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) 2003-2010 |
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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_COST_SCALING_H |
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20 | #define LEMON_COST_SCALING_H |
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21 | |
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22 | /// \ingroup min_cost_flow_algs |
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23 | /// \file |
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24 | /// \brief Cost scaling algorithm for finding a minimum cost flow. |
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25 | |
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26 | #include <vector> |
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27 | #include <deque> |
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28 | #include <limits> |
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29 | |
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30 | #include <lemon/core.h> |
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31 | #include <lemon/maps.h> |
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32 | #include <lemon/math.h> |
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33 | #include <lemon/static_graph.h> |
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34 | #include <lemon/circulation.h> |
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35 | #include <lemon/bellman_ford.h> |
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36 | |
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37 | namespace lemon { |
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38 | |
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39 | /// \brief Default traits class of CostScaling algorithm. |
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40 | /// |
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41 | /// Default traits class of CostScaling algorithm. |
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42 | /// \tparam GR Digraph type. |
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43 | /// \tparam V The number type used for flow amounts, capacity bounds |
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44 | /// and supply values. By default it is \c int. |
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45 | /// \tparam C The number type used for costs and potentials. |
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46 | /// By default it is the same as \c V. |
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47 | #ifdef DOXYGEN |
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48 | template <typename GR, typename V = int, typename C = V> |
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49 | #else |
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50 | template < typename GR, typename V = int, typename C = V, |
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51 | bool integer = std::numeric_limits<C>::is_integer > |
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52 | #endif |
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53 | struct CostScalingDefaultTraits |
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54 | { |
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55 | /// The type of the digraph |
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56 | typedef GR Digraph; |
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57 | /// The type of the flow amounts, capacity bounds and supply values |
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58 | typedef V Value; |
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59 | /// The type of the arc costs |
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60 | typedef C Cost; |
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61 | |
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62 | /// \brief The large cost type used for internal computations |
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63 | /// |
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64 | /// The large cost type used for internal computations. |
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65 | /// It is \c long \c long if the \c Cost type is integer, |
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66 | /// otherwise it is \c double. |
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67 | /// \c Cost must be convertible to \c LargeCost. |
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68 | typedef double LargeCost; |
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69 | }; |
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70 | |
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71 | // Default traits class for integer cost types |
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72 | template <typename GR, typename V, typename C> |
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73 | struct CostScalingDefaultTraits<GR, V, C, true> |
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74 | { |
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75 | typedef GR Digraph; |
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76 | typedef V Value; |
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77 | typedef C Cost; |
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78 | #ifdef LEMON_HAVE_LONG_LONG |
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79 | typedef long long LargeCost; |
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80 | #else |
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81 | typedef long LargeCost; |
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82 | #endif |
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83 | }; |
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84 | |
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85 | |
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86 | /// \addtogroup min_cost_flow_algs |
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87 | /// @{ |
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88 | |
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89 | /// \brief Implementation of the Cost Scaling algorithm for |
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90 | /// finding a \ref min_cost_flow "minimum cost flow". |
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91 | /// |
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92 | /// \ref CostScaling implements a cost scaling algorithm that performs |
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93 | /// push/augment and relabel operations for finding a \ref min_cost_flow |
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94 | /// "minimum cost flow" \ref amo93networkflows, \ref goldberg90approximation, |
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95 | /// \ref goldberg97efficient, \ref bunnagel98efficient. |
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96 | /// It is a highly efficient primal-dual solution method, which |
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97 | /// can be viewed as the generalization of the \ref Preflow |
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98 | /// "preflow push-relabel" algorithm for the maximum flow problem. |
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99 | /// |
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100 | /// In general, \ref NetworkSimplex and \ref CostScaling are the fastest |
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101 | /// implementations available in LEMON for this problem. |
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102 | /// |
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103 | /// Most of the parameters of the problem (except for the digraph) |
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104 | /// can be given using separate functions, and the algorithm can be |
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105 | /// executed using the \ref run() function. If some parameters are not |
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106 | /// specified, then default values will be used. |
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107 | /// |
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108 | /// \tparam GR The digraph type the algorithm runs on. |
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109 | /// \tparam V The number type used for flow amounts, capacity bounds |
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110 | /// and supply values in the algorithm. By default, it is \c int. |
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111 | /// \tparam C The number type used for costs and potentials in the |
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112 | /// algorithm. By default, it is the same as \c V. |
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113 | /// \tparam TR The traits class that defines various types used by the |
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114 | /// algorithm. By default, it is \ref CostScalingDefaultTraits |
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115 | /// "CostScalingDefaultTraits<GR, V, C>". |
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116 | /// In most cases, this parameter should not be set directly, |
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117 | /// consider to use the named template parameters instead. |
