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_CIRCULATION_H |
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20 | #define LEMON_CIRCULATION_H |
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21 | |
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22 | #include <lemon/tolerance.h> |
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23 | #include <lemon/elevator.h> |
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24 | |
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25 | ///\ingroup max_flow |
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26 | ///\file |
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27 | ///\brief Push-relabel algorithm for finding a feasible circulation. |
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28 | /// |
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29 | namespace lemon { |
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30 | |
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31 | /// \brief Default traits class of Circulation class. |
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32 | /// |
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33 | /// Default traits class of Circulation class. |
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34 | /// \tparam GR Digraph type. |
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35 | /// \tparam LM Lower bound capacity map type. |
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36 | /// \tparam UM Upper bound capacity map type. |
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37 | /// \tparam DM Delta map type. |
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38 | template <typename GR, typename LM, |
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39 | typename UM, typename DM> |
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40 | struct CirculationDefaultTraits { |
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41 | |
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42 | /// \brief The type of the digraph the algorithm runs on. |
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43 | typedef GR Digraph; |
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44 | |
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45 | /// \brief The type of the map that stores the circulation lower |
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46 | /// bound. |
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47 | /// |
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48 | /// The type of the map that stores the circulation lower bound. |
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49 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
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50 | typedef LM LCapMap; |
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51 | |
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52 | /// \brief The type of the map that stores the circulation upper |
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53 | /// bound. |
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54 | /// |
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55 | /// The type of the map that stores the circulation upper bound. |
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56 | /// It must meet the \ref concepts::ReadMap "ReadMap" concept. |
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57 | typedef UM UCapMap; |
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58 | |
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59 | /// \brief The type of the map that stores the lower bound for |
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60 | /// the supply of the nodes. |
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61 | /// |
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62 | /// The type of the map that stores the lower bound for the supply |
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63 | /// of the nodes. It must meet the \ref concepts::ReadMap "ReadMap" |
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64 | /// concept. |
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65 | typedef DM DeltaMap; |
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66 | |
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67 | /// \brief The type of the flow values. |
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68 | typedef typename DeltaMap::Value Value; |
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69 | |
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70 | /// \brief The type of the map that stores the flow values. |
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71 | /// |
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72 | /// The type of the map that stores the flow values. |
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73 | /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept. |
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74 | typedef typename Digraph::template ArcMap<Value> FlowMap; |
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75 | |
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76 | /// \brief Instantiates a FlowMap. |
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77 | /// |
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78 | /// This function instantiates a \ref FlowMap. |
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79 | /// \param digraph The digraph, to which we would like to define |
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80 | /// the flow map. |
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81 | static FlowMap* createFlowMap(const Digraph& digraph) { |
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82 | return new FlowMap(digraph); |
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83 | } |
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84 | |
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85 | /// \brief The elevator type used by the algorithm. |
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86 | /// |
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87 | /// The elevator type used by the algorithm. |
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88 | /// |
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89 | /// \sa Elevator |
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90 | /// \sa LinkedElevator |
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91 | typedef lemon::Elevator<Digraph, typename Digraph::Node> Elevator; |
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92 | |
