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 | #include <limits> |
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25 | |
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26 | ///\ingroup max_flow |
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27 | ///\file |
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28 | ///\brief Push-relabel algorithm for finding a feasible circulation. |
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29 | /// |
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30 | namespace lemon { |
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31 | |
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32 | /// \brief Default traits class of Circulation class. |
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33 | /// |
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34 | /// Default traits class of Circulation class. |
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35 | /// |
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36 | /// \tparam GR Type of the digraph the algorithm runs on. |
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37 | /// \tparam LM The type of the lower bound map. |
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38 | /// \tparam UM The type of the upper bound (capacity) map. |
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39 | /// \tparam SM The type of the supply map. |
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40 | template <typename GR, typename LM, |
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41 | typename UM, typename SM> |
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42 | struct CirculationDefaultTraits { |
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43 | |
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44 | /// \brief The type of the digraph the algorithm runs on. |
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45 | typedef GR Digraph; |
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46 | |
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47 | /// \brief The type of the lower bound map. |
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48 | /// |
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49 | /// The type of the map that stores the lower bounds on the arcs. |
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50 | /// It must conform to the \ref concepts::ReadMap "ReadMap" concept. |
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51 | typedef LM LowerMap; |
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52 | |
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53 | /// \brief The type of the upper bound (capacity) map. |
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54 | /// |
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55 | /// The type of the map that stores the upper bounds (capacities) |
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56 | /// on the arcs. |
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57 | /// It must conform to the \ref concepts::ReadMap "ReadMap" concept. |
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58 | typedef UM UpperMap; |
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59 | |
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60 | /// \brief The type of supply map. |
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61 | /// |
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62 | /// The type of the map that stores the signed supply values of the |
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63 | /// nodes. |
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64 | /// It must conform to the \ref concepts::ReadMap "ReadMap" concept. |
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65 | typedef SM SupplyMap; |
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66 | |
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67 | /// \brief The type of the flow and supply values. |
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68 | typedef typename SupplyMap::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 conform to the \ref concepts::ReadWriteMap "ReadWriteMap" |
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74 | /// concept. |
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75 | #ifdef DOXYGEN |
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76 | typedef GR::ArcMap<Value> FlowMap; |
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77 | #else |
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78 | typedef typename Digraph::template ArcMap<Value> FlowMap; |
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79 | #endif |
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80 | |
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81 | /// \brief Instantiates a FlowMap. |
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82 | /// |
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83 | /// This function instantiates a \ref FlowMap. |
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84 | /// \param digraph The digraph for which we would like to define |
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85 | /// the flow map. |
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86 | static FlowMap* createFlowMap(const Digraph& digraph) { |
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87 | return new FlowMap(digraph); |
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88 | } |
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89 | |
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90 | /// \brief The elevator type used by the algorithm. |
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91 | /// |
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92 | /// The elevator type used by the algorithm. |
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93 | /// |
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94 | /// \sa Elevator, LinkedElevator |
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95 | #ifdef DOXYGEN |
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96 | typedef lemon::Elevator<GR, GR::Node> Elevator; |
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97 | #else |
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98 | typedef lemon::Elevator<Digraph, typename Digraph::Node> Elevator; |
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99 | #endif |
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100 | |
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101 | /// \brief Instantiates an Elevator. |
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102 | /// |
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103 | /// This function instantiates an \ref Elevator. |