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118 | /// |
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119 | /// \warning Both \c V and \c C must be signed number types. |
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120 | /// \warning All input data (capacities, supply values, and costs) must |
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121 | /// be integer. |
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122 | /// \warning This algorithm does not support negative costs for |
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123 | /// arcs having infinite upper bound. |
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124 | /// |
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125 | /// \note %CostScaling provides three different internal methods, |
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126 | /// from which the most efficient one is used by default. |
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127 | /// For more information, see \ref Method. |
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128 | #ifdef DOXYGEN |
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129 | template <typename GR, typename V, typename C, typename TR> |
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130 | #else |
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131 | template < typename GR, typename V = int, typename C = V, |
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132 | typename TR = CostScalingDefaultTraits<GR, V, C> > |
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133 | #endif |
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134 | class CostScaling |
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135 | { |
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136 | public: |
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137 | |
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138 | /// The type of the digraph |
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139 | typedef typename TR::Digraph Digraph; |
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140 | /// The type of the flow amounts, capacity bounds and supply values |
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141 | typedef typename TR::Value Value; |
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142 | /// The type of the arc costs |
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143 | typedef typename TR::Cost Cost; |
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144 | |
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145 | /// \brief The large cost type |
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146 | /// |
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147 | /// The large cost type used for internal computations. |
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148 | /// By default, it is \c long \c long if the \c Cost type is integer, |
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149 | /// otherwise it is \c double. |
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150 | typedef typename TR::LargeCost LargeCost; |
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151 | |
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152 | /// The \ref CostScalingDefaultTraits "traits class" of the algorithm |
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153 | typedef TR Traits; |
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154 | |
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155 | public: |
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156 | |
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157 | /// \brief Problem type constants for the \c run() function. |
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158 | /// |
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159 | /// Enum type containing the problem type constants that can be |
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160 | /// returned by the \ref run() function of the algorithm. |
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161 | enum ProblemType { |
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162 | /// The problem has no feasible solution (flow). |
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163 | INFEASIBLE, |
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164 | /// The problem has optimal solution (i.e. it is feasible and |
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165 | /// bounded), and the algorithm has found optimal flow and node |
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166 | /// potentials (primal and dual solutions). |
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167 | OPTIMAL, |
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168 | /// The digraph contains an arc of negative cost and infinite |
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169 | /// upper bound. It means that the objective function is unbounded |
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170 | /// on that arc, however, note that it could actually be bounded |
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171 | /// over the feasible flows, but this algroithm cannot handle |
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172 | /// these cases. |
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173 | UNBOUNDED |
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174 | }; |
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175 | |
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176 | /// \brief Constants for selecting the internal method. |
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177 | /// |
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178 | /// Enum type containing constants for selecting the internal method |
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179 | /// for the \ref run() function. |
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180 | /// |
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181 | /// \ref CostScaling provides three internal methods that differ mainly |
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182 | /// in their base operations, which are used in conjunction with the |
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183 | /// relabel operation. |
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184 | /// By default, the so called \ref PARTIAL_AUGMENT |
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185 | /// "Partial Augment-Relabel" method is used, which turned out to be |
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186 | /// the most efficient and the most robust on various test inputs. |
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187 | /// However, the other methods can be selected using the \ref run() |
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188 | /// function with the proper parameter. |
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189 | enum Method { |
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190 | /// Local push operations are used, i.e. flow is moved only on one |
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191 | /// admissible arc at once. |
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192 | PUSH, |
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193 | /// Augment operations are used, i.e. flow is moved on admissible |
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194 | /// paths from a node with excess to a node with deficit. |
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195 | AUGMENT, |
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196 | /// Partial augment operations are used, i.e. flow is moved on |
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197 | /// admissible paths started from a node with excess, but the |
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198 | /// lengths of these paths are limited. This method can be viewed |
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199 | /// as a combined version of the previous two operations. |
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200 | PARTIAL_AUGMENT |
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201 | }; |
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202 | |
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203 | private: |
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204 | |
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205 | TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
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206 | |
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207 | typedef std::vector<int> IntVector; |
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208 | typedef std::vector<Value> ValueVector; |
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209 | typedef std::vector<Cost> CostVector; |
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210 | typedef std::vector<LargeCost> LargeCostVector; |
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211 | typedef std::vector<char> BoolVector; |
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212 | // Note: vector<char> is used instead of vector<bool> for efficiency reasons |
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213 | |
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214 | private: |
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215 | |