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93 | /// \brief Instantiates an Elevator. |
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94 | /// |
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95 | /// This function instantiates an \ref Elevator. |
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96 | /// \param digraph The digraph, to which we would like to define |
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97 | /// the elevator. |
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98 | /// \param max_level The maximum level of the elevator. |
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99 | static Elevator* createElevator(const Digraph& digraph, int max_level) { |
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100 | return new Elevator(digraph, max_level); |
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101 | } |
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102 | |
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103 | /// \brief The tolerance used by the algorithm |
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104 | /// |
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105 | /// The tolerance used by the algorithm to handle inexact computation. |
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106 | typedef lemon::Tolerance<Value> Tolerance; |
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107 | |
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108 | }; |
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109 | |
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110 | /** |
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111 | \brief Push-relabel algorithm for the network circulation problem. |
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112 | |
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113 | \ingroup max_flow |
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114 | This class implements a push-relabel algorithm for the network |
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115 | circulation problem. |
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116 | It is to find a feasible circulation when lower and upper bounds |
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117 | are given for the flow values on the arcs and lower bounds |
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118 | are given for the supply values of the nodes. |
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119 | |
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120 | The exact formulation of this problem is the following. |
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121 | Let \f$G=(V,A)\f$ be a digraph, |
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122 | \f$lower, upper: A\rightarrow\mathbf{R}^+_0\f$, |
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123 | \f$delta: V\rightarrow\mathbf{R}\f$. Find a feasible circulation |
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124 | \f$f: A\rightarrow\mathbf{R}^+_0\f$ so that |
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125 | \f[ \sum_{a\in\delta_{out}(v)} f(a) - \sum_{a\in\delta_{in}(v)} f(a) |
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126 | \geq delta(v) \quad \forall v\in V, \f] |
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127 | \f[ lower(a)\leq f(a) \leq upper(a) \quad \forall a\in A. \f] |
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128 | \note \f$delta(v)\f$ specifies a lower bound for the supply of node |
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129 | \f$v\f$. It can be either positive or negative, however note that |
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130 | \f$\sum_{v\in V}delta(v)\f$ should be zero or negative in order to |
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131 | have a feasible solution. |
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132 | |
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133 | \note A special case of this problem is when |
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134 | \f$\sum_{v\in V}delta(v) = 0\f$. Then the supply of each node \f$v\f$ |
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135 | will be \e equal \e to \f$delta(v)\f$, if a circulation can be found. |
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136 | Thus a feasible solution for the |
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137 | \ref min_cost_flow "minimum cost flow" problem can be calculated |
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138 | in this way. |
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139 | |
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140 | \tparam GR The type of the digraph the algorithm runs on. |
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141 | \tparam LM The type of the lower bound capacity map. The default |
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142 | map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
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143 | \tparam UM The type of the upper bound capacity map. The default |
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144 | map type is \c LM. |
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145 | \tparam DM The type of the map that stores the lower bound |
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146 | for the supply of the nodes. The default map type is |
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147 | \ref concepts::Digraph::NodeMap "GR::NodeMap<UM::Value>". |
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148 | */ |
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149 | #ifdef DOXYGEN |
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150 | template< typename GR, |
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151 | typename LM, |
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152 | typename UM, |
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153 | typename DM, |
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154 | typename TR > |
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155 | #else |
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156 | template< typename GR, |
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157 | typename LM = typename GR::template ArcMap<int>, |
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158 | typename UM = LM, |
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159 | typename DM = typename GR::template NodeMap<typename UM::Value>, |
