { |
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| 566 | _candidates[_curr_length++] = e; |
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[603] | 567 | last_arc = e; |
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[601] | 568 | } |
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| 569 | if (--cnt == 0) { |
---|
| 570 | if (_curr_length > limit) break; |
---|
| 571 | limit = 0; |
---|
| 572 | cnt = _block_size; |
---|
| 573 | } |
---|
| 574 | } |
---|
| 575 | } |
---|
| 576 | if (_curr_length == 0) return false; |
---|
[603] | 577 | _next_arc = last_arc + 1; |
---|
[601] | 578 | |
---|
| 579 | // Make heap of the candidate list (approximating a partial sort) |
---|
| 580 | make_heap( _candidates.begin(), _candidates.begin() + _curr_length, |
---|
| 581 | _sort_func ); |
---|
| 582 | |
---|
| 583 | // Pop the first element of the heap |
---|
| 584 | _in_arc = _candidates[0]; |
---|
| 585 | pop_heap( _candidates.begin(), _candidates.begin() + _curr_length, |
---|
| 586 | _sort_func ); |
---|
| 587 | _curr_length = std::min(_head_length, _curr_length - 1); |
---|
| 588 | return true; |
---|
| 589 | } |
---|
| 590 | |
---|
| 591 | }; //class AlteringListPivotRule |
---|
| 592 | |
---|
| 593 | public: |
---|
| 594 | |
---|
| 595 | /// \brief General constructor (with lower bounds). |
---|
| 596 | /// |
---|
| 597 | /// General constructor (with lower bounds). |
---|
| 598 | /// |
---|
[603] | 599 | /// \param graph The digraph the algorithm runs on. |
---|
[601] | 600 | /// \param lower The lower bounds of the arcs. |
---|
| 601 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
| 602 | /// \param cost The cost (length) values of the arcs. |
---|
| 603 | /// \param supply The supply values of the nodes (signed). |
---|
[603] | 604 | NetworkSimplex( const Digraph &graph, |
---|
[601] | 605 | const LowerMap &lower, |
---|
| 606 | const CapacityMap &capacity, |
---|
| 607 | const CostMap &cost, |
---|
| 608 | const SupplyMap &supply ) : |
---|
[603] | 609 | _graph(graph), _orig_lower(&lower), _orig_cap(capacity), |
---|
[601] | 610 | _orig_cost(cost), _orig_supply(&supply), |
---|
[603] | 611 | _flow_map(NULL), _potential_map(NULL), |
---|
[601] | 612 | _local_flow(false), _local_potential(false), |
---|
[603] | 613 | _node_id(graph) |
---|
[601] | 614 | {} |
---|
| 615 | |
---|
| 616 | /// \brief General constructor (without lower bounds). |
---|
| 617 | /// |
---|
| 618 | /// General constructor (without lower bounds). |
---|
| 619 | /// |
---|
[603] | 620 | /// \param graph The digraph the algorithm runs on. |
---|
[601] | 621 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
| 622 | /// \param cost The cost (length) values of the arcs. |
---|
| 623 | /// \param supply The supply values of the nodes (signed). |
---|
[603] | 624 | NetworkSimplex( const Digraph &graph, |
---|
[601] | 625 | const CapacityMap &capacity, |
---|
| 626 | const CostMap &cost, |
---|
| 627 | const SupplyMap &supply ) : |
---|
[603] | 628 | _graph(graph), _orig_lower(NULL), _orig_cap(capacity), |
---|
[601] | 629 | _orig_cost(cost), _orig_supply(&supply), |
---|
[603] | 630 | _flow_map(NULL), _potential_map(NULL), |
---|
[601] | 631 | _local_flow(false), _local_potential(false), |
---|
[603] | 632 | _node_id(graph) |
---|
[601] | 633 | {} |
---|
| 634 | |
---|
| 635 | /// \brief Simple constructor (with lower bounds). |
---|
| 636 | /// |
---|
| 637 | /// Simple constructor (with lower bounds). |
---|
| 638 | /// |
---|
[603] | 639 | /// \param graph The digraph the algorithm runs on. |
---|
[601] | 640 | /// \param lower The lower bounds of the arcs. |
---|