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216 | template <typename KT, typename VT> |
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217 | class StaticVectorMap { |
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218 | public: |
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219 | typedef KT Key; |
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220 | typedef VT Value; |
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221 | |
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222 | StaticVectorMap(std::vector<Value>& v) : _v(v) {} |
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223 | |
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224 | const Value& operator[](const Key& key) const { |
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225 | return _v[StaticDigraph::id(key)]; |
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226 | } |
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227 | |
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228 | Value& operator[](const Key& key) { |
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229 | return _v[StaticDigraph::id(key)]; |
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230 | } |
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231 | |
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232 | void set(const Key& key, const Value& val) { |
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233 | _v[StaticDigraph::id(key)] = val; |
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234 | } |
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235 | |
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236 | private: |
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237 | std::vector<Value>& _v; |
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238 | }; |
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239 | |
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240 | typedef StaticVectorMap<StaticDigraph::Arc, LargeCost> LargeCostArcMap; |
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241 | |
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242 | private: |
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243 | |
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244 | // Data related to the underlying digraph |
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245 | const GR &_graph; |
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246 | int _node_num; |
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247 | int _arc_num; |
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248 | int _res_node_num; |
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249 | int _res_arc_num; |
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250 | int _root; |
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251 | |
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252 | // Parameters of the problem |
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253 | bool _have_lower; |
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254 | Value _sum_supply; |
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255 | int _sup_node_num; |
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256 | |
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257 | // Data structures for storing the digraph |
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258 | IntNodeMap _node_id; |
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259 | IntArcMap _arc_idf; |
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260 | IntArcMap _arc_idb; |
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261 | IntVector _first_out; |
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262 | BoolVector _forward; |
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263 | IntVector _source; |
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264 | IntVector _target; |
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265 | IntVector _reverse; |
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266 | |
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267 | // Node and arc data |
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268 | ValueVector _lower; |
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269 | ValueVector _upper; |
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270 | CostVector _scost; |
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271 | ValueVector _supply; |
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272 | |
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273 | ValueVector _res_cap; |
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274 | LargeCostVector _cost; |
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275 | LargeCostVector _pi; |
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276 | ValueVector _excess; |
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277 | IntVector _next_out; |
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278 | std::deque<int> _active_nodes; |
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279 | |
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280 | // Data for scaling |
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281 | LargeCost _epsilon; |
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282 | int _alpha; |
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283 | |
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284 | IntVector _buckets; |
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285 | IntVector _bucket_next; |
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286 | IntVector _bucket_prev; |
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287 | IntVector _rank; |
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288 | int _max_rank; |
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289 | |
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290 | public: |
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291 | |
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292 | /// \brief Constant for infinite upper bounds (capacities). |
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293 | /// |
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294 | /// Constant for infinite upper bounds (capacities). |
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295 | /// It is \c std::numeric_limits<Value>::infinity() if available, |
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296 | /// \c std::numeric_limits<Value>::max() otherwise. |
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297 | const Value INF; |
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298 | |
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299 | public: |
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300 | |
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301 | /// \name Named Template Parameters |
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302 | /// @{ |
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303 | |
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304 | template <typename T> |
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305 | struct SetLargeCostTraits : public Traits { |
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306 | typedef T LargeCost; |
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307 | }; |
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308 | |
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309 | /// \brief \ref named-templ-param "Named parameter" for setting |
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310 | /// \c LargeCost type. |
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311 | /// |
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312 | /// \ref named-templ-param "Named parameter" for setting \c LargeCost |
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313 | /// type, which is used for internal computations in the algorithm. |
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314 | /// \c Cost must be convertible to \c LargeCost. |
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315 | template <typename T> |
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316 | struct SetLargeCost |
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317 | : public CostScaling<GR, V, C, SetLargeCostTraits<T> > { |
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318 | typedef CostScaling<GR, V, C, SetLargeCostTraits<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 | CostScaling() {} |
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326 | |
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327 | public: |
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328 | |
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329 | /// \brief 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 | CostScaling(const GR& graph) : |
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335 | _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph), |
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336 | INF(std::numeric_limits<Value>::has_infinity ? |
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337 | std::numeric_limits<Value>::infinity() : |
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338 | std::numeric_limits<Value>::max()) |
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339 | { |