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160 | typename TR = CirculationDefaultTraits<GR, LM, UM, DM> > |
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161 | #endif |
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162 | class Circulation { |
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163 | public: |
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164 | |
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165 | ///The \ref CirculationDefaultTraits "traits class" of the algorithm. |
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166 | typedef TR Traits; |
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167 | ///The type of the digraph the algorithm runs on. |
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168 | typedef typename Traits::Digraph Digraph; |
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169 | ///The type of the flow values. |
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170 | typedef typename Traits::Value Value; |
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171 | |
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172 | /// The type of the lower bound capacity map. |
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173 | typedef typename Traits::LCapMap LCapMap; |
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174 | /// The type of the upper bound capacity map. |
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175 | typedef typename Traits::UCapMap UCapMap; |
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176 | /// \brief The type of the map that stores the lower bound for |
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177 | /// the supply of the nodes. |
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178 | typedef typename Traits::DeltaMap DeltaMap; |
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179 | ///The type of the flow map. |
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180 | typedef typename Traits::FlowMap FlowMap; |
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181 | |
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182 | ///The type of the elevator. |
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183 | typedef typename Traits::Elevator Elevator; |
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184 | ///The type of the tolerance. |
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185 | typedef typename Traits::Tolerance Tolerance; |
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186 | |
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187 | private: |
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188 | |
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189 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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190 | |
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191 | const Digraph &_g; |
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192 | int _node_num; |
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193 | |
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194 | const LCapMap *_lo; |
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195 | const UCapMap *_up; |
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196 | const DeltaMap *_delta; |
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197 | |
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198 | FlowMap *_flow; |
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199 | bool _local_flow; |
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200 | |
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201 | Elevator* _level; |
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202 | bool _local_level; |
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203 | |
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204 | typedef typename Digraph::template NodeMap<Value> ExcessMap; |
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205 | ExcessMap* _excess; |
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206 | |
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207 | Tolerance _tol; |
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208 | int _el; |
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209 | |
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210 | public: |
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211 | |
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212 | typedef Circulation Create; |
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213 | |
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214 | ///\name Named Template Parameters |
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215 | |
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216 | ///@{ |
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217 | |
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218 | template <typename T> |
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219 | struct SetFlowMapTraits : public Traits { |
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220 | typedef T FlowMap; |
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221 | static FlowMap *createFlowMap(const Digraph&) { |
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222 | LEMON_ASSERT(false, "FlowMap is not initialized"); |
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223 | return 0; // ignore warnings |
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224 | } |
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225 | }; |
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226 | |
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227 | /// \brief \ref named-templ-param "Named parameter" for setting |
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228 | /// FlowMap type |
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229 | /// |
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230 | /// \ref named-templ-param "Named parameter" for setting FlowMap |
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231 | /// type. |
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232 | template <typename T> |
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233 | struct SetFlowMap |
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234 | : public Circulation<Digraph, LCapMap, UCapMap, DeltaMap, |
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235 | SetFlowMapTraits<T> > { |
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236 | typedef Circulation<Digraph, LCapMap, UCapMap, DeltaMap, |
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237 | SetFlowMapTraits<T> > Create; |