| 641 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
| 642 | /// \param cost The cost (length) values of the arcs. |
---|
| 643 | /// \param s The source node. |
---|
| 644 | /// \param t The target node. |
---|
| 645 | /// \param flow_value The required amount of flow from node \c s |
---|
| 646 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
---|
[603] | 647 | NetworkSimplex( const Digraph &graph, |
---|
[601] | 648 | const LowerMap &lower, |
---|
| 649 | const CapacityMap &capacity, |
---|
| 650 | const CostMap &cost, |
---|
| 651 | Node s, Node t, |
---|
| 652 | Capacity flow_value ) : |
---|
[603] | 653 | _graph(graph), _orig_lower(&lower), _orig_cap(capacity), |
---|
[601] | 654 | _orig_cost(cost), _orig_supply(NULL), |
---|
| 655 | _orig_source(s), _orig_target(t), _orig_flow_value(flow_value), |
---|
[603] | 656 | _flow_map(NULL), _potential_map(NULL), |
---|
[601] | 657 | _local_flow(false), _local_potential(false), |
---|
[603] | 658 | _node_id(graph) |
---|
[601] | 659 | {} |
---|
| 660 | |
---|
| 661 | /// \brief Simple constructor (without lower bounds). |
---|
| 662 | /// |
---|
| 663 | /// Simple constructor (without lower bounds). |
---|
| 664 | /// |
---|
[603] | 665 | /// \param graph The digraph the algorithm runs on. |
---|
[601] | 666 | /// \param capacity The capacities (upper bounds) of the arcs. |
---|
| 667 | /// \param cost The cost (length) values of the arcs. |
---|
| 668 | /// \param s The source node. |
---|
| 669 | /// \param t The target node. |
---|
| 670 | /// \param flow_value The required amount of flow from node \c s |
---|
| 671 | /// to node \c t (i.e. the supply of \c s and the demand of \c t). |
---|
[603] | 672 | NetworkSimplex( const Digraph &graph, |
---|
[601] | 673 | const CapacityMap &capacity, |
---|
| 674 | const CostMap &cost, |
---|
| 675 | Node s, Node t, |
---|
| 676 | Capacity flow_value ) : |
---|
[603] | 677 | _graph(graph), _orig_lower(NULL), _orig_cap(capacity), |
---|
[601] | 678 | _orig_cost(cost), _orig_supply(NULL), |
---|
| 679 | _orig_source(s), _orig_target(t), _orig_flow_value(flow_value), |
---|
[603] | 680 | _flow_map(NULL), _potential_map(NULL), |
---|
[601] | 681 | _local_flow(false), _local_potential(false), |
---|
[603] | 682 | _node_id(graph) |
---|
[601] | 683 | {} |
---|
| 684 | |
---|
| 685 | /// Destructor. |
---|
| 686 | ~NetworkSimplex() { |
---|
[603] | 687 | if (_local_flow) delete _flow_map; |
---|
| 688 | if (_local_potential) delete _potential_map; |
---|
[601] | 689 | } |
---|
| 690 | |
---|
| 691 | /// \brief Set the flow map. |
---|
| 692 | /// |
---|
| 693 | /// This function sets the flow map. |
---|
| 694 | /// |
---|
| 695 | /// \return <tt>(*this)</tt> |
---|
| 696 | NetworkSimplex& flowMap(FlowMap &map) { |
---|
| 697 | if (_local_flow) { |
---|
[603] | 698 | delete _flow_map; |
---|
[601] | 699 | _local_flow = false; |
---|
| 700 | } |
---|
[603] | 701 | _flow_map = ↦ |
---|
[601] | 702 | return *this; |
---|
| 703 | } |
---|
| 704 | |
---|
| 705 | /// \brief Set the potential map. |
---|
| 706 | /// |
---|
| 707 | /// This function sets the potential map. |
---|
| 708 | /// |
---|
| 709 | /// \return <tt>(*this)</tt> |
---|
| 710 | NetworkSimplex& potentialMap(PotentialMap &map) { |
---|
| 711 | if (_local_potential) { |
---|
[603] | 712 | delete _potential_map; |
---|
[601] | 713 | _local_potential = false; |
---|
| 714 | } |
---|
[603] | 715 | _potential_map = ↦ |
---|
[601] | 716 | return *this; |
---|
| 717 | } |
---|
| 718 | |
---|
| 719 | /// \name Execution control |
---|
| 720 | /// The algorithm can be executed using the |
---|