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104 | /// \param digraph The digraph for which we would like to define |
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105 | /// the elevator. |
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106 | /// \param max_level The maximum level of the elevator. |
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107 | static Elevator* createElevator(const Digraph& digraph, int max_level) { |
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108 | return new Elevator(digraph, max_level); |
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109 | } |
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110 | |
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111 | /// \brief The tolerance used by the algorithm |
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112 | /// |
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113 | /// The tolerance used by the algorithm to handle inexact computation. |
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114 | typedef lemon::Tolerance<Value> Tolerance; |
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115 | |
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116 | }; |
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117 | |
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118 | /** |
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119 | \brief Push-relabel algorithm for the network circulation problem. |
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120 | |
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121 | \ingroup max_flow |
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122 | This class implements a push-relabel algorithm for the \e network |
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123 | \e circulation problem. |
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124 | It is to find a feasible circulation when lower and upper bounds |
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125 | are given for the flow values on the arcs and lower bounds are |
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126 | given for the difference between the outgoing and incoming flow |
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127 | at the nodes. |
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128 | |
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129 | The exact formulation of this problem is the following. |
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130 | Let \f$G=(V,A)\f$ be a digraph, \f$lower: A\rightarrow\mathbf{R}\f$ |
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131 | \f$upper: A\rightarrow\mathbf{R}\cup\{\infty\}\f$ denote the lower and |
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132 | upper bounds on the arcs, for which \f$lower(uv) \leq upper(uv)\f$ |
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133 | holds for all \f$uv\in A\f$, and \f$sup: V\rightarrow\mathbf{R}\f$ |
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134 | denotes the signed supply values of the nodes. |
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135 | If \f$sup(u)>0\f$, then \f$u\f$ is a supply node with \f$sup(u)\f$ |
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136 | supply, if \f$sup(u)<0\f$, then \f$u\f$ is a demand node with |
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137 | \f$-sup(u)\f$ demand. |
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138 | A feasible circulation is an \f$f: A\rightarrow\mathbf{R}\f$ |
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139 | solution of the following problem. |
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140 | |
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141 | \f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) |
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142 | \geq sup(u) \quad \forall u\in V, \f] |
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143 | \f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A. \f] |
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144 | |
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145 | The sum of the supply values, i.e. \f$\sum_{u\in V} sup(u)\f$ must be |
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146 | zero or negative in order to have a feasible solution (since the sum |
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147 | of the expressions on the left-hand side of the inequalities is zero). |
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148 | It means that the total demand must be greater or equal to the total |
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149 | supply and all the supplies have to be carried out from the supply nodes, |
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150 | but there could be demands that are not satisfied. |
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151 | If \f$\sum_{u\in V} sup(u)\f$ is zero, then all the supply/demand |
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152 | constraints have to be satisfied with equality, i.e. all demands |
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153 | have to be satisfied and all supplies have to be used. |
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154 | |
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155 | If you need the opposite inequalities in the supply/demand constraints |
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156 | (i.e. the total demand is less than the total supply and all the demands |
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157 | have to be satisfied while there could be supplies that are not used), |
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158 | then you could easily transform the problem to the above form by reversing |
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159 | the direction of the arcs and taking the negative of the supply values |
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160 | (e.g. using \ref ReverseDigraph and \ref NegMap adaptors). |
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161 | |
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162 | This algorithm either calculates a feasible circulation, or provides |
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163 | a \ref barrier() "barrier", which prooves that a feasible soultion |
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164 | cannot exist. |
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165 | |
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166 | Note that this algorithm also provides a feasible solution for the |
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167 | \ref min_cost_flow "minimum cost flow problem". |
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168 | |