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238 | }; |
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239 | |
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240 | template <typename T> |
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241 | struct SetElevatorTraits : public Traits { |
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242 | typedef T Elevator; |
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243 | static Elevator *createElevator(const Digraph&, int) { |
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244 | LEMON_ASSERT(false, "Elevator is not initialized"); |
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245 | return 0; // ignore warnings |
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246 | } |
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247 | }; |
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248 | |
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249 | /// \brief \ref named-templ-param "Named parameter" for setting |
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250 | /// Elevator type |
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251 | /// |
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252 | /// \ref named-templ-param "Named parameter" for setting Elevator |
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253 | /// type. If this named parameter is used, then an external |
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254 | /// elevator object must be passed to the algorithm using the |
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255 | /// \ref elevator(Elevator&) "elevator()" function before calling |
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256 | /// \ref run() or \ref init(). |
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257 | /// \sa SetStandardElevator |
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258 | template <typename T> |
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259 | struct SetElevator |
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260 | : public Circulation<Digraph, LCapMap, UCapMap, DeltaMap, |
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261 | SetElevatorTraits<T> > { |
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262 | typedef Circulation<Digraph, LCapMap, UCapMap, DeltaMap, |
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263 | SetElevatorTraits<T> > Create; |
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264 | }; |
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265 | |
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266 | template <typename T> |
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267 | struct SetStandardElevatorTraits : public Traits { |
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268 | typedef T Elevator; |
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269 | static Elevator *createElevator(const Digraph& digraph, int max_level) { |
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270 | return new Elevator(digraph, max_level); |
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271 | } |
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272 | }; |
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273 | |
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274 | /// \brief \ref named-templ-param "Named parameter" for setting |
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275 | /// Elevator type with automatic allocation |
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276 | /// |
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277 | /// \ref named-templ-param "Named parameter" for setting Elevator |
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278 | /// type with automatic allocation. |
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279 | /// The Elevator should have standard constructor interface to be |
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280 | /// able to automatically created by the algorithm (i.e. the |
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281 | /// digraph and the maximum level should be passed to it). |
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282 | /// However an external elevator object could also be passed to the |
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283 | /// algorithm with the \ref elevator(Elevator&) "elevator()" function |
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284 | /// before calling \ref run() or \ref init(). |
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285 | /// \sa SetElevator |
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286 | template <typename T> |
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287 | struct SetStandardElevator |
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288 | : public Circulation<Digraph, LCapMap, UCapMap, DeltaMap, |
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289 | SetStandardElevatorTraits<T> > { |
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290 | typedef Circulation<Digraph, LCapMap, UCapMap, DeltaMap, |
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291 | SetStandardElevatorTraits<T> > Create; |
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292 | }; |
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293 | |
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294 | /// @} |
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295 | |
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296 | protected: |
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297 | |
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298 | Circulation() {} |
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299 | |
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300 | public: |
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301 | |
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302 | /// The constructor of the class. |
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303 | |
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304 | /// The constructor of the class. |
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305 | /// \param g The digraph the algorithm runs on. |
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306 | /// \param lo The lower bound capacity of the arcs. |
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307 | /// \param up The upper bound capacity of the arcs. |
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308 | /// \param delta The lower bound for the supply of the nodes. |