| 721 | /// \ref lemon::NetworkSimplex::run() "run()" function. |
---|
| 722 | /// @{ |
---|
| 723 | |
---|
| 724 | /// \brief Run the algorithm. |
---|
| 725 | /// |
---|
| 726 | /// This function runs the algorithm. |
---|
| 727 | /// |
---|
| 728 | /// \param pivot_rule The pivot rule that is used during the |
---|
| 729 | /// algorithm. |
---|
| 730 | /// |
---|
| 731 | /// The available pivot rules: |
---|
| 732 | /// |
---|
| 733 | /// - FIRST_ELIGIBLE_PIVOT The next eligible arc is selected in |
---|
| 734 | /// a wraparound fashion in every iteration |
---|
| 735 | /// (\ref FirstEligiblePivotRule). |
---|
| 736 | /// |
---|
| 737 | /// - BEST_ELIGIBLE_PIVOT The best eligible arc is selected in |
---|
| 738 | /// every iteration (\ref BestEligiblePivotRule). |
---|
| 739 | /// |
---|
| 740 | /// - BLOCK_SEARCH_PIVOT A specified number of arcs are examined in |
---|
| 741 | /// every iteration in a wraparound fashion and the best eligible |
---|
| 742 | /// arc is selected from this block (\ref BlockSearchPivotRule). |
---|
| 743 | /// |
---|
| 744 | /// - CANDIDATE_LIST_PIVOT In a major iteration a candidate list is |
---|
| 745 | /// built from eligible arcs in a wraparound fashion and in the |
---|
| 746 | /// following minor iterations the best eligible arc is selected |
---|
| 747 | /// from this list (\ref CandidateListPivotRule). |
---|
| 748 | /// |
---|
| 749 | /// - ALTERING_LIST_PIVOT It is a modified version of the |
---|
| 750 | /// "Candidate List" pivot rule. It keeps only the several best |
---|
| 751 | /// eligible arcs from the former candidate list and extends this |
---|
| 752 | /// list in every iteration (\ref AlteringListPivotRule). |
---|
| 753 | /// |
---|
| 754 | /// According to our comprehensive benchmark tests the "Block Search" |
---|
| 755 | /// pivot rule proved to be the fastest and the most robust on |
---|
| 756 | /// various test inputs. Thus it is the default option. |
---|
| 757 | /// |
---|
| 758 | /// \return \c true if a feasible flow can be found. |
---|
| 759 | bool run(PivotRuleEnum pivot_rule = BLOCK_SEARCH_PIVOT) { |
---|
| 760 | return init() && start(pivot_rule); |
---|
| 761 | } |
---|
| 762 | |
---|
| 763 | /// @} |
---|
| 764 | |
---|
| 765 | /// \name Query Functions |
---|
| 766 | /// The results of the algorithm can be obtained using these |
---|
| 767 | /// functions.\n |
---|
| 768 | /// \ref lemon::NetworkSimplex::run() "run()" must be called before |
---|
| 769 | /// using them. |
---|
| 770 | /// @{ |
---|
| 771 | |
---|
| 772 | /// \brief Return a const reference to the flow map. |
---|
| 773 | /// |
---|
| 774 | /// This function returns a const reference to an arc map storing |
---|
| 775 | /// the found flow. |
---|
| 776 | /// |
---|
| 777 | /// \pre \ref run() must be called before using this function. |
---|
| 778 | const FlowMap& flowMap() const { |
---|
[603] | 779 | return *_flow_map; |
---|
[601] | 780 | } |
---|
| 781 | |
---|
| 782 | /// \brief Return a const reference to the potential map |
---|
| 783 | /// (the dual solution). |
---|
| 784 | /// |
---|
| 785 | /// This function returns a const reference to a node map storing |
---|
| 786 | /// the found potentials (the dual solution). |
---|
| 787 | /// |
---|
| 788 | /// \pre \ref run() must be called before using this function. |
---|
| 789 | const PotentialMap& potentialMap() const { |
---|
[603] | 790 | return *_potential_map; |
---|
[601] | 791 | } |
---|
| 792 | |
---|
| 793 | /// \brief Return the flow on the given arc. |
---|
| 794 | /// |
---|
| 795 | /// This function returns the flow on the given arc. |
---|
| 796 | /// |
---|