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340 | // Check the number types |
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341 | LEMON_ASSERT(std::numeric_limits<Value>::is_signed, |
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342 | "The flow type of CostScaling must be signed"); |
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343 | LEMON_ASSERT(std::numeric_limits<Cost>::is_signed, |
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344 | "The cost type of CostScaling must be signed"); |
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345 | |
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346 | // Reset data structures |
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347 | reset(); |
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348 | } |
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349 | |
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350 | /// \name Parameters |
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351 | /// The parameters of the algorithm can be specified using these |
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352 | /// functions. |
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353 | |
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354 | /// @{ |
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355 | |
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356 | /// \brief Set the lower bounds on the arcs. |
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357 | /// |
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358 | /// This function sets the lower bounds on the arcs. |
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359 | /// If it is not used before calling \ref run(), the lower bounds |
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360 | /// will be set to zero on all arcs. |
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361 | /// |
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362 | /// \param map An arc map storing the lower bounds. |
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363 | /// Its \c Value type must be convertible to the \c Value type |
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364 | /// of the algorithm. |
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365 | /// |
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366 | /// \return <tt>(*this)</tt> |
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367 | template <typename LowerMap> |
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368 | CostScaling& lowerMap(const LowerMap& map) { |
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369 | _have_lower = true; |
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370 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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371 | _lower[_arc_idf[a]] = map[a]; |
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372 | _lower[_arc_idb[a]] = map[a]; |
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373 | } |
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374 | return *this; |
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375 | } |
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376 | |
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377 | /// \brief Set the upper bounds (capacities) on the arcs. |
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378 | /// |
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379 | /// This function sets the upper bounds (capacities) on the arcs. |
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380 | /// If it is not used before calling \ref run(), the upper bounds |
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381 | /// will be set to \ref INF on all arcs (i.e. the flow value will be |
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382 | /// unbounded from above). |
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383 | /// |
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384 | /// \param map An arc map storing the upper bounds. |
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385 | /// Its \c Value type must be convertible to the \c Value type |
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386 | /// of the algorithm. |
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387 | /// |
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388 | /// \return <tt>(*this)</tt> |
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389 | template<typename UpperMap> |
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390 | CostScaling& upperMap(const UpperMap& map) { |
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391 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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392 | _upper[_arc_idf[a]] = map[a]; |
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393 | } |
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394 | return *this; |
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395 | } |
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396 | |
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397 | /// \brief Set the costs of the arcs. |
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398 | /// |
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399 | /// This function sets the costs of the arcs. |
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400 | /// If it is not used before calling \ref run(), the costs |
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401 | /// will be set to \c 1 on all arcs. |
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402 | /// |
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403 | /// \param map An arc map storing the costs. |
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404 | /// Its \c Value type must be convertible to the \c Cost type |
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405 | /// of the algorithm. |
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406 | /// |
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407 | /// \return <tt>(*this)</tt> |
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408 | template<typename CostMap> |
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409 | CostScaling& costMap(const CostMap& map) { |
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410 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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411 | _scost[_arc_idf[a]] = map[a]; |
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412 | _scost[_arc_idb[a]] = -map[a]; |
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413 | } |
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414 | return *this; |
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415 | } |
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416 | |
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417 | /// \brief Set the supply values of the nodes. |
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418 | /// |
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419 | /// This function sets the supply values of the nodes. |
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420 | /// If neither this function nor \ref stSupply() is used before |
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421 | /// calling \ref run(), the supply of each node will be set to zero. |
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422 | /// |
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423 | /// \param map A node map storing the supply values. |
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424 | /// Its \c Value type must be convertible to the \c Value type |
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425 | /// of the algorithm. |
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426 | /// |
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427 | /// \return <tt>(*this)</tt> |
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428 | template<typename SupplyMap> |
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429 | CostScaling& supplyMap(const SupplyMap& map) { |
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430 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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431 | _supply[_node_id[n]] = map[n]; |
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432 | } |
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433 | return *this; |
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434 | } |
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435 | |
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436 | /// \brief Set single source and target nodes and a supply value. |
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437 | /// |
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438 | /// This function sets a single source node and a single target node |
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439 | /// and the required flow value. |
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440 | /// If neither this function nor \ref supplyMap() is used before |
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441 | /// calling \ref run(), the supply of each node will be set to zero. |
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442 | /// |
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443 | /// Using this function has the same effect as using \ref supplyMap() |
