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