| 797 | /// \pre \ref run() must be called before using this function. |
---|
| 798 | Capacity flow(const Arc& arc) const { |
---|
[603] | 799 | return (*_flow_map)[arc]; |
---|
[601] | 800 | } |
---|
| 801 | |
---|
| 802 | /// \brief Return the potential of the given node. |
---|
| 803 | /// |
---|
| 804 | /// This function returns the potential of the given node. |
---|
| 805 | /// |
---|
| 806 | /// \pre \ref run() must be called before using this function. |
---|
| 807 | Cost potential(const Node& node) const { |
---|
[603] | 808 | return (*_potential_map)[node]; |
---|
[601] | 809 | } |
---|
| 810 | |
---|
| 811 | /// \brief Return the total cost of the found flow. |
---|
| 812 | /// |
---|
| 813 | /// This function returns the total cost of the found flow. |
---|
| 814 | /// The complexity of the function is \f$ O(e) \f$. |
---|
| 815 | /// |
---|
| 816 | /// \pre \ref run() must be called before using this function. |
---|
| 817 | Cost totalCost() const { |
---|
| 818 | Cost c = 0; |
---|
[603] | 819 | for (ArcIt e(_graph); e != INVALID; ++e) |
---|
| 820 | c += (*_flow_map)[e] * _orig_cost[e]; |
---|
[601] | 821 | return c; |
---|
| 822 | } |
---|
| 823 | |
---|
| 824 | /// @} |
---|
| 825 | |
---|
| 826 | private: |
---|
| 827 | |
---|
| 828 | // Initialize internal data structures |
---|
| 829 | bool init() { |
---|
| 830 | // Initialize result maps |
---|
[603] | 831 | if (!_flow_map) { |
---|
| 832 | _flow_map = new FlowMap(_graph); |
---|
[601] | 833 | _local_flow = true; |
---|
| 834 | } |
---|
[603] | 835 | if (!_potential_map) { |
---|
| 836 | _potential_map = new PotentialMap(_graph); |
---|
[601] | 837 | _local_potential = true; |
---|
| 838 | } |
---|
| 839 | |
---|
| 840 | // Initialize vectors |
---|
[603] | 841 | _node_num = countNodes(_graph); |
---|
| 842 | _arc_num = countArcs(_graph); |
---|
[601] | 843 | int all_node_num = _node_num + 1; |
---|
[603] | 844 | int all_arc_num = _arc_num + _node_num; |
---|
[601] | 845 | |
---|
[603] | 846 | _arc_ref.resize(_arc_num); |
---|
| 847 | _source.resize(all_arc_num); |
---|
| 848 | _target.resize(all_arc_num); |
---|
[601] | 849 | |
---|
[603] | 850 | _cap.resize(all_arc_num); |
---|
| 851 | _cost.resize(all_arc_num); |
---|
[601] | 852 | _supply.resize(all_node_num); |
---|
[603] | 853 | _flow.resize(all_arc_num, 0); |
---|
[601] | 854 | _pi.resize(all_node_num, 0); |
---|
| 855 | |
---|
| 856 | _parent.resize(all_node_num); |
---|
| 857 | _pred.resize(all_node_num); |
---|
[603] | 858 | _forward.resize(all_node_num); |
---|
[601] | 859 | _thread.resize(all_node_num); |
---|
[604] | 860 | _rev_thread.resize(all_node_num); |
---|
| 861 | _succ_num.resize(all_node_num); |
---|
| 862 | _last_succ.resize(all_node_num); |
---|
[603] | 863 | _state.resize(all_arc_num, STATE_LOWER); |
---|
[601] | 864 | |
---|
| 865 | // Initialize node related data |
---|
| 866 | bool valid_supply = true; |
---|
| 867 | if (_orig_supply) { |
---|
| 868 | Supply sum = 0; |
---|
| 869 | int i = 0; |
---|
[603] | 870 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
---|
[601] | 871 | _node_id[n] = i; |
---|
| 872 | _supply[i] = (*_orig_supply)[n]; |
---|
| 873 | sum += _supply[i]; |
---|
| 874 | } |
---|
| 875 | valid_supply = (sum == 0); |
---|
| 876 | } else { |
---|
| 877 | int i = 0; |
---|
[603] | 878 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
---|
[601] | 879 | _node_id[n] = i; |
---|
| 880 | _supply[i] = 0; |
---|
| 881 | } |
---|
| 882 | _supply[_node_id[_orig_source]] = _orig_flow_value; |
---|
| 883 | _supply[_node_id[_orig_target]] = -_orig_flow_value; |
---|
| 884 | } |
---|
| 885 | if (!valid_supply) return false; |