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444 | /// with a map in which \c k is assigned to \c s, \c -k is |
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445 | /// assigned to \c t and all other nodes have zero supply value. |
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446 | /// |
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447 | /// \param s The source node. |
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448 | /// \param t The target node. |
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449 | /// \param k The required amount of flow from node \c s to node \c t |
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450 | /// (i.e. the supply of \c s and the demand of \c t). |
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451 | /// |
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452 | /// \return <tt>(*this)</tt> |
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453 | CostScaling& stSupply(const Node& s, const Node& t, Value k) { |
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454 | for (int i = 0; i != _res_node_num; ++i) { |
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455 | _supply[i] = 0; |
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456 | } |
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457 | _supply[_node_id[s]] = k; |
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458 | _supply[_node_id[t]] = -k; |
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459 | return *this; |
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460 | } |
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461 | |
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462 | /// @} |
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463 | |
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464 | /// \name Execution control |
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465 | /// The algorithm can be executed using \ref run(). |
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466 | |
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467 | /// @{ |
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468 | |
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469 | /// \brief Run the algorithm. |
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470 | /// |
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471 | /// This function runs the algorithm. |
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472 | /// The paramters can be specified using functions \ref lowerMap(), |
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473 | /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(). |
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474 | /// For example, |
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475 | /// \code |
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476 | /// CostScaling<ListDigraph> cs(graph); |
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477 | /// cs.lowerMap(lower).upperMap(upper).costMap(cost) |
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478 | /// .supplyMap(sup).run(); |
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479 | /// \endcode |
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480 | /// |
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481 | /// This function can be called more than once. All the given parameters |
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482 | /// are kept for the next call, unless \ref resetParams() or \ref reset() |
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483 | /// is used, thus only the modified parameters have to be set again. |
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484 | /// If the underlying digraph was also modified after the construction |
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485 | /// of the class (or the last \ref reset() call), then the \ref reset() |
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486 | /// function must be called. |
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487 | /// |
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488 | /// \param method The internal method that will be used in the |
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489 | /// algorithm. For more information, see \ref Method. |
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490 | /// \param factor The cost scaling factor. It must be larger than one. |
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491 | /// |
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492 | /// \return \c INFEASIBLE if no feasible flow exists, |
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493 | /// \n \c OPTIMAL if the problem has optimal solution |
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494 | /// (i.e. it is feasible and bounded), and the algorithm has found |
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495 | /// optimal flow and node potentials (primal and dual solutions), |
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496 | /// \n \c UNBOUNDED if the digraph contains an arc of negative cost |
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497 | /// and infinite upper bound. It means that the objective function |
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498 | /// is unbounded on that arc, however, note that it could actually be |
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499 | /// bounded over the feasible flows, but this algroithm cannot handle |
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500 | /// these cases. |
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501 | /// |
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502 | /// \see ProblemType, Method |
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503 | /// \see resetParams(), reset() |
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504 | ProblemType run(Method method = PARTIAL_AUGMENT, int factor = 8) { |
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505 | _alpha = factor; |
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506 | ProblemType pt = init(); |
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507 | if (pt != OPTIMAL) return pt; |
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508 | start(method); |
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509 | return OPTIMAL; |
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510 | } |
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511 | |
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512 | /// \brief Reset all the parameters that have been given before. |
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513 | /// |
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514 | /// This function resets all the paramaters that have been given |
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515 | /// before using functions \ref lowerMap(), \ref upperMap(), |
---|
516 | /// \ref costMap(), \ref supplyMap(), \ref stSupply(). |
---|
517 | /// |
---|
518 | /// It is useful for multiple \ref run() calls. Basically, all the given |
---|
519 | /// parameters are kept for the next \ref run() call, unless |
---|
520 | /// \ref resetParams() or \ref reset() is used. |
---|
521 | /// If the underlying digraph was also modified after the construction |
---|
522 | /// of the class or the last \ref reset() call, then the \ref reset() |
---|
523 | /// function must be used, otherwise \ref resetParams() is sufficient. |
---|
524 | /// |
---|
525 | /// For example, |
---|
526 | /// \code |
---|
527 | /// CostScaling<ListDigraph> cs(graph); |
---|
528 | /// |
---|
529 | /// // First run |
---|
530 | /// cs.lowerMap(lower).upperMap(upper).costMap(cost) |
---|
531 | /// .supplyMap(sup).run(); |
---|
532 | /// |
---|
533 | /// // Run again with modified cost map (resetParams() is not called, |
---|
534 | /// // so only the cost map have to be set again) |
---|
535 | /// cost[e] += 100; |
---|
536 | /// cs.costMap(cost).run(); |
---|
537 | /// |
---|
538 | /// // Run again from scratch using resetParams() |
---|
539 | /// // (the lower bounds will be set to zero on all arcs) |
---|
540 | /// cs.resetParams(); |
---|
541 | /// cs.upperMap(capacity).costMap(cost) |
---|
542 | /// .supplyMap(sup).run(); |
---|
543 | /// \endcode |
---|
544 | /// |
---|
545 | /// \return <tt>(*this)</tt> |
---|
546 | /// |
---|
547 | /// \see reset(), run() |
---|
548 | CostScaling& resetParams() { |
---|
549 | for (int i = 0; i != _res_node_num; ++i) { |
---|
550 | _supply[i] = 0; |
---|
551 | } |
---|
552 | int limit = _first_out[_root]; |
---|
553 | for (int j = 0; j != limit; ++j) { |
---|
554 | _lower[j] = 0; |
---|
555 | _upper[j] = INF; |
---|
556 | _scost[j] = _forward[j] ? 1 : -1; |
---|
557 | } |
---|
558 | for (int j = limit; j != _res_arc_num; ++j) { |
---|
559 | _lower[j] = 0; |
---|
560 | _upper[j] = INF; |
---|
561 | _scost[j] = 0; |
---|
562 | _scost[_reverse[j]] = 0; |
---|
563 | } |
---|
564 | _have_lower = false; |
---|
565 | return *this; |
---|
566 | } |
---|
567 | |
---|
568 | /// \brief Reset the internal data structures and all the parameters |
---|
569 | /// that have been given before. |
---|
570 | /// |
---|
571 | /// This function resets the internal data structures and all the |
---|
572 | /// paramaters that have been given before using functions \ref lowerMap(), |
---|