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169 | \tparam GR The type of the digraph the algorithm runs on. |
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170 | \tparam LM The type of the lower bound map. The default |
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171 | map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
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172 | \tparam UM The type of the upper bound (capacity) map. |
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173 | The default map type is \c LM. |
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174 | \tparam SM The type of the supply map. The default map type is |
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175 | \ref concepts::Digraph::NodeMap "GR::NodeMap<UM::Value>". |
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176 | */ |
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177 | #ifdef DOXYGEN |
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178 | template< typename GR, |
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179 | typename LM, |
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180 | typename UM, |
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181 | typename SM, |
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182 | typename TR > |
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183 | #else |
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184 | template< typename GR, |
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185 | typename LM = typename GR::template ArcMap<int>, |
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186 | typename UM = LM, |
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187 | typename SM = typename GR::template NodeMap<typename UM::Value>, |
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188 | typename TR = CirculationDefaultTraits<GR, LM, UM, SM> > |
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189 | #endif |
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190 | class Circulation { |
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191 | public: |
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192 | |
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193 | ///The \ref CirculationDefaultTraits "traits class" of the algorithm. |
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194 | typedef TR Traits; |
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195 | ///The type of the digraph the algorithm runs on. |
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196 | typedef typename Traits::Digraph Digraph; |
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197 | ///The type of the flow and supply values. |
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198 | typedef typename Traits::Value Value; |
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199 | |
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200 | ///The type of the lower bound map. |
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201 | typedef typename Traits::LowerMap LowerMap; |
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202 | ///The type of the upper bound (capacity) map. |
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203 | typedef typename Traits::UpperMap UpperMap; |
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204 | ///The type of the supply map. |
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205 | typedef typename Traits::SupplyMap SupplyMap; |
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206 | ///The type of the flow map. |
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207 | typedef typename Traits::FlowMap FlowMap; |
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208 | |
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209 | ///The type of the elevator. |
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210 | typedef typename Traits::Elevator Elevator; |
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211 | ///The type of the tolerance. |
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212 | typedef typename Traits::Tolerance Tolerance; |
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213 | |
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214 | private: |
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215 | |
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216 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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217 | |
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218 | const Digraph &_g; |
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219 | int _node_num; |
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220 | |
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221 | const LowerMap *_lo; |
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222 | const UpperMap *_up; |
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223 | const SupplyMap *_supply; |
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224 | |
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225 | FlowMap *_flow; |
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226 | bool _local_flow; |
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227 | |
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228 | Elevator* _level; |
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229 | bool _local_level; |
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230 | |
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231 | typedef typename Digraph::template NodeMap<Value> ExcessMap; |
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232 | ExcessMap* _excess; |
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233 | |
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234 | Tolerance _tol; |
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235 | int _el; |
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236 | |
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237 | public: |
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238 | |
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239 | typedef Circulation Create; |
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240 | |
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241 | ///\name Named Template Parameters |
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242 | |
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243 | ///@{ |
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244 | |
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245 | template <typename T> |
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246 | struct SetFlowMapTraits : public Traits { |
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247 | typedef T FlowMap; |