---|
| 886 | |
---|
| 887 | // Set data for the artificial root node |
---|
| 888 | _root = _node_num; |
---|
| 889 | _parent[_root] = -1; |
---|
| 890 | _pred[_root] = -1; |
---|
| 891 | _thread[_root] = 0; |
---|
[604] | 892 | _rev_thread[0] = _root; |
---|
| 893 | _succ_num[_root] = all_node_num; |
---|
| 894 | _last_succ[_root] = _root - 1; |
---|
[601] | 895 | _supply[_root] = 0; |
---|
| 896 | _pi[_root] = 0; |
---|
| 897 | |
---|
| 898 | // Store the arcs in a mixed order |
---|
| 899 | int k = std::max(int(sqrt(_arc_num)), 10); |
---|
| 900 | int i = 0; |
---|
[603] | 901 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
| 902 | _arc_ref[i] = e; |
---|
[601] | 903 | if ((i += k) >= _arc_num) i = (i % k) + 1; |
---|
| 904 | } |
---|
| 905 | |
---|
| 906 | // Initialize arc maps |
---|
| 907 | for (int i = 0; i != _arc_num; ++i) { |
---|
[603] | 908 | Arc e = _arc_ref[i]; |
---|
| 909 | _source[i] = _node_id[_graph.source(e)]; |
---|
| 910 | _target[i] = _node_id[_graph.target(e)]; |
---|
[601] | 911 | _cost[i] = _orig_cost[e]; |
---|
| 912 | _cap[i] = _orig_cap[e]; |
---|
| 913 | } |
---|
| 914 | |
---|
| 915 | // Remove non-zero lower bounds |
---|
| 916 | if (_orig_lower) { |
---|
| 917 | for (int i = 0; i != _arc_num; ++i) { |
---|
[603] | 918 | Capacity c = (*_orig_lower)[_arc_ref[i]]; |
---|
[601] | 919 | if (c != 0) { |
---|
| 920 | _cap[i] -= c; |
---|
| 921 | _supply[_source[i]] -= c; |
---|
| 922 | _supply[_target[i]] += c; |
---|
| 923 | } |
---|
| 924 | } |
---|
| 925 | } |
---|
| 926 | |
---|
| 927 | // Add artificial arcs and initialize the spanning tree data structure |
---|
| 928 | Cost max_cost = std::numeric_limits<Cost>::max() / 4; |
---|
| 929 | Capacity max_cap = std::numeric_limits<Capacity>::max(); |
---|
| 930 | for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) { |
---|
| 931 | _thread[u] = u + 1; |
---|
[604] | 932 | _rev_thread[u + 1] = u; |
---|
| 933 | _succ_num[u] = 1; |
---|
| 934 | _last_succ[u] = u; |
---|
[601] | 935 | _parent[u] = _root; |
---|
| 936 | _pred[u] = e; |
---|
| 937 | if (_supply[u] >= 0) { |
---|
| 938 | _flow[e] = _supply[u]; |
---|
| 939 | _forward[u] = true; |
---|
| 940 | _pi[u] = -max_cost; |
---|
| 941 | } else { |
---|
| 942 | _flow[e] = -_supply[u]; |
---|
| 943 | _forward[u] = false; |
---|
| 944 | _pi[u] = max_cost; |
---|
| 945 | } |
---|
| 946 | _cost[e] = max_cost; |
---|
| 947 | _cap[e] = max_cap; |
---|
| 948 | _state[e] = STATE_TREE; |
---|
| 949 | } |
---|
| 950 | |
---|
| 951 | return true; |
---|
| 952 | } |
---|
| 953 | |
---|
| 954 | // Find the join node |
---|
| 955 | void findJoinNode() { |
---|
[603] | 956 | int u = _source[in_arc]; |
---|
| 957 | int v = _target[in_arc]; |
---|
[601] | 958 | while (u != v) { |
---|
[604] | 959 | if (_succ_num[u] < _succ_num[v]) { |
---|
| 960 | u = _parent[u]; |
---|
| 961 | } else { |
---|
| 962 | v = _parent[v]; |
---|
| 963 | } |
---|
[601] | 964 | } |
---|
| 965 | join = u; |
---|
| 966 | } |
---|
| 967 | |
---|
| 968 | // Find the leaving arc of the cycle and returns true if the |
---|
| 969 | // leaving arc is not the same as the entering arc |
---|
| 970 | bool findLeavingArc() { |
---|
| 971 | // Initialize first and second nodes according to the direction |
---|
| 972 | // of the cycle |
---|
[603] | 973 | if (_state[in_arc] == STATE_LOWER) { |
---|
| 974 | first = _source[in_arc]; |
---|
| 975 | second = _target[in_arc]; |
---|
[601] | 976 | } else { |
---|
[603] | 977 | first = _target[in_arc]; |
---|
| 978 | second = _source[in_arc]; |
---|
[601] | 979 | } |
---|
[603] | 980 | delta = _cap[in_arc]; |
---|
[601] | 981 | int result = 0; |