573 | /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(). |
---|
574 | /// |
---|
575 | /// It is useful for multiple \ref run() calls. By default, all the given |
---|
576 | /// parameters are kept for the next \ref run() call, unless |
---|
577 | /// \ref resetParams() or \ref reset() is used. |
---|
578 | /// If the underlying digraph was also modified after the construction |
---|
579 | /// of the class or the last \ref reset() call, then the \ref reset() |
---|
580 | /// function must be used, otherwise \ref resetParams() is sufficient. |
---|
581 | /// |
---|
582 | /// See \ref resetParams() for examples. |
---|
583 | /// |
---|
584 | /// \return <tt>(*this)</tt> |
---|
585 | /// |
---|
586 | /// \see resetParams(), run() |
---|
587 | CostScaling& reset() { |
---|
588 | // Resize vectors |
---|
589 | _node_num = countNodes(_graph); |
---|
590 | _arc_num = countArcs(_graph); |
---|
591 | _res_node_num = _node_num + 1; |
---|
592 | _res_arc_num = 2 * (_arc_num + _node_num); |
---|
593 | _root = _node_num; |
---|
594 | |
---|
595 | _first_out.resize(_res_node_num + 1); |
---|
596 | _forward.resize(_res_arc_num); |
---|
597 | _source.resize(_res_arc_num); |
---|
598 | _target.resize(_res_arc_num); |
---|
599 | _reverse.resize(_res_arc_num); |
---|
600 | |
---|
601 | _lower.resize(_res_arc_num); |
---|
602 | _upper.resize(_res_arc_num); |
---|
603 | _scost.resize(_res_arc_num); |
---|
604 | _supply.resize(_res_node_num); |
---|
605 | |
---|
606 | _res_cap.resize(_res_arc_num); |
---|
607 | _cost.resize(_res_arc_num); |
---|
608 | _pi.resize(_res_node_num); |
---|
609 | _excess.resize(_res_node_num); |
---|
610 | _next_out.resize(_res_node_num); |
---|
611 | |
---|
612 | // Copy the graph |
---|
613 | int i = 0, j = 0, k = 2 * _arc_num + _node_num; |
---|
614 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
---|
615 | _node_id[n] = i; |
---|
616 | } |
---|
617 | i = 0; |
---|
618 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
---|
619 | _first_out[i] = j; |
---|
620 | for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) { |
---|
621 | _arc_idf[a] = j; |
---|
622 | _forward[j] = true; |
---|
623 | _source[j] = i; |
---|
624 | _target[j] = _node_id[_graph.runningNode(a)]; |
---|
625 | } |
---|
626 | for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) { |
---|
627 | _arc_idb[a] = j; |
---|
628 | _forward[j] = false; |
---|
629 | _source[j] = i; |
---|
630 | _target[j] = _node_id[_graph.runningNode(a)]; |
---|
631 | } |
---|
632 | _forward[j] = false; |
---|
633 | _source[j] = i; |
---|
634 | _target[j] = _root; |
---|
635 | _reverse[j] = k; |
---|
636 | _forward[k] = true; |
---|
637 | _source[k] = _root; |
---|
638 | _target[k] = i; |
---|
639 | _reverse[k] = j; |
---|
640 | ++j; ++k; |
---|
641 | } |
---|
642 | _first_out[i] = j; |
---|
643 | _first_out[_res_node_num] = k; |
---|
644 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
645 | int fi = _arc_idf[a]; |
---|
646 | int bi = _arc_idb[a]; |
---|
647 | _reverse[fi] = bi; |
---|
648 | _reverse[bi] = fi; |
---|
649 | } |
---|
650 | |
---|
651 | // Reset parameters |
---|
652 | resetParams(); |
---|
653 | return *this; |
---|
654 | } |
---|
655 | |
---|
656 | /// @} |
---|
657 | |
---|
658 | /// \name Query Functions |
---|
659 | /// The results of the algorithm can be obtained using these |
---|
660 | /// functions.\n |
---|
661 | /// The \ref run() function must be called before using them. |
---|
662 | |
---|
663 | /// @{ |
---|
664 | |
---|
665 | /// \brief Return the total cost of the found flow. |
---|
666 | /// |
---|
667 | /// This function returns the total cost of the found flow. |
---|
668 | /// Its complexity is O(e). |
---|
669 | /// |
---|
670 | /// \note The return type of the function can be specified as a |
---|
671 | /// template parameter. For example, |
---|
672 | /// \code |
---|
673 | /// cs.totalCost<double>(); |
---|
674 | /// \endcode |
---|
675 | /// It is useful if the total cost cannot be stored in the \c Cost |
---|
676 | /// type of the algorithm, which is the default return type of the |
---|
677 | /// function. |
---|
678 | /// |
---|
679 | /// \pre \ref run() must be called before using this function. |
---|
680 | template <typename Number> |
---|
681 | Number totalCost() const { |
---|
682 | Number c = 0; |
---|
683 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
684 | int i = _arc_idb[a]; |
---|
685 | c += static_cast<Number>(_res_cap[i]) * |
---|
686 | (-static_cast<Number>(_scost[i])); |
---|
687 | } |
---|
688 | return c; |
---|
689 | } |
---|
690 | |
---|
691 | #ifndef DOXYGEN |
---|
692 | Cost totalCost() const { |
---|
693 | return totalCost<Cost>(); |
---|
694 | } |
---|
695 | #endif |
---|
696 | |
---|
697 | /// \brief Return the flow on the given arc. |
---|
698 | /// |
---|
699 | /// This function returns the flow on the given arc. |
---|
700 | /// |
---|
701 | /// \pre \ref run() must be called before using this function. |
---|
702 | Value flow(const Arc& a) const { |
---|
703 | return _res_cap[_arc_idb[a]]; |
---|
704 | } |
---|
705 | |
---|
706 | /// \brief Return the flow map (the primal solution). |
---|
707 | /// |
---|
708 | /// This function copies the flow value on each arc into the given |
---|
709 | /// map. The \c Value type of the algorithm must be convertible to |
---|
710 | /// the \c Value type of the map. |
---|
711 | /// |
---|
712 | /// \pre \ref run() must be called before using this function. |
---|
713 | template <typename FlowMap> |
---|
714 | void flowMap(FlowMap &map) const { |
---|
715 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
716 | map.set(a, _res_cap[_arc_idb[a]]); |
---|
717 | } |
---|
718 | } |
---|
719 | |
---|
720 | /// \brief Return the potential (dual value) of the given node. |
---|
721 | /// |
---|
722 | /// This function returns the potential (dual value) of the |
---|
723 | /// given node. |
---|
724 | /// |
---|
725 | /// \pre \ref run() must be called before using this function. |
---|
726 | Cost potential(const Node& n) const { |
---|
727 | return static_cast<Cost>(_pi[_node_id[n]]); |
---|
728 | } |
---|
729 | |
---|
730 | /// \brief Return the potential map (the dual solution). |
---|
731 | /// |
---|
732 | /// This function copies the potential (dual value) of each node |
---|
733 | /// into the given map. |
---|
734 | /// The \c Cost type of the algorithm must be convertible to the |
---|
735 | /// \c Value type of the map. |
---|
736 | /// |
---|
737 | /// \pre \ref run() must be called before using this function. |
---|
738 | template <typename PotentialMap> |
---|
739 | void potentialMap(PotentialMap &map) const { |
---|
740 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
741 | map.set(n, static_cast<Cost>(_pi[_node_id[n]])); |
---|
742 | } |
---|
743 | } |
---|
744 | |
---|
745 | /// @} |
---|
746 | |
---|
747 | private: |
---|
748 | |
---|
749 | // Initialize the algorithm |
---|
750 | ProblemType init() { |
---|
751 | if (_res_node_num <= 1) return INFEASIBLE; |
---|
752 | |
---|
753 | // Check the sum of supply values |
---|
754 | _sum_supply = 0; |
---|
755 | for (int i = 0; i != _root; ++i) { |
---|
756 | _sum_supply += _supply[i]; |
---|
757 | } |
---|
758 | if (_sum_supply > 0) return INFEASIBLE; |
---|
759 | |
---|
760 | |
---|
761 | // Initialize vectors |
---|
762 | for (int i = 0; i != _res_node_num; ++i) { |
---|
763 | _pi[i] = 0; |
---|
764 | _excess[i] = _supply[i]; |
---|
765 | } |
---|
766 | |
---|
767 | // Remove infinite upper bounds and check negative arcs |
---|
768 | const Value MAX = std::numeric_limits<Value>::max(); |
---|
769 | int last_out; |
---|
770 | if (_have_lower) { |
---|
771 | for (int i = 0; i != _root; ++i) { |
---|
772 | last_out = _first_out[i+1]; |
---|
773 | for (int j = _first_out[i]; j != last_out; ++j) { |
---|
774 | if (_forward[j]) { |
---|
775 | Value c = _scost[j] < 0 ? _upper[j] : _lower[j]; |
---|
776 | if (c >= MAX) return UNBOUNDED; |
---|
777 | _excess[i] -= c; |
---|
778 | _excess[_target[j]] += c; |
---|
779 | } |
---|
780 | } |
---|
781 | } |
---|
782 | } else { |
---|
783 | for (int i = 0; i != _root; ++i) { |
---|
784 | last_out = _first_out[i+1]; |
---|
785 | for (int j = _first_out[i]; j != last_out; ++j) { |
---|
786 | if (_forward[j] && _scost[j] < 0) { |
---|
787 | Value c = _upper[j]; |
---|
788 | if (c >= MAX) return UNBOUNDED; |
---|
789 | _excess[i] -= c; |
---|
790 | _excess[_target[j]] += c; |
---|
791 | } |
---|
792 | } |
---|
793 | } |
---|
794 | } |
---|
795 | Value ex, max_cap = 0; |
---|
796 | for (int i = 0; i != _res_node_num; ++i) { |
---|
797 | ex = _excess[i]; |
---|
798 | _excess[i] = 0; |
---|
799 | if (ex < 0) max_cap -= ex; |
---|
800 | } |
---|
801 | for (int j = 0; j != _res_arc_num; ++j) { |
---|
802 | if (_upper[j] >= MAX) _upper[j] = max_cap; |
---|
803 | } |
---|
804 | |
---|
805 | // Initialize the large cost vector and the epsilon parameter |
---|
806 | _epsilon = 0; |
---|
807 | LargeCost lc; |
---|
808 | for (int i = 0; i != _root; ++i) { |
---|
809 | last_out = _first_out[i+1]; |
---|
810 | for (int j = _first_out[i]; j != last_out; ++j) { |
---|
811 | lc = static_cast<LargeCost>(_scost[j]) * _res_node_num * _alpha; |
---|
812 | _cost[j] = lc; |
---|
813 | if (lc > _epsilon) _epsilon = lc; |
---|
814 | } |
---|
815 | } |
---|
816 | _epsilon /= _alpha; |
---|
817 | |
---|
818 | // Initialize maps for Circulation and remove non-zero lower bounds |
---|
819 | ConstMap<Arc, Value> low(0); |