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309 | Circulation(const Digraph &g,const LCapMap &lo, |
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310 | const UCapMap &up,const DeltaMap &delta) |
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311 | : _g(g), _node_num(), |
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312 | _lo(&lo),_up(&up),_delta(&delta),_flow(0),_local_flow(false), |
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313 | _level(0), _local_level(false), _excess(0), _el() {} |
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314 | |
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315 | /// Destructor. |
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316 | ~Circulation() { |
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317 | destroyStructures(); |
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318 | } |
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319 | |
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320 | |
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321 | private: |
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322 | |
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323 | void createStructures() { |
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324 | _node_num = _el = countNodes(_g); |
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325 | |
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326 | if (!_flow) { |
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327 | _flow = Traits::createFlowMap(_g); |
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328 | _local_flow = true; |
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329 | } |
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330 | if (!_level) { |
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331 | _level = Traits::createElevator(_g, _node_num); |
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332 | _local_level = true; |
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333 | } |
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334 | if (!_excess) { |
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335 | _excess = new ExcessMap(_g); |
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336 | } |
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337 | } |
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338 | |
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339 | void destroyStructures() { |
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340 | if (_local_flow) { |
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341 | delete _flow; |
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342 | } |
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343 | if (_local_level) { |
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344 | delete _level; |
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345 | } |
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346 | if (_excess) { |
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347 | delete _excess; |
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348 | } |
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349 | } |
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350 | |
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351 | public: |
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352 | |
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353 | /// Sets the lower bound capacity map. |
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354 | |
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355 | /// Sets the lower bound capacity map. |
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356 | /// \return <tt>(*this)</tt> |
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357 | Circulation& lowerCapMap(const LCapMap& map) { |
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358 | _lo = ↦ |
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359 | return *this; |
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360 | } |
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361 | |
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362 | /// Sets the upper bound capacity map. |
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363 | |
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364 | /// Sets the upper bound capacity map. |
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365 | /// \return <tt>(*this)</tt> |
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366 | Circulation& upperCapMap(const LCapMap& map) { |
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367 | _up = ↦ |
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368 | return *this; |
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369 | } |
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370 | |
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371 | /// Sets the lower bound map for the supply of the nodes. |
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372 | |
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373 | /// Sets the lower bound map for the supply of the nodes. |
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374 | /// \return <tt>(*this)</tt> |
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375 | Circulation& deltaMap(const DeltaMap& map) { |
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376 | _delta = ↦ |
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377 | return *this; |
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378 | } |
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379 | |
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380 | /// \brief Sets the flow map. |
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381 | /// |
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382 | /// Sets the flow map. |
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383 | /// If you don't use this function before calling \ref run() or |
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384 | /// \ref init(), an instance will be allocated automatically. |
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385 | /// The destructor deallocates this automatically allocated map, |
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386 | /// of course. |
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387 | /// \return <tt>(*this)</tt> |
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388 | Circulation& flowMap(FlowMap& map) { |
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389 | if (_local_flow) { |