---|
| 982 | Capacity d; |
---|
| 983 | int e; |
---|
| 984 | |
---|
| 985 | // Search the cycle along the path form the first node to the root |
---|
| 986 | for (int u = first; u != join; u = _parent[u]) { |
---|
| 987 | e = _pred[u]; |
---|
| 988 | d = _forward[u] ? _flow[e] : _cap[e] - _flow[e]; |
---|
| 989 | if (d < delta) { |
---|
| 990 | delta = d; |
---|
| 991 | u_out = u; |
---|
| 992 | result = 1; |
---|
| 993 | } |
---|
| 994 | } |
---|
| 995 | // Search the cycle along the path form the second node to the root |
---|
| 996 | for (int u = second; u != join; u = _parent[u]) { |
---|
| 997 | e = _pred[u]; |
---|
| 998 | d = _forward[u] ? _cap[e] - _flow[e] : _flow[e]; |
---|
| 999 | if (d <= delta) { |
---|
| 1000 | delta = d; |
---|
| 1001 | u_out = u; |
---|
| 1002 | result = 2; |
---|
| 1003 | } |
---|
| 1004 | } |
---|
| 1005 | |
---|
| 1006 | if (result == 1) { |
---|
| 1007 | u_in = first; |
---|
| 1008 | v_in = second; |
---|
| 1009 | } else { |
---|
| 1010 | u_in = second; |
---|
| 1011 | v_in = first; |
---|
| 1012 | } |
---|
| 1013 | return result != 0; |
---|
| 1014 | } |
---|
| 1015 | |
---|
| 1016 | // Change _flow and _state vectors |
---|
| 1017 | void changeFlow(bool change) { |
---|
| 1018 | // Augment along the cycle |
---|
| 1019 | if (delta > 0) { |
---|
[603] | 1020 | Capacity val = _state[in_arc] * delta; |
---|
| 1021 | _flow[in_arc] += val; |
---|
| 1022 | for (int u = _source[in_arc]; u != join; u = _parent[u]) { |
---|
[601] | 1023 | _flow[_pred[u]] += _forward[u] ? -val : val; |
---|
| 1024 | } |
---|
[603] | 1025 | for (int u = _target[in_arc]; u != join; u = _parent[u]) { |
---|
[601] | 1026 | _flow[_pred[u]] += _forward[u] ? val : -val; |
---|
| 1027 | } |
---|
| 1028 | } |
---|
| 1029 | // Update the state of the entering and leaving arcs |
---|
| 1030 | if (change) { |
---|
[603] | 1031 | _state[in_arc] = STATE_TREE; |
---|
[601] | 1032 | _state[_pred[u_out]] = |
---|
| 1033 | (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER; |
---|
| 1034 | } else { |
---|
[603] | 1035 | _state[in_arc] = -_state[in_arc]; |
---|
[601] | 1036 | } |
---|
| 1037 | } |
---|
| 1038 | |
---|
[604] | 1039 | // Update the tree structure |
---|
| 1040 | void updateTreeStructure() { |
---|
| 1041 | int u, w; |
---|
| 1042 | int old_rev_thread = _rev_thread[u_out]; |
---|
| 1043 | int old_succ_num = _succ_num[u_out]; |
---|
| 1044 | int old_last_succ = _last_succ[u_out]; |
---|
[601] | 1045 | v_out = _parent[u_out]; |
---|
| 1046 | |
---|
[604] | 1047 | u = _last_succ[u_in]; // the last successor of u_in |
---|
| 1048 | right = _thread[u]; // the node after it |
---|
| 1049 | |
---|
| 1050 | // Handle the case when old_rev_thread equals to v_in |
---|
| 1051 | // (it also means that join and v_out coincide) |
---|
| 1052 | if (old_rev_thread == v_in) { |
---|
| 1053 | last = _thread[_last_succ[u_out]]; |
---|
| 1054 | } else { |
---|
| 1055 | last = _thread[v_in]; |
---|
[601] | 1056 | } |
---|
| 1057 | |
---|
[604] | 1058 | // Update _thread and _parent along the stem nodes (i.e. the nodes |
---|
| 1059 | // between u_in and u_out, whose parent have to be changed) |
---|
[601] | 1060 | _thread[v_in] = stem = u_in; |
---|
[604] | 1061 | _dirty_revs.clear(); |
---|
| 1062 | _dirty_revs.push_back(v_in); |
---|
[601] | 1063 | par_stem = v_in; |
---|
| 1064 | while (stem != u_out) { |
---|
[604] | 1065 | // Insert the next stem node into the thread list |
---|
| 1066 | new_stem = _parent[stem]; |
---|
| 1067 | _thread[u] = new_stem; |
---|
| 1068 | _dirty_revs.push_back(u); |
---|
[601] | 1069 | |
---|
[604] | 1070 | // Remove the subtree of stem from the thread list |