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248 | static FlowMap *createFlowMap(const Digraph&) { |
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249 | LEMON_ASSERT(false, "FlowMap is not initialized"); |
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250 | return 0; // ignore warnings |
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251 | } |
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252 | }; |
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253 | |
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254 | /// \brief \ref named-templ-param "Named parameter" for setting |
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255 | /// FlowMap type |
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256 | /// |
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257 | /// \ref named-templ-param "Named parameter" for setting FlowMap |
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258 | /// type. |
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259 | template <typename T> |
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260 | struct SetFlowMap |
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261 | : public Circulation<Digraph, LowerMap, UpperMap, SupplyMap, |
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262 | SetFlowMapTraits<T> > { |
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263 | typedef Circulation<Digraph, LowerMap, UpperMap, SupplyMap, |
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264 | SetFlowMapTraits<T> > Create; |
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265 | }; |
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266 | |
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267 | template <typename T> |
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268 | struct SetElevatorTraits : public Traits { |
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269 | typedef T Elevator; |
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270 | static Elevator *createElevator(const Digraph&, int) { |
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271 | LEMON_ASSERT(false, "Elevator is not initialized"); |
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272 | return 0; // ignore warnings |
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273 | } |
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274 | }; |
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275 | |
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276 | /// \brief \ref named-templ-param "Named parameter" for setting |
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277 | /// Elevator type |
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278 | /// |
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279 | /// \ref named-templ-param "Named parameter" for setting Elevator |
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280 | /// type. If this named parameter is used, then an external |
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281 | /// elevator object must be passed to the algorithm using the |
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282 | /// \ref elevator(Elevator&) "elevator()" function before calling |
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283 | /// \ref run() or \ref init(). |
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284 | /// \sa SetStandardElevator |
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285 | template <typename T> |
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286 | struct SetElevator |
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287 | : public Circulation<Digraph, LowerMap, UpperMap, SupplyMap, |
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288 | SetElevatorTraits<T> > { |
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289 | typedef Circulation<Digraph, LowerMap, UpperMap, SupplyMap, |
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290 | SetElevatorTraits<T> > Create; |
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291 | }; |
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292 | |
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293 | template <typename T> |
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294 | struct SetStandardElevatorTraits : public Traits { |
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295 | typedef T Elevator; |
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296 | static Elevator *createElevator(const Digraph& digraph, int max_level) { |
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297 | return new Elevator(digraph, max_level); |
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298 | } |
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299 | }; |
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300 | |
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301 | /// \brief \ref named-templ-param "Named parameter" for setting |
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302 | /// Elevator type with automatic allocation |
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303 | /// |
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304 | /// \ref named-templ-param "Named parameter" for setting Elevator |
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305 | /// type with automatic allocation. |
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306 | /// The Elevator should have standard constructor interface to be |
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307 | /// able to automatically created by the algorithm (i.e. the |
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308 | /// digraph and the maximum level should be passed to it). |
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309 | /// However an external elevator object could also be passed to the |
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310 | /// algorithm with the \ref elevator(Elevator&) "elevator()" function |
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311 | /// before calling \ref run() or \ref init(). |
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312 | /// \sa SetElevator |
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313 | template <typename T> |
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314 | struct SetStandardElevator |
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315 | : public Circulation<Digraph, LowerMap, UpperMap, SupplyMap, |
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316 | SetStandardElevatorTraits<T> > { |
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317 | typedef Circulation<Digraph, LowerMap, UpperMap, SupplyMap, |
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318 | SetStandardElevatorTraits<T> > Create; |
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319 | }; |