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390 | delete _flow; |
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391 | _local_flow = false; |
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392 | } |
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393 | _flow = ↦ |
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394 | return *this; |
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395 | } |
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396 | |
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397 | /// \brief Sets the elevator used by algorithm. |
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398 | /// |
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399 | /// Sets the elevator used by algorithm. |
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400 | /// If you don't use this function before calling \ref run() or |
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401 | /// \ref init(), an instance will be allocated automatically. |
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402 | /// The destructor deallocates this automatically allocated elevator, |
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403 | /// of course. |
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404 | /// \return <tt>(*this)</tt> |
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405 | Circulation& elevator(Elevator& elevator) { |
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406 | if (_local_level) { |
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407 | delete _level; |
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408 | _local_level = false; |
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409 | } |
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410 | _level = &elevator; |
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411 | return *this; |
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412 | } |
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413 | |
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414 | /// \brief Returns a const reference to the elevator. |
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415 | /// |
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416 | /// Returns a const reference to the elevator. |
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417 | /// |
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418 | /// \pre Either \ref run() or \ref init() must be called before |
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419 | /// using this function. |
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420 | const Elevator& elevator() const { |
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421 | return *_level; |
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422 | } |
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423 | |
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424 | /// \brief Sets the tolerance used by algorithm. |
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425 | /// |
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426 | /// Sets the tolerance used by algorithm. |
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427 | Circulation& tolerance(const Tolerance& tolerance) const { |
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428 | _tol = tolerance; |
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429 | return *this; |
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430 | } |
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431 | |
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432 | /// \brief Returns a const reference to the tolerance. |
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433 | /// |
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434 | /// Returns a const reference to the tolerance. |
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435 | const Tolerance& tolerance() const { |
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436 | return tolerance; |
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437 | } |
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438 | |
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439 | /// \name Execution Control |
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440 | /// The simplest way to execute the algorithm is to call \ref run().\n |
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441 | /// If you need more control on the initial solution or the execution, |
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442 | /// first you have to call one of the \ref init() functions, then |
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443 | /// the \ref start() function. |
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444 | |
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445 | ///@{ |
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446 | |
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447 | /// Initializes the internal data structures. |
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448 | |
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449 | /// Initializes the internal data structures and sets all flow values |
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450 | /// to the lower bound. |
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451 | void init() |
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452 | { |
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453 | createStructures(); |
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454 | |
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455 | for(NodeIt n(_g);n!=INVALID;++n) { |
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456 | (*_excess)[n] = (*_delta)[n]; |
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457 | } |
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458 | |
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459 | for (ArcIt e(_g);e!=INVALID;++e) { |
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460 | _flow->set(e, (*_lo)[e]); |
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461 | (*_excess)[_g.target(e)] += (*_flow)[e]; |
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462 | (*_excess)[_g.source(e)] -= (*_flow)[e]; |
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463 | } |
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464 | |
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465 | // global relabeling tested, but in general case it provides |
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466 | // worse performance for random digraphs |