---|
| 1071 | w = _rev_thread[stem]; |
---|
| 1072 | _thread[w] = right; |
---|
| 1073 | _rev_thread[right] = w; |
---|
[601] | 1074 | |
---|
[604] | 1075 | // Change the parent node and shift stem nodes |
---|
[601] | 1076 | _parent[stem] = par_stem; |
---|
| 1077 | par_stem = stem; |
---|
| 1078 | stem = new_stem; |
---|
| 1079 | |
---|
[604] | 1080 | // Update u and right |
---|
| 1081 | u = _last_succ[stem] == _last_succ[par_stem] ? |
---|
| 1082 | _rev_thread[par_stem] : _last_succ[stem]; |
---|
[601] | 1083 | right = _thread[u]; |
---|
| 1084 | } |
---|
| 1085 | _parent[u_out] = par_stem; |
---|
| 1086 | _thread[u] = last; |
---|
[604] | 1087 | _rev_thread[last] = u; |
---|
| 1088 | _last_succ[u_out] = u; |
---|
[601] | 1089 | |
---|
[604] | 1090 | // Remove the subtree of u_out from the thread list except for |
---|
| 1091 | // the case when old_rev_thread equals to v_in |
---|
| 1092 | // (it also means that join and v_out coincide) |
---|
| 1093 | if (old_rev_thread != v_in) { |
---|
| 1094 | _thread[old_rev_thread] = right; |
---|
| 1095 | _rev_thread[right] = old_rev_thread; |
---|
| 1096 | } |
---|
| 1097 | |
---|
| 1098 | // Update _rev_thread using the new _thread values |
---|
| 1099 | for (int i = 0; i < int(_dirty_revs.size()); ++i) { |
---|
| 1100 | u = _dirty_revs[i]; |
---|
| 1101 | _rev_thread[_thread[u]] = u; |
---|
| 1102 | } |
---|
| 1103 | |
---|
| 1104 | // Update _pred, _forward, _last_succ and _succ_num for the |
---|
| 1105 | // stem nodes from u_out to u_in |
---|
| 1106 | int tmp_sc = 0, tmp_ls = _last_succ[u_out]; |
---|
| 1107 | u = u_out; |
---|
| 1108 | while (u != u_in) { |
---|
| 1109 | w = _parent[u]; |
---|
| 1110 | _pred[u] = _pred[w]; |
---|
| 1111 | _forward[u] = !_forward[w]; |
---|
| 1112 | tmp_sc += _succ_num[u] - _succ_num[w]; |
---|
| 1113 | _succ_num[u] = tmp_sc; |
---|
| 1114 | _last_succ[w] = tmp_ls; |
---|
| 1115 | u = w; |
---|
| 1116 | } |
---|
| 1117 | _pred[u_in] = in_arc; |
---|
| 1118 | _forward[u_in] = (u_in == _source[in_arc]); |
---|
| 1119 | _succ_num[u_in] = old_succ_num; |
---|
| 1120 | |
---|
| 1121 | // Set limits for updating _last_succ form v_in and v_out |
---|
| 1122 | // towards the root |
---|
| 1123 | int up_limit_in = -1; |
---|
| 1124 | int up_limit_out = -1; |
---|
| 1125 | if (_last_succ[join] == v_in) { |
---|
| 1126 | up_limit_out = join; |
---|
[601] | 1127 | } else { |
---|
[604] | 1128 | up_limit_in = join; |
---|
| 1129 | } |
---|
| 1130 | |
---|
| 1131 | // Update _last_succ from v_in towards the root |
---|
| 1132 | for (u = v_in; u != up_limit_in && _last_succ[u] == v_in; |
---|
| 1133 | u = _parent[u]) { |
---|
| 1134 | _last_succ[u] = _last_succ[u_out]; |
---|
| 1135 | } |
---|
| 1136 | // Update _last_succ from v_out towards the root |
---|
| 1137 | if (join != old_rev_thread && v_in != old_rev_thread) { |
---|
| 1138 | for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; |
---|
| 1139 | u = _parent[u]) { |
---|
| 1140 | _last_succ[u] = old_rev_thread; |
---|
| 1141 | } |
---|
| 1142 | } else { |
---|
| 1143 | for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ; |
---|
| 1144 | u = _parent[u]) { |
---|
| 1145 | _last_succ[u] = _last_succ[u_out]; |
---|
| 1146 | } |
---|
| 1147 | } |
---|
| 1148 | |
---|
| 1149 | // Update _succ_num from v_in to join |
---|
| 1150 | for (u = v_in; u != join; u = _parent[u]) { |
---|
| 1151 | _succ_num[u] += old_succ_num; |
---|
| 1152 | } |
---|
| 1153 | // Update _succ_num from v_out to join |
---|
| 1154 | for (u = v_out; u != join; u = _parent[u]) { |
---|
| 1155 | _succ_num[u] -= old_succ_num; |
---|