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320 | |
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321 | /// @} |
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322 | |
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323 | protected: |
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324 | |
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325 | Circulation() {} |
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326 | |
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327 | public: |
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328 | |
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329 | /// Constructor. |
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330 | |
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331 | /// The constructor of the class. |
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332 | /// |
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333 | /// \param graph The digraph the algorithm runs on. |
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334 | /// \param lower The lower bounds for the flow values on the arcs. |
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335 | /// \param upper The upper bounds (capacities) for the flow values |
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336 | /// on the arcs. |
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337 | /// \param supply The signed supply values of the nodes. |
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338 | Circulation(const Digraph &graph, const LowerMap &lower, |
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339 | const UpperMap &upper, const SupplyMap &supply) |
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340 | : _g(graph), _lo(&lower), _up(&upper), _supply(&supply), |
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341 | _flow(NULL), _local_flow(false), _level(NULL), _local_level(false), |
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342 | _excess(NULL) {} |
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343 | |
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344 | /// Destructor. |
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345 | ~Circulation() { |
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346 | destroyStructures(); |
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347 | } |
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348 | |
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349 | |
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350 | private: |
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351 | |
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352 | bool checkBoundMaps() { |
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353 | for (ArcIt e(_g);e!=INVALID;++e) { |
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354 | if (_tol.less((*_up)[e], (*_lo)[e])) return false; |
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355 | } |
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356 | return true; |
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357 | } |
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358 | |
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359 | void createStructures() { |
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360 | _node_num = _el = countNodes(_g); |
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361 | |
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362 | if (!_flow) { |
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363 | _flow = Traits::createFlowMap(_g); |
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364 | _local_flow = true; |
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365 | } |
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366 | if (!_level) { |
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367 | _level = Traits::createElevator(_g, _node_num); |
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368 | _local_level = true; |
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369 | } |
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370 | if (!_excess) { |
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371 | _excess = new ExcessMap(_g); |
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372 | } |
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373 | } |
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374 | |
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375 | void destroyStructures() { |
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376 | if (_local_flow) { |
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377 | delete _flow; |
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378 | } |
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379 | if (_local_level) { |
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380 | delete _level; |
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381 | } |
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382 | if (_excess) { |
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383 | delete _excess; |
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384 | } |
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385 | } |
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386 | |
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387 | public: |
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388 | |
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389 | /// Sets the lower bound map. |
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390 | |
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391 | /// Sets the lower bound map. |
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392 | /// \return <tt>(*this)</tt> |
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393 | Circulation& lowerMap(const LowerMap& map) { |
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394 | _lo = ↦ |
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395 | return *this; |
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396 | } |
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397 | |
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398 | /// Sets the upper bound (capacity) map. |
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399 | |
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400 | /// Sets the upper bound (capacity) map. |
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401 | /// \return <tt>(*this)</tt> |
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402 | Circulation& upperMap(const UpperMap& map) { |
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403 | _up = ↦ |
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404 | return *this; |