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467 | _level->initStart(); |
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468 | for(NodeIt n(_g);n!=INVALID;++n) |
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469 | _level->initAddItem(n); |
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470 | _level->initFinish(); |
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471 | for(NodeIt n(_g);n!=INVALID;++n) |
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472 | if(_tol.positive((*_excess)[n])) |
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473 | _level->activate(n); |
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474 | } |
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475 | |
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476 | /// Initializes the internal data structures using a greedy approach. |
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477 | |
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478 | /// Initializes the internal data structures using a greedy approach |
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479 | /// to construct the initial solution. |
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480 | void greedyInit() |
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481 | { |
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482 | createStructures(); |
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483 | |
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484 | for(NodeIt n(_g);n!=INVALID;++n) { |
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485 | (*_excess)[n] = (*_delta)[n]; |
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486 | } |
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487 | |
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488 | for (ArcIt e(_g);e!=INVALID;++e) { |
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489 | if (!_tol.positive((*_excess)[_g.target(e)] + (*_up)[e])) { |
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490 | _flow->set(e, (*_up)[e]); |
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491 | (*_excess)[_g.target(e)] += (*_up)[e]; |
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492 | (*_excess)[_g.source(e)] -= (*_up)[e]; |
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493 | } else if (_tol.positive((*_excess)[_g.target(e)] + (*_lo)[e])) { |
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494 | _flow->set(e, (*_lo)[e]); |
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495 | (*_excess)[_g.target(e)] += (*_lo)[e]; |
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496 | (*_excess)[_g.source(e)] -= (*_lo)[e]; |
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497 | } else { |
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498 | Value fc = -(*_excess)[_g.target(e)]; |
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499 | _flow->set(e, fc); |
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500 | (*_excess)[_g.target(e)] = 0; |
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501 | (*_excess)[_g.source(e)] -= fc; |
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502 | } |
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503 | } |
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504 | |
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505 | _level->initStart(); |
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506 | for(NodeIt n(_g);n!=INVALID;++n) |
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507 | _level->initAddItem(n); |
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508 | _level->initFinish(); |
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509 | for(NodeIt n(_g);n!=INVALID;++n) |
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510 | if(_tol.positive((*_excess)[n])) |
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511 | _level->activate(n); |
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512 | } |
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513 | |
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514 | ///Executes the algorithm |
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515 | |
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516 | ///This function executes the algorithm. |
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517 | /// |
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518 | ///\return \c true if a feasible circulation is found. |
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519 | /// |
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520 | ///\sa barrier() |
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521 | ///\sa barrierMap() |
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522 | bool start() |
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523 | { |
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524 | |
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525 | Node act; |
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526 | Node bact=INVALID; |
---|
527 | Node last_activated=INVALID; |
---|
528 | while((act=_level->highestActive())!=INVALID) { |
---|
529 | int actlevel=(*_level)[act]; |
---|
530 | int mlevel=_node_num; |
---|
531 | Value exc=(*_excess)[act]; |
---|
532 | |
---|
533 | for(OutArcIt e(_g,act);e!=INVALID; ++e) { |
---|
534 | Node v = _g.target(e); |
---|
535 | Value fc=(*_up)[e]-(*_flow)[e]; |
---|
536 | if(!_tol.positive(fc)) continue; |
---|
537 | if((*_level)[v]<actlevel) { |
---|
538 | if(!_tol.less(fc, exc)) { |
---|
539 | _flow->set(e, (*_flow)[e] + exc); |
---|
540 | (*_excess)[v] += exc; |
---|
541 | if(!_level->active(v) && _tol.positive((*_excess)[v])) |
---|
542 | _level->activate(v); |
---|
543 | (*_excess)[act] = 0; |
---|
544 | _level->deactivate(act); |
---|
545 | goto next_l; |
---|
546 | } |
---|
547 | else { |
---|
548 | _flow->set(e, (*_up)[e]); |
---|
549 | (*_excess)[v] += fc; |
---|
550 | if(!_level->active(v) && _tol.positive((*_excess)[v])) |
---|
551 | _level->activate(v); |
---|
552 | exc-=fc; |
---|
553 | } |
---|
554 | } |
---|
555 | else if((*_level)[v]<mlevel) mlevel=(*_level)[v]; |
---|
556 | } |
---|
557 | for(InArcIt e(_g,act);e!=INVALID; ++e) { |
---|
558 | Node v = _g.source(e); |
---|
559 | Value fc=(*_flow)[e]-(*_lo)[e]; |
---|
560 | if(!_tol.positive(fc)) continue; |
---|
561 | if((*_level)[v]<actlevel) { |
---|
562 | if(!_tol.less(fc, exc)) { |
---|
563 | _flow->set(e, (*_flow)[e] - exc); |
---|
564 | (*_excess)[v] += exc; |
---|
565 | if(!_level->active(v) && _tol.positive((*_excess)[v])) |
---|
566 | _level->activate(v); |