[601] | 1156 | } |
---|
| 1157 | } |
---|
| 1158 | |
---|
[604] | 1159 | // Update potentials |
---|
| 1160 | void updatePotential() { |
---|
[601] | 1161 | Cost sigma = _forward[u_in] ? |
---|
| 1162 | _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] : |
---|
| 1163 | _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]]; |
---|
[604] | 1164 | if (_succ_num[u_in] > _node_num / 2) { |
---|
| 1165 | // Update in the upper subtree (which contains the root) |
---|
| 1166 | int before = _rev_thread[u_in]; |
---|
| 1167 | int after = _thread[_last_succ[u_in]]; |
---|
| 1168 | _thread[before] = after; |
---|
| 1169 | _pi[_root] -= sigma; |
---|
| 1170 | for (int u = _thread[_root]; u != _root; u = _thread[u]) { |
---|
| 1171 | _pi[u] -= sigma; |
---|
| 1172 | } |
---|
| 1173 | _thread[before] = u_in; |
---|
| 1174 | } else { |
---|
| 1175 | // Update in the lower subtree (which has been moved) |
---|
| 1176 | int end = _thread[_last_succ[u_in]]; |
---|
| 1177 | for (int u = u_in; u != end; u = _thread[u]) { |
---|
| 1178 | _pi[u] += sigma; |
---|
| 1179 | } |
---|
[601] | 1180 | } |
---|
| 1181 | } |
---|
| 1182 | |
---|
| 1183 | // Execute the algorithm |
---|
| 1184 | bool start(PivotRuleEnum pivot_rule) { |
---|
| 1185 | // Select the pivot rule implementation |
---|
| 1186 | switch (pivot_rule) { |
---|
| 1187 | case FIRST_ELIGIBLE_PIVOT: |
---|
| 1188 | return start<FirstEligiblePivotRule>(); |
---|
| 1189 | case BEST_ELIGIBLE_PIVOT: |
---|
| 1190 | return start<BestEligiblePivotRule>(); |
---|
| 1191 | case BLOCK_SEARCH_PIVOT: |
---|
| 1192 | return start<BlockSearchPivotRule>(); |
---|
| 1193 | case CANDIDATE_LIST_PIVOT: |
---|
| 1194 | return start<CandidateListPivotRule>(); |
---|
| 1195 | case ALTERING_LIST_PIVOT: |
---|
| 1196 | return start<AlteringListPivotRule>(); |
---|
| 1197 | } |
---|
| 1198 | return false; |
---|
| 1199 | } |
---|
| 1200 | |
---|
| 1201 | template<class PivotRuleImplementation> |
---|
| 1202 | bool start() { |
---|
| 1203 | PivotRuleImplementation pivot(*this); |
---|
| 1204 | |
---|
| 1205 | // Execute the network simplex algorithm |
---|
| 1206 | while (pivot.findEnteringArc()) { |
---|
| 1207 | findJoinNode(); |
---|
| 1208 | bool change = findLeavingArc(); |
---|
| 1209 | changeFlow(change); |
---|
| 1210 | if (change) { |
---|
[604] | 1211 | updateTreeStructure(); |
---|
| 1212 | updatePotential(); |
---|
[601] | 1213 | } |
---|
| 1214 | } |
---|
| 1215 | |
---|
| 1216 | // Check if the flow amount equals zero on all the artificial arcs |
---|
| 1217 | for (int e = _arc_num; e != _arc_num + _node_num; ++e) { |
---|
| 1218 | if (_flow[e] > 0) return false; |
---|
| 1219 | } |
---|
| 1220 | |
---|
[603] | 1221 | // Copy flow values to _flow_map |
---|
[601] | 1222 | if (_orig_lower) { |
---|
| 1223 | for (int i = 0; i != _arc_num; ++i) { |
---|
[603] | 1224 | Arc e = _arc_ref[i]; |
---|
| 1225 | _flow_map->set(e, (*_orig_lower)[e] + _flow[i]); |
---|
[601] | 1226 | } |
---|
| 1227 | } else { |
---|
| 1228 | for (int i = 0; i != _arc_num; ++i) { |
---|
[603] | 1229 | _flow_map->set(_arc_ref[i], _flow[i]); |
---|
[601] | 1230 | } |
---|
| 1231 | } |
---|
[603] | 1232 | // Copy potential values to _potential_map |
---|
| 1233 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
| 1234 | _potential_map->set(n, _pi[_node_id[n]]); |
---|
[601] | 1235 | } |
---|
| 1236 | |
---|
| 1237 | return true; |
---|
| 1238 | } |
---|
| 1239 | |
---|
| 1240 | }; //class NetworkSimplex |
---|
| 1241 | |
---|
| 1242 | ///@} |
---|
| 1243 | |
---|
| 1244 | } //namespace lemon |
---|
| 1245 | |
---|
| 1246 | #endif //LEMON_NETWORK_SIMPLEX_H |
---|