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405 | } |
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406 | |
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407 | /// Sets the supply map. |
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408 | |
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409 | /// Sets the supply map. |
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410 | /// \return <tt>(*this)</tt> |
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411 | Circulation& supplyMap(const SupplyMap& map) { |
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412 | _supply = ↦ |
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413 | return *this; |
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414 | } |
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415 | |
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416 | /// \brief Sets the flow map. |
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417 | /// |
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418 | /// Sets the flow map. |
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419 | /// If you don't use this function before calling \ref run() or |
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420 | /// \ref init(), an instance will be allocated automatically. |
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421 | /// The destructor deallocates this automatically allocated map, |
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422 | /// of course. |
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423 | /// \return <tt>(*this)</tt> |
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424 | Circulation& flowMap(FlowMap& map) { |
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425 | if (_local_flow) { |
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426 | delete _flow; |
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427 | _local_flow = false; |
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428 | } |
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429 | _flow = ↦ |
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430 | return *this; |
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431 | } |
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432 | |
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433 | /// \brief Sets the elevator used by algorithm. |
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434 | /// |
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435 | /// Sets the elevator used by algorithm. |
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436 | /// If you don't use this function before calling \ref run() or |
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437 | /// \ref init(), an instance will be allocated automatically. |
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438 | /// The destructor deallocates this automatically allocated elevator, |
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439 | /// of course. |
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440 | /// \return <tt>(*this)</tt> |
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441 | Circulation& elevator(Elevator& elevator) { |
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442 | if (_local_level) { |
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443 | delete _level; |
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444 | _local_level = false; |
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445 | } |
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446 | _level = &elevator; |
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447 | return *this; |
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448 | } |
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449 | |
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450 | /// \brief Returns a const reference to the elevator. |
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451 | /// |
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452 | /// Returns a const reference to the elevator. |
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453 | /// |
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454 | /// \pre Either \ref run() or \ref init() must be called before |
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455 | /// using this function. |
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456 | const Elevator& elevator() const { |
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457 | return *_level; |
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458 | } |
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459 | |
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460 | /// \brief Sets the tolerance used by the algorithm. |
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461 | /// |
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462 | /// Sets the tolerance object used by the algorithm. |
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463 | /// \return <tt>(*this)</tt> |
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464 | Circulation& tolerance(const Tolerance& tolerance) { |
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465 | _tol = tolerance; |
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466 | return *this; |
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467 | } |
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468 | |
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469 | /// \brief Returns a const reference to the tolerance. |
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470 | /// |
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471 | /// Returns a const reference to the tolerance object used by |
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472 | /// the algorithm. |
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473 | const Tolerance& tolerance() const { |
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474 | return _tol; |
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475 | } |
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476 | |
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477 | /// \name Execution Control |
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478 | /// The simplest way to execute the algorithm is to call \ref run().\n |
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479 | /// If you need better control on the initial solution or the execution, |
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480 | /// you have to call one of the \ref init() functions first, then |
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481 | /// the \ref start() function. |
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482 | |
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483 | ///@{ |