---|
820 | typedef typename Digraph::template ArcMap<Value> ValueArcMap; |
---|
821 | typedef typename Digraph::template NodeMap<Value> ValueNodeMap; |
---|
822 | ValueArcMap cap(_graph), flow(_graph); |
---|
823 | ValueNodeMap sup(_graph); |
---|
824 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
825 | sup[n] = _supply[_node_id[n]]; |
---|
826 | } |
---|
827 | if (_have_lower) { |
---|
828 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
829 | int j = _arc_idf[a]; |
---|
830 | Value c = _lower[j]; |
---|
831 | cap[a] = _upper[j] - c; |
---|
832 | sup[_graph.source(a)] -= c; |
---|
833 | sup[_graph.target(a)] += c; |
---|
834 | } |
---|
835 | } else { |
---|
836 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
837 | cap[a] = _upper[_arc_idf[a]]; |
---|
838 | } |
---|
839 | } |
---|
840 | |
---|
841 | _sup_node_num = 0; |
---|
842 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
843 | if (sup[n] > 0) ++_sup_node_num; |
---|
844 | } |
---|
845 | |
---|
846 | // Find a feasible flow using Circulation |
---|
847 | Circulation<Digraph, ConstMap<Arc, Value>, ValueArcMap, ValueNodeMap> |
---|
848 | circ(_graph, low, cap, sup); |
---|
849 | if (!circ.flowMap(flow).run()) return INFEASIBLE; |
---|
850 | |
---|
851 | // Set residual capacities and handle GEQ supply type |
---|
852 | if (_sum_supply < 0) { |
---|
853 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
854 | Value fa = flow[a]; |
---|
855 | _res_cap[_arc_idf[a]] = cap[a] - fa; |
---|
856 | _res_cap[_arc_idb[a]] = fa; |
---|
857 | sup[_graph.source(a)] -= fa; |
---|
858 | sup[_graph.target(a)] += fa; |
---|
859 | } |
---|
860 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
861 | _excess[_node_id[n]] = sup[n]; |
---|
862 | } |
---|
863 | for (int a = _first_out[_root]; a != _res_arc_num; ++a) { |
---|
864 | int u = _target[a]; |
---|
865 | int ra = _reverse[a]; |
---|
866 | _res_cap[a] = -_sum_supply + 1; |
---|
867 | _res_cap[ra] = -_excess[u]; |
---|
868 | _cost[a] = 0; |
---|
869 | _cost[ra] = 0; |
---|
870 | _excess[u] = 0; |
---|
871 | } |
---|
872 | } else { |
---|
873 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
874 | Value fa = flow[a]; |
---|
875 | _res_cap[_arc_idf[a]] = cap[a] - fa; |
---|
876 | _res_cap[_arc_idb[a]] = fa; |
---|
877 | } |
---|
878 | for (int a = _first_out[_root]; a != _res_arc_num; ++a) { |
---|
879 | int ra = _reverse[a]; |
---|
880 | _res_cap[a] = 0; |
---|
881 | _res_cap[ra] = 0; |
---|
882 | _cost[a] = 0; |
---|
883 | _cost[ra] = 0; |
---|
884 | } |
---|
885 | } |
---|
886 | |
---|
887 | // Initialize data structures for buckets |
---|
888 | _max_rank = _alpha * _res_node_num; |
---|
889 | _buckets.resize(_max_rank); |
---|
890 | _bucket_next.resize(_res_node_num + 1); |
---|
891 | _bucket_prev.resize(_res_node_num + 1); |
---|
892 | _rank.resize(_res_node_num + 1); |
---|
893 | |
---|
894 | return OPTIMAL; |
---|
895 | } |
---|
896 | |
---|
897 | // Execute the algorithm and transform the results |
---|
898 | void start(Method method) { |
---|
899 | const int MAX_PARTIAL_PATH_LENGTH = 4; |
---|
900 | |
---|
901 | switch (method) { |
---|
902 | case PUSH: |
---|
903 | startPush(); |
---|
904 | break; |
---|
905 | case AUGMENT: |
---|
906 | startAugment(_res_node_num - 1); |
---|
907 | break; |
---|
908 | case PARTIAL_AUGMENT: |
---|
909 | startAugment(MAX_PARTIAL_PATH_LENGTH); |
---|
910 | break; |
---|
911 | } |
---|
912 | |
---|
913 | // Compute node potentials (dual solution) |
---|
914 | for (int i = 0; i != _res_node_num; ++i) { |
---|
915 | _pi[i] = static_cast<Cost>(_pi[i] / (_res_node_num * _alpha)); |
---|
916 | } |
---|
917 | bool optimal = true; |
---|
918 | for (int i = 0; optimal && i != _res_node_num; ++i) { |
---|
919 | LargeCost pi_i = _pi[i]; |
---|
920 | int last_out = _first_out[i+1]; |
---|
921 | for (int j = _first_out[i]; j != last_out; ++j) { |
---|
922 | if (_res_cap[j] > 0 && _scost[j] + pi_i - _pi[_target[j]] < 0) { |
---|
923 | optimal = false; |
---|
924 | break; |
---|
925 | } |
---|
926 | } |
---|
927 | } |
---|
928 | |
---|
929 | if (!optimal) { |
---|
930 | // Compute node potentials for the original costs with BellmanFord |
---|
931 | // (if it is necessary) |
---|
932 | typedef std::pair<int, int> IntPair; |
---|
933 | StaticDigraph sgr; |
---|
934 | std::vector<IntPair> arc_vec; |
---|
935 | std::vector<LargeCost> cost_vec; |
---|
936 | LargeCostArcMap cost_map(cost_vec); |
---|
937 | |
---|
938 | arc_vec.clear(); |
---|
939 | cost_vec.clear(); |
---|
940 | for (int j = 0; j != _res_arc_num; ++j) { |
---|
941 | if (_res_cap[j] > 0) { |
---|
942 | int u = _source[j], v = _target[j]; |
---|
943 | arc_vec.push_back(IntPair(u, v)); |
---|
944 | cost_vec.push_back(_scost[j] + _pi[u] - _pi[v]); |
---|
945 | } |
---|
946 | } |
---|
947 | sgr.build(_res_node_num, arc_vec.begin(), arc_vec.end()); |
---|
948 | |
---|
949 | typename BellmanFord<StaticDigraph, LargeCostArcMap>::Create |
---|
950 | bf(sgr, cost_map); |
---|
951 | bf.init(0); |
---|
952 | bf.start(); |
---|
953 | |
---|
954 | for (int i = 0; i != _res_node_num; ++i) { |
---|
955 | _pi[i] += bf.dist(sgr.node(i)); |
---|
956 | } |
---|
957 | } |
---|
958 | |
---|
959 | // Shift potentials to meet the requirements of the GEQ type |
---|
960 | // optimality conditions |
---|
961 | LargeCost max_pot = _pi[_root]; |
---|
962 | for (int i = 0; i != _res_node_num; ++i) { |
---|
963 | if (_pi[i] > max_pot) max_pot = _pi[i]; |
---|
964 | } |
---|
965 | if (max_pot != 0) { |
---|
966 | for (int i = 0; i != _res_node_num; ++i) { |
---|
967 | _pi[i] -= max_pot; |
---|
968 | } |
---|
969 | } |
---|
970 | |
---|
971 | // Handle non-zero lower bounds |
---|
972 | if (_have_lower) { |
---|
973 | int limit = _first_out[_root]; |
---|
974 | for (int j = 0; j != limit; ++j) { |
---|
975 | if (!_forward[j]) _res_cap[j] += _lower[j]; |
---|
976 | } |
---|
977 | } |
---|
978 | } |
---|
979 | |
---|
980 | // Initialize a cost scaling phase |
---|
981 | void initPhase() { |
---|
982 | // Saturate arcs not satisfying the optimality condition |
---|
983 | for (int u = 0; u != _res_node_num; ++u) { |
---|
984 | int last_out = _first_out[u+1]; |
---|
985 | LargeCost pi_u = _pi[u]; |
---|
986 | for (int a = _first_out[u]; a != last_out; ++a) { |
---|
987 | Value delta = _res_cap[a]; |
---|
988 | if (delta > 0) { |
---|
989 | int v = _target[a]; |
---|
990 | if (_cost[a] + pi_u - _pi[v] < 0) { |
---|
991 | _excess[u] -= delta; |
---|
992 | _excess[v] += delta; |
---|
993 | _res_cap[a] = 0; |
---|
994 | _res_cap[_reverse[a]] += delta; |
---|
995 | } |
---|
996 | } |
---|
997 | } |
---|
998 | } |
---|
999 | |
---|
1000 | // Find active nodes (i.e. nodes with positive excess) |
---|
1001 | for (int u = 0; u != _res_node_num; ++u) { |
---|
1002 | if (_excess[u] > 0) _active_nodes.push_back(u); |
---|
1003 | } |
---|
1004 | |
---|
1005 | // Initialize the next arcs |
---|
1006 | for (int u = 0; u != _res_node_num; ++u) { |
---|
1007 | _next_out[u] = _first_out[u]; |
---|
1008 | } |
---|
1009 | } |
---|
1010 | |
---|
1011 | // Price (potential) refinement heuristic |
---|
1012 | bool priceRefinement() { |
---|
1013 | |
---|
1014 | // Stack for stroing the topological order |
---|
1015 | IntVector stack(_res_node_num); |
---|
1016 | int stack_top; |
---|
1017 | |
---|
1018 | // Perform phases |
---|
1019 | while (topologicalSort(stack, stack_top)) { |
---|
1020 | |
---|
1021 | // Compute node ranks in the acyclic admissible network and |
---|
1022 | // store the nodes in buckets |
---|
1023 | for (int i = 0; i != _res_node_num; ++i) { |
---|
1024 | _rank[i] = 0; |
---|
1025 | } |
---|
1026 | const int bucket_end = _root + 1; |
---|
1027 | for (int r = 0; r != _max_rank; ++r) { |
---|
1028 | _buckets[r] = bucket_end; |
---|
1029 | } |
---|
1030 | int top_rank = 0; |
---|
1031 | for ( ; stack_top >= 0; --stack_top) { |
---|
1032 | int u = stack[stack_top], v; |
---|
1033 | int rank_u = _rank[u]; |
---|
1034 | |
---|
1035 | LargeCost rc, pi_u = _pi[u]; |
---|
1036 | int last_out = _first_out[u+1]; |
---|
1037 | for (int a = _first_out[u]; a != last_out; ++a) { |
---|
1038 | if (_res_cap[a] > 0) { |
---|
1039 | v = _target[a]; |
---|
1040 | rc = _cost[a] + pi_u - _pi[v]; |
---|
1041 | if (rc < 0) { |
---|
1042 | LargeCost nrc = static_cast<LargeCost>((-rc - 0.5) / _epsilon); |
---|
1043 | if (nrc < LargeCost(_max_rank)) { |
---|
1044 | int new_rank_v = rank_u + static_cast<int>(nrc); |
---|
1045 | if (new_rank_v > _rank[v]) { |
---|
1046 | _rank[v] = new_rank_v; |
---|
1047 | } |
---|
1048 | } |
---|
1049 | } |
---|
1050 | } |
---|
1051 | } |
---|
1052 | |
---|
1053 | if (rank_u > 0) { |
---|
1054 | top_rank = std::max(top_rank, rank_u); |
---|
1055 | int bfirst = _buckets[rank_u]; |
---|
1056 | _bucket_next[u] = bfirst; |
---|
1057 | _bucket_prev[bfirst] = u; |
---|
1058 | _buckets[rank_u] = u; |
---|
1059 | } |
---|
1060 | } |
---|
1061 | |
---|
1062 | // Check if the current flow is epsilon-optimal |
---|
1063 | if (top_rank == 0) { |
---|
1064 | return true; |
---|
1065 | } |
---|
1066 | |
---|
1067 | // Process buckets in top-down order |
---|
1068 | for (int rank = top_rank; rank > 0; --rank) { |
---|
1069 | while (_buckets[rank] != bucket_end) { |
---|
1070 | // Remove the first node from the current bucket |
---|
1071 | int u = _buckets[rank]; |
---|
1072 | _buckets[rank] = _bucket_next[u]; |
---|
1073 | |
---|
1074 | // Search the outgoing arcs of u |