---|
567 | (*_excess)[act] = 0; |
---|
568 | _level->deactivate(act); |
---|
569 | goto next_l; |
---|
570 | } |
---|
571 | else { |
---|
572 | _flow->set(e, (*_lo)[e]); |
---|
573 | (*_excess)[v] += fc; |
---|
574 | if(!_level->active(v) && _tol.positive((*_excess)[v])) |
---|
575 | _level->activate(v); |
---|
576 | exc-=fc; |
---|
577 | } |
---|
578 | } |
---|
579 | else if((*_level)[v]<mlevel) mlevel=(*_level)[v]; |
---|
580 | } |
---|
581 | |
---|
582 | (*_excess)[act] = exc; |
---|
583 | if(!_tol.positive(exc)) _level->deactivate(act); |
---|
584 | else if(mlevel==_node_num) { |
---|
585 | _level->liftHighestActiveToTop(); |
---|
586 | _el = _node_num; |
---|
587 | return false; |
---|
588 | } |
---|
589 | else { |
---|
590 | _level->liftHighestActive(mlevel+1); |
---|
591 | if(_level->onLevel(actlevel)==0) { |
---|
592 | _el = actlevel; |
---|
593 | return false; |
---|
594 | } |
---|
595 | } |
---|
596 | next_l: |
---|
597 | ; |
---|
598 | } |
---|
599 | return true; |
---|
600 | } |
---|
601 | |
---|
602 | /// Runs the algorithm. |
---|
603 | |
---|
604 | /// This function runs the algorithm. |
---|
605 | /// |
---|
606 | /// \return \c true if a feasible circulation is found. |
---|
607 | /// |
---|
608 | /// \note Apart from the return value, c.run() is just a shortcut of |
---|
609 | /// the following code. |
---|
610 | /// \code |
---|
611 | /// c.greedyInit(); |
---|
612 | /// c.start(); |
---|
613 | /// \endcode |
---|
614 | bool run() { |
---|
615 | greedyInit(); |
---|
616 | return start(); |
---|
617 | } |
---|
618 | |
---|
619 | /// @} |
---|
620 | |
---|
621 | /// \name Query Functions |
---|
622 | /// The results of the circulation algorithm can be obtained using |
---|
623 | /// these functions.\n |
---|
624 | /// Either \ref run() or \ref start() should be called before |
---|
625 | /// using them. |
---|
626 | |
---|
627 | ///@{ |
---|
628 | |
---|
629 | /// \brief Returns the flow on the given arc. |
---|
630 | /// |
---|
631 | /// Returns the flow on the given arc. |
---|
632 | /// |
---|
633 | /// \pre Either \ref run() or \ref init() must be called before |
---|
634 | /// using this function. |
---|
635 | Value flow(const Arc& arc) const { |
---|
636 | return (*_flow)[arc]; |
---|
637 | } |
---|
638 | |
---|
639 | /// \brief Returns a const reference to the flow map. |
---|
640 | /// |
---|
641 | /// Returns a const reference to the arc map storing the found flow. |
---|
642 | /// |
---|
643 | /// \pre Either \ref run() or \ref init() must be called before |
---|
644 | /// using this function. |
---|
645 | const FlowMap& flowMap() const { |
---|
646 | return *_flow; |
---|
647 | } |
---|
648 | |
---|
649 | /** |
---|
650 | \brief Returns \c true if the given node is in a barrier. |
---|
651 | |
---|
652 | Barrier is a set \e B of nodes for which |
---|
653 | |
---|
654 | \f[ \sum_{a\in\delta_{out}(B)} upper(a) - |
---|
655 | \sum_{a\in\delta_{in}(B)} lower(a) < \sum_{v\in B}delta(v) \f] |
---|
656 | |
---|
657 | holds. The existence of a set with this property prooves that a |
---|
658 | feasible circualtion cannot exist. |
---|
659 | |
---|
660 | This function returns \c true if the given node is in the found |
---|
661 | barrier. If a feasible circulation is found, the function |
---|
662 | gives back \c false for every node. |
---|
663 | |
---|
664 | \pre Either \ref run() or \ref init() must be called before |
---|
665 | using this function. |
---|
666 | |
---|
667 | \sa barrierMap() |
---|
668 | \sa checkBarrier() |
---|
669 | */ |
---|
670 | bool barrier(const Node& node) const |
---|
671 | { |
---|
672 | return (*_level)[node] >= _el; |
---|
673 | } |
---|
674 | |
---|
675 | /// \brief Gives back a barrier. |
---|
676 | /// |
---|
677 | /// This function sets \c bar to the characteristic vector of the |
---|
678 | /// found barrier. \c bar should be a \ref concepts::WriteMap "writable" |
---|
679 | /// node map with \c bool (or convertible) value type. |
---|
680 | /// |
---|
681 | /// If a feasible circulation is found, the function gives back an |
---|
682 | /// empty set, so \c bar[v] will be \c false for all nodes \c v. |
---|
683 | /// |
---|
684 | /// \note This function calls \ref barrier() for each node, |
---|
685 | /// so it runs in O(n) time. |
---|
686 | /// |
---|
687 | /// \pre Either \ref run() or \ref init() must be called before |
---|
688 | /// using this function. |
---|
689 | /// |
---|
690 | /// \sa barrier() |
---|
691 | /// \sa checkBarrier() |
---|
692 | template<class BarrierMap> |
---|
693 | void barrierMap(BarrierMap &bar) const |
---|
694 | { |
---|
695 | for(NodeIt n(_g);n!=INVALID;++n) |
---|
696 | bar.set(n, (*_level)[n] >= _el); |
---|
697 | } |
---|
698 | |
---|
699 | /// @} |
---|
700 | |
---|
701 | /// \name Checker Functions |
---|
702 | /// The feasibility of the results can be checked using |
---|
703 | /// these functions.\n |
---|
704 | /// Either \ref run() or \ref start() should be called before |
---|
705 | /// using them. |
---|
706 | |
---|
707 | ///@{ |
---|
708 | |
---|
709 | ///Check if the found flow is a feasible circulation |
---|
710 | |
---|
711 | ///Check if the found flow is a feasible circulation, |
---|
712 | /// |
---|
713 | bool checkFlow() const { |
---|
714 | for(ArcIt e(_g);e!=INVALID;++e) |
---|
715 | if((*_flow)[e]<(*_lo)[e]||(*_flow)[e]>(*_up)[e]) return false; |
---|
716 | for(NodeIt n(_g);n!=INVALID;++n) |
---|
717 | { |
---|
718 | Value dif=-(*_delta)[n]; |
---|
719 | for(InArcIt e(_g,n);e!=INVALID;++e) dif-=(*_flow)[e]; |
---|
720 | for(OutArcIt e(_g,n);e!=INVALID;++e) dif+=(*_flow)[e]; |
---|
721 | if(_tol.negative(dif)) return false; |
---|
722 | } |
---|
723 | return true; |
---|
724 | } |
---|
725 | |
---|
726 | ///Check whether or not the last execution provides a barrier |
---|
727 | |
---|
728 | ///Check whether or not the last execution provides a barrier. |
---|
729 | ///\sa barrier() |
---|
730 | ///\sa barrierMap() |
---|
731 | bool checkBarrier() const |
---|
732 | { |
---|
733 | Value delta=0; |
---|
734 | for(NodeIt n(_g);n!=INVALID;++n) |
---|
735 | if(barrier(n)) |
---|
736 | delta-=(*_delta)[n]; |
---|
737 | for(ArcIt e(_g);e!=INVALID;++e) |
---|
738 | { |
---|
739 | Node s=_g.source(e); |
---|
740 | Node t=_g.target(e); |
---|
741 | if(barrier(s)&&!barrier(t)) delta+=(*_up)[e]; |
---|
742 | else if(barrier(t)&&!barrier(s)) delta-=(*_lo)[e]; |
---|
743 | } |
---|
744 | return _tol.negative(delta); |
---|
745 | } |
---|
746 | |
---|
747 | /// @} |
---|
748 | |
---|
749 | }; |
---|
750 | |
---|
751 | } |
---|
752 | |
---|
753 | #endif |
---|