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484 | |
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485 | /// Initializes the internal data structures. |
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486 | |
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487 | /// Initializes the internal data structures and sets all flow values |
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488 | /// to the lower bound. |
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489 | void init() |
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490 | { |
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491 | LEMON_DEBUG(checkBoundMaps(), |
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492 | "Upper bounds must be greater or equal to the lower bounds"); |
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493 | |
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494 | createStructures(); |
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495 | |
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496 | for(NodeIt n(_g);n!=INVALID;++n) { |
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497 | (*_excess)[n] = (*_supply)[n]; |
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498 | } |
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499 | |
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500 | for (ArcIt e(_g);e!=INVALID;++e) { |
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501 | _flow->set(e, (*_lo)[e]); |
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502 | (*_excess)[_g.target(e)] += (*_flow)[e]; |
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503 | (*_excess)[_g.source(e)] -= (*_flow)[e]; |
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504 | } |
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505 | |
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506 | // global relabeling tested, but in general case it provides |
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507 | // worse performance for random digraphs |
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508 | _level->initStart(); |
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509 | for(NodeIt n(_g);n!=INVALID;++n) |
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510 | _level->initAddItem(n); |
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511 | _level->initFinish(); |
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512 | for(NodeIt n(_g);n!=INVALID;++n) |
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513 | if(_tol.positive((*_excess)[n])) |
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514 | _level->activate(n); |
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515 | } |
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516 | |
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517 | /// Initializes the internal data structures using a greedy approach. |
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518 | |
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519 | /// Initializes the internal data structures using a greedy approach |
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520 | /// to construct the initial solution. |
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521 | void greedyInit() |
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522 | { |
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523 | LEMON_DEBUG(checkBoundMaps(), |
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524 | "Upper bounds must be greater or equal to the lower bounds"); |
---|
525 | |
---|
526 | createStructures(); |
---|
527 | |
---|
528 | for(NodeIt n(_g);n!=INVALID;++n) { |
---|
529 | (*_excess)[n] = (*_supply)[n]; |
---|
530 | } |
---|
531 | |
---|
532 | for (ArcIt e(_g);e!=INVALID;++e) { |
---|
533 | if (!_tol.less(-(*_excess)[_g.target(e)], (*_up)[e])) { |
---|
534 | _flow->set(e, (*_up)[e]); |
---|
535 | (*_excess)[_g.target(e)] += (*_up)[e]; |
---|
536 | (*_excess)[_g.source(e)] -= (*_up)[e]; |
---|
537 | } else if (_tol.less(-(*_excess)[_g.target(e)], (*_lo)[e])) { |
---|
538 | _flow->set(e, (*_lo)[e]); |
---|
539 | (*_excess)[_g.target(e)] += (*_lo)[e]; |
---|
540 | (*_excess)[_g.source(e)] -= (*_lo)[e]; |
---|
541 | } else { |
---|
542 | Value fc = -(*_excess)[_g.target(e)]; |
---|
543 | _flow->set(e, fc); |
---|
544 | (*_excess)[_g.target(e)] = 0; |
---|
545 | (*_excess)[_g.source(e)] -= fc; |
---|
546 | } |
---|
547 | } |
---|
548 | |
---|
549 | _level->initStart(); |
---|
550 | for(NodeIt n(_g);n!=INVALID;++n) |
---|
551 | _level->initAddItem(n); |
---|
552 | _level->initFinish(); |
---|
553 | for(NodeIt n(_g);n!=INVALID;++n) |
---|
554 | if(_tol.positive((*_excess)[n])) |
---|
555 | _level->activate(n); |
---|
556 | } |
---|
557 | |
---|
558 | ///Executes the algorithm |
---|
559 | |
---|
560 | ///This function executes the algorithm. |
---|
561 | /// |
---|
562 | ///\return \c true if a feasible circulation is found. |
---|
563 | /// |
---|
564 | ///\sa barrier() |
---|
565 | ///\sa barrierMap() |
---|
566 | bool start() |
---|
567 | { |
---|
568 | |
---|
569 | Node act; |
---|
570 | Node bact=INVALID; |
---|
571 | Node last_activated=INVALID; |
---|
572 | while((act=_level->highestActive())!=INVALID) { |
---|
573 | int actlevel=(*_level)[act]; |
---|
574 | int mlevel=_node_num; |
---|
575 | Value exc=(*_excess)[act]; |
---|
576 | |
---|
577 | for(OutArcIt e(_g,act);e!=INVALID; ++e) { |
---|
578 | Node v = _g.target(e); |
---|
579 | Value fc=(*_up)[e]-(*_flow)[e]; |
---|
580 | if(!_tol.positive(fc)) continue; |
---|
581 | if((*_level)[v]<actlevel) { |
---|
582 | if(!_tol.less(fc, exc)) { |
---|
583 | _flow->set(e, (*_flow)[e] + exc); |
---|
584 | (*_excess)[v] += exc; |
---|
585 | if(!_level->active(v) && _tol.positive((*_excess)[v])) |
---|
586 | _level->activate(v); |
---|
587 | (*_excess)[act] = 0; |
---|
588 | _level->deactivate(act); |
---|
589 | goto next_l; |
---|
590 | } |
---|
591 | else { |
---|
592 | _flow->set(e, (*_up)[e]); |
---|
593 | (*_excess)[v] += fc; |
---|
594 | if(!_level->active(v) && _tol.positive((*_excess)[v])) |
---|
595 | _level->activate(v); |
---|
596 | exc-=fc; |
---|
597 | } |
---|
598 | } |
---|
599 | else if((*_level)[v]<mlevel) mlevel=(*_level)[v]; |
---|
600 | } |
---|
601 | for(InArcIt e(_g,act);e!=INVALID; ++e) { |
---|
602 | Node v = _g.source(e); |
---|
603 | Value fc=(*_flow)[e]-(*_lo)[e]; |
---|
604 | if(!_tol.positive(fc)) continue; |
---|
605 | if((*_level)[v]<actlevel) { |
---|
606 | if(!_tol.less(fc, exc)) { |
---|
607 | _flow->set(e, (*_flow)[e] - exc); |
---|
608 | (*_excess)[v] += exc; |
---|
609 | if(!_level->active(v) && _tol.positive((*_excess)[v])) |
---|
610 | _level->activate(v); |
---|
611 | (*_excess)[act] = 0; |
---|
612 | _level->deactivate(act); |
---|
613 | goto next_l; |
---|
614 | } |
---|
615 | else { |
---|
616 | _flow->set(e, (*_lo)[e]); |
---|
617 | (*_excess)[v] += fc; |
---|
618 | if(!_level->active(v) && _tol.positive((*_excess)[v])) |
---|
619 | _level->activate(v); |
---|
620 | exc-=fc; |
---|
621 | } |
---|
622 | } |
---|
623 | else if((*_level)[v]<mlevel) mlevel=(*_level)[v]; |
---|
624 | } |
---|
625 | |
---|
626 | (*_excess)[act] = exc; |
---|
627 | if(!_tol.positive(exc)) _level->deactivate(act); |
---|
628 | else if(mlevel==_node_num) { |
---|
629 | _level->liftHighestActiveToTop(); |
---|
630 | _el = _node_num; |
---|
631 | return false; |
---|
632 | } |
---|
633 | else { |
---|
634 | _level->liftHighestActive(mlevel+1); |
---|
635 | if(_level->onLevel(actlevel)==0) { |
---|
636 | _el = actlevel; |
---|
637 | return false; |
---|
638 | } |
---|
639 | } |
---|
640 | next_l: |
---|
641 | ; |
---|
642 | } |
---|
643 | return true; |
---|
644 | } |
---|
645 | |
---|
646 | /// Runs the algorithm. |
---|
647 | |
---|
648 | /// This function runs the algorithm. |
---|
649 | /// |
---|
650 | /// \return \c true if a feasible circulation is found. |
---|
651 | /// |
---|
652 | /// \note Apart from the return value, c.run() is just a shortcut of |
---|
653 | /// the following code. |
---|
654 | /// \code |
---|
655 | /// c.greedyInit(); |
---|
656 | /// c.start(); |
---|
657 | /// \endcode |
---|
658 | bool run() { |
---|
659 | greedyInit(); |
---|
660 | return start(); |
---|
661 | } |
---|
662 | |
---|
663 | /// @} |
---|
664 | |
---|
665 | /// \name Query Functions |
---|
666 | /// The results of the circulation algorithm can be obtained using |
---|
667 | /// these functions.\n |
---|
668 | /// Either \ref run() or \ref start() should be called before |
---|
669 | /// using them. |
---|
670 | |
---|
671 | ///@{ |
---|
672 | |
---|
673 | /// \brief Returns the flow value on the given arc. |
---|
674 | /// |
---|
675 | /// Returns the flow value on the given arc. |
---|
676 | /// |
---|
677 | /// \pre Either \ref run() or \ref init() must be called before |
---|
678 | /// using this function. |
---|
679 | Value flow(const Arc& arc) const { |
---|
680 | return (*_flow)[arc]; |
---|
681 | } |
---|
682 | |
---|
683 | /// \brief Returns a const reference to the flow map. |
---|
684 | /// |
---|
685 | /// Returns a const reference to the arc map storing the found flow. |
---|
686 | /// |
---|
687 | /// \pre Either \ref run() or \ref init() must be called before |
---|
688 | /// using this function. |
---|
689 | const FlowMap& flowMap() const { |
---|
690 | return *_flow; |
---|
691 | } |
---|
692 | |
---|
693 | /** |
---|
694 | \brief Returns \c true if the given node is in a barrier. |
---|
695 | |
---|
696 | Barrier is a set \e B of nodes for which |
---|
697 | |
---|
698 | \f[ \sum_{uv\in A: u\in B} upper(uv) - |
---|
699 | \sum_{uv\in A: v\in B} lower(uv) < \sum_{v\in B} sup(v) \f] |
---|
700 | |
---|
701 | holds. The existence of a set with this property prooves that a |
---|
702 | feasible circualtion cannot exist. |
---|
703 | |
---|
704 | This function returns \c true if the given node is in the found |
---|
705 | barrier. If a feasible circulation is found, the function |
---|
706 | gives back \c false for every node. |
---|
707 | |
---|
708 | \pre Either \ref run() or \ref init() must be called before |
---|
709 | using this function. |
---|
710 | |
---|
711 | \sa barrierMap() |
---|
712 | \sa checkBarrier() |
---|
713 | */ |
---|
714 | bool barrier(const Node& node) const |
---|
715 | { |
---|
716 | return (*_level)[node] >= _el; |
---|
717 | } |
---|
718 | |
---|
719 | /// \brief Gives back a barrier. |
---|
720 | /// |
---|
721 | /// This function sets \c bar to the characteristic vector of the |
---|
722 | /// found barrier. \c bar should be a \ref concepts::WriteMap "writable" |
---|
723 | /// node map with \c bool (or convertible) value type. |
---|
724 | /// |
---|
725 | /// If a feasible circulation is found, the function gives back an |
---|
726 | /// empty set, so \c bar[v] will be \c false for all nodes \c v. |
---|
727 | /// |
---|
728 | /// \note This function calls \ref barrier() for each node, |
---|
729 | /// so it runs in O(n) time. |
---|
730 | /// |
---|
731 | /// \pre Either \ref run() or \ref init() must be called before |
---|
732 | /// using this function. |
---|
733 | /// |
---|
734 | /// \sa barrier() |
---|
735 | /// \sa checkBarrier() |
---|
736 | template<class BarrierMap> |
---|
737 | void barrierMap(BarrierMap &bar) const |
---|
738 | { |
---|
739 | for(NodeIt n(_g);n!=INVALID;++n) |
---|
740 | bar.set(n, (*_level)[n] >= _el); |
---|
741 | } |
---|
742 | |
---|
743 | /// @} |
---|
744 | |
---|
745 | /// \name Checker Functions |
---|
746 | /// The feasibility of the results can be checked using |
---|
747 | /// these functions.\n |
---|
748 | /// Either \ref run() or \ref start() should be called before |
---|
749 | /// using them. |
---|
750 | |
---|
751 | ///@{ |
---|
752 | |
---|
753 | ///Check if the found flow is a feasible circulation |
---|
754 | |
---|
755 | ///Check if the found flow is a feasible circulation, |
---|
756 | /// |
---|
757 | bool checkFlow() const { |
---|
758 | for(ArcIt e(_g);e!=INVALID;++e) |
---|
759 | if((*_flow)[e]<(*_lo)[e]||(*_flow)[e]>(*_up)[e]) return false; |
---|
760 | for(NodeIt n(_g);n!=INVALID;++n) |
---|
761 | { |
---|
762 | Value dif=-(*_supply)[n]; |
---|
763 | for(InArcIt e(_g,n);e!=INVALID;++e) dif-=(*_flow)[e]; |
---|
764 | for(OutArcIt e(_g,n);e!=INVALID;++e) dif+=(*_flow)[e]; |
---|
765 | if(_tol.negative(dif)) return false; |
---|
766 | } |
---|
767 | return true; |
---|
768 | } |
---|
769 | |
---|
770 | ///Check whether or not the last execution provides a barrier |
---|
771 | |
---|
772 | ///Check whether or not the last execution provides a barrier. |
---|
773 | ///\sa barrier() |
---|
774 | ///\sa barrierMap() |
---|
775 | bool checkBarrier() const |
---|
776 | { |
---|
777 | Value delta=0; |
---|
778 | Value inf_cap = std::numeric_limits<Value>::has_infinity ? |
---|
779 | std::numeric_limits<Value>::infinity() : |
---|
780 | std::numeric_limits<Value>::max(); |
---|
781 | for(NodeIt n(_g);n!=INVALID;++n) |
---|
782 | if(barrier(n)) |
---|
783 | delta-=(*_supply)[n]; |
---|
784 | for(ArcIt e(_g);e!=INVALID;++e) |
---|
785 | { |
---|
786 | Node s=_g.source(e); |
---|
787 | Node t=_g.target(e); |
---|
788 | if(barrier(s)&&!barrier(t)) { |
---|
789 | if (_tol.less(inf_cap - (*_up)[e], delta)) return false; |
---|
790 | delta+=(*_up)[e]; |
---|
791 | } |
---|
792 | else if(barrier(t)&&!barrier(s)) delta-=(*_lo)[e]; |
---|
793 | } |
---|
794 | return _tol.negative(delta); |
---|
795 | } |
---|
796 | |
---|
797 | /// @} |
---|
798 | |
---|
799 | }; |
---|
800 | |
---|
801 | } |
---|
802 | |
---|
803 | #endif |
---|