---|
1075 | LargeCost rc, pi_u = _pi[u]; |
---|
1076 | int last_out = _first_out[u+1]; |
---|
1077 | int v, old_rank_v, new_rank_v; |
---|
1078 | for (int a = _first_out[u]; a != last_out; ++a) { |
---|
1079 | if (_res_cap[a] > 0) { |
---|
1080 | v = _target[a]; |
---|
1081 | old_rank_v = _rank[v]; |
---|
1082 | |
---|
1083 | if (old_rank_v < rank) { |
---|
1084 | |
---|
1085 | // Compute the new rank of node v |
---|
1086 | rc = _cost[a] + pi_u - _pi[v]; |
---|
1087 | if (rc < 0) { |
---|
1088 | new_rank_v = rank; |
---|
1089 | } else { |
---|
1090 | LargeCost nrc = rc / _epsilon; |
---|
1091 | new_rank_v = 0; |
---|
1092 | if (nrc < LargeCost(_max_rank)) { |
---|
1093 | new_rank_v = rank - 1 - static_cast<int>(nrc); |
---|
1094 | } |
---|
1095 | } |
---|
1096 | |
---|
1097 | // Change the rank of node v |
---|
1098 | if (new_rank_v > old_rank_v) { |
---|
1099 | _rank[v] = new_rank_v; |
---|
1100 | |
---|
1101 | // Remove v from its old bucket |
---|
1102 | if (old_rank_v > 0) { |
---|
1103 | if (_buckets[old_rank_v] == v) { |
---|
1104 | _buckets[old_rank_v] = _bucket_next[v]; |
---|
1105 | } else { |
---|
1106 | int pv = _bucket_prev[v], nv = _bucket_next[v]; |
---|
1107 | _bucket_next[pv] = nv; |
---|
1108 | _bucket_prev[nv] = pv; |
---|
1109 | } |
---|
1110 | } |
---|
1111 | |
---|
1112 | // Insert v into its new bucket |
---|
1113 | int nv = _buckets[new_rank_v]; |
---|
1114 | _bucket_next[v] = nv; |
---|
1115 | _bucket_prev[nv] = v; |
---|
1116 | _buckets[new_rank_v] = v; |
---|
1117 | } |
---|
1118 | } |
---|
1119 | } |
---|
1120 | } |
---|
1121 | |
---|
1122 | // Refine potential of node u |
---|
1123 | _pi[u] -= rank * _epsilon; |
---|
1124 | } |
---|
1125 | } |
---|
1126 | |
---|
1127 | } |
---|
1128 | |
---|
1129 | return false; |
---|
1130 | } |
---|
1131 | |
---|
1132 | // Find and cancel cycles in the admissible network and |
---|
1133 | // determine topological order using DFS |
---|
1134 | bool topologicalSort(IntVector &stack, int &stack_top) { |
---|
1135 | const int MAX_CYCLE_CANCEL = 1; |
---|
1136 | |
---|
1137 | BoolVector reached(_res_node_num, false); |
---|
1138 | BoolVector processed(_res_node_num, false); |
---|
1139 | IntVector pred(_res_node_num); |
---|
1140 | for (int i = 0; i != _res_node_num; ++i) { |
---|
1141 | _next_out[i] = _first_out[i]; |
---|
1142 | } |
---|
1143 | stack_top = -1; |
---|
1144 | |
---|
1145 | int cycle_cnt = 0; |
---|
1146 | for (int start = 0; start != _res_node_num; ++start) { |
---|
1147 | if (reached[start]) continue; |
---|
1148 | |
---|
1149 | // Start DFS search from this start node |
---|
1150 | pred[start] = -1; |
---|
1151 | int tip = start, v; |
---|
1152 | while (true) { |
---|
1153 | // Check the outgoing arcs of the current tip node |
---|
1154 | reached[tip] = true; |
---|
1155 | LargeCost pi_tip = _pi[tip]; |
---|
1156 | int a, last_out = _first_out[tip+1]; |
---|
1157 | for (a = _next_out[tip]; a != last_out; ++a) { |
---|
1158 | if (_res_cap[a] > 0) { |
---|
1159 | v = _target[a]; |
---|
1160 | if (_cost[a] + pi_tip - _pi[v] < 0) { |
---|
1161 | if (!reached[v]) { |
---|
1162 | // A new node is reached |
---|
1163 | reached[v] = true; |
---|
1164 | pred[v] = tip; |
---|
1165 | _next_out[tip] = a; |
---|
1166 | tip = v; |
---|
1167 | a = _next_out[tip]; |
---|
1168 | last_out = _first_out[tip+1]; |
---|
1169 | break; |
---|
1170 | } |
---|
1171 | else if (!processed[v]) { |
---|
1172 | // A cycle is found |
---|
1173 | ++cycle_cnt; |
---|
1174 | _next_out[tip] = a; |
---|
1175 | |
---|
1176 | // Find the minimum residual capacity along the cycle |
---|
1177 | Value d, delta = _res_cap[a]; |
---|
1178 | int u, delta_node = tip; |
---|
1179 | for (u = tip; u != v; ) { |
---|
1180 | u = pred[u]; |
---|
1181 | d = _res_cap[_next_out[u]]; |
---|
1182 | if (d <= delta) { |
---|
1183 | delta = d; |
---|
1184 | delta_node = u; |
---|
1185 | } |
---|
1186 | } |
---|
1187 | |
---|
1188 | // Augment along the cycle |
---|
1189 | _res_cap[a] -= delta; |
---|
1190 | _res_cap[_reverse[a]] += delta; |
---|
1191 | for (u = tip; u != v; ) { |
---|
1192 | u = pred[u]; |
---|
1193 | int ca = _next_out[u]; |
---|
1194 | _res_cap[ca] -= delta; |
---|
1195 | _res_cap[_reverse[ca]] += delta; |
---|
1196 | } |
---|
1197 | |
---|
1198 | // Check the maximum number of cycle canceling |
---|
1199 | if (cycle_cnt >= MAX_CYCLE_CANCEL) { |
---|
1200 | return false; |
---|
1201 | } |
---|
1202 | |
---|
1203 | // Roll back search to delta_node |
---|
1204 | if (delta_node != tip) { |
---|
1205 | for (u = tip; u != delta_node; u = pred[u]) { |
---|
1206 | reached[u] = false; |
---|
1207 | } |
---|
1208 | tip = delta_node; |
---|
1209 | a = _next_out[tip] + 1; |
---|
1210 | last_out = _first_out[tip+1]; |
---|
1211 | break; |
---|
1212 | } |
---|
1213 | } |
---|
1214 | } |
---|
1215 | } |
---|
1216 | } |
---|
1217 | |
---|
1218 | // Step back to the previous node |
---|
1219 | if (a == last_out) { |
---|
1220 | processed[tip] = true; |
---|
1221 | stack[++stack_top] = tip; |
---|
1222 | tip = pred[tip]; |
---|
1223 | if (tip < 0) { |
---|
1224 | // Finish DFS from the current start node |
---|
1225 | break; |
---|
1226 | } |
---|
1227 | ++_next_out[tip]; |
---|
1228 | } |
---|
1229 | } |
---|
1230 | |
---|
1231 | } |
---|
1232 | |
---|
1233 | return (cycle_cnt == 0); |
---|
1234 | } |
---|
1235 | |
---|
1236 | // Global potential update heuristic |
---|
1237 | void globalUpdate() { |
---|
1238 | const int bucket_end = _root + 1; |
---|
1239 | |
---|
1240 | // Initialize buckets |
---|
1241 | for (int r = 0; r != _max_rank; ++r) { |
---|
1242 | _buckets[r] = bucket_end; |
---|
1243 | } |
---|
1244 | Value total_excess = 0; |
---|
1245 | int b0 = bucket_end; |
---|
1246 | for (int i = 0; i != _res_node_num; ++i) { |
---|
1247 | if (_excess[i] < 0) { |
---|
1248 | _rank[i] = 0; |
---|
1249 | _bucket_next[i] = b0; |
---|
1250 | _bucket_prev[b0] = i; |
---|
1251 | b0 = i; |
---|
1252 | } else { |
---|
1253 | total_excess += _excess[i]; |
---|
1254 | _rank[i] = _max_rank; |
---|
1255 | } |
---|
1256 | } |
---|
1257 | if (total_excess == 0) return; |
---|
1258 | _buckets[0] = b0; |
---|
1259 | |
---|
1260 | // Search the buckets |
---|
1261 | int r = 0; |
---|
1262 | for ( ; r != _max_rank; ++r) { |
---|
1263 | while (_buckets[r] != bucket_end) { |
---|
1264 | // Remove the first node from the current bucket |
---|
1265 | int u = _buckets[r]; |
---|
1266 | _buckets[r] = _bucket_next[u]; |
---|
1267 | |
---|
1268 | // Search the incomming arcs of u |
---|
1269 | LargeCost pi_u = _pi[u]; |
---|
1270 | int last_out = _first_out[u+1]; |
---|
1271 | for (int a = _first_out[u]; a != last_out; ++a) { |
---|
1272 | int ra = _reverse[a]; |
---|
1273 | if (_res_cap[ra] > 0) { |
---|
1274 | int v = _source[ra]; |
---|
1275 | int old_rank_v = _rank[v]; |
---|
1276 | if (r < old_rank_v) { |
---|
1277 | // Compute the new rank of v |
---|
1278 | LargeCost nrc = (_cost[ra] + _pi[v] - pi_u) / _epsilon; |
---|
1279 | int new_rank_v = old_rank_v; |
---|
1280 | if (nrc < LargeCost(_max_rank)) { |
---|
1281 | new_rank_v = r + 1 + static_cast<int>(nrc); |
---|
1282 | } |
---|
1283 | |
---|
1284 | // Change the rank of v |
---|
1285 | if (new_rank_v < old_rank_v) { |
---|
1286 | _rank[v] = new_rank_v; |
---|
1287 | _next_out[v] = _first_out[v]; |
---|
1288 | |
---|
1289 | // Remove v from its old bucket |
---|
1290 | if (old_rank_v < _max_rank) { |
---|
1291 | if (_buckets[old_rank_v] == v) { |
---|
1292 | _buckets[old_rank_v] = _bucket_next[v]; |
---|
1293 | } else { |
---|
1294 | int pv = _bucket_prev[v], nv = _bucket_next[v]; |
---|
1295 | _bucket_next[pv] = nv; |
---|
1296 | _bucket_prev[nv] = pv; |
---|
1297 | } |
---|
1298 | } |
---|
1299 | |
---|
1300 | // Insert v into its new bucket |
---|
1301 | int nv = _buckets[new_rank_v]; |
---|
1302 | _bucket_next[v] = nv; |
---|
1303 | _bucket_prev[nv] = v; |
---|
1304 | _buckets[new_rank_v] = v; |
---|
1305 | } |
---|
1306 | } |
---|
1307 | } |
---|
1308 | } |
---|
1309 | |
---|
1310 | // Finish search if there are no more active nodes |
---|
1311 | if (_excess[u] > 0) { |
---|
1312 | total_excess -= _excess[u]; |
---|
1313 | if (total_excess <= 0) break; |
---|
1314 | } |
---|
1315 | } |
---|
1316 | if (total_excess <= 0) break; |
---|
1317 | } |
---|
1318 | |
---|
1319 | // Relabel nodes |
---|
1320 | for (int u = 0; u != _res_node_num; ++u) { |
---|
1321 | int k = std::min(_rank[u], r); |
---|
1322 | if (k > 0) { |
---|
1323 | _pi[u] -= _epsilon * k; |
---|
1324 | _next_out[u] = _first_out[u]; |
---|
1325 | } |
---|
1326 | } |
---|
1327 | } |
---|
1328 | |
---|
1329 | /// Execute the algorithm performing augment and relabel operations |
---|
1330 | void startAugment(int max_length) { |
---|
1331 | // Paramters for heuristics |
---|
1332 | const int PRICE_REFINEMENT_LIMIT = 2; |
---|
1333 | const double GLOBAL_UPDATE_FACTOR = 1.0; |
---|
1334 | const int global_update_skip = static_cast<int>(GLOBAL_UPDATE_FACTOR * |
---|
1335 | (_res_node_num + _sup_node_num * _sup_node_num)); |
---|
1336 | int next_global_update_limit = global_update_skip; |
---|
1337 | |
---|
1338 | // Perform cost scaling phases |
---|
1339 | IntVector path; |
---|
1340 | BoolVector path_arc(_res_arc_num, false); |
---|
1341 | int relabel_cnt = 0; |
---|
1342 | int eps_phase_cnt = 0; |
---|
1343 | for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ? |
---|
1344 | 1 : _epsilon / _alpha ) |
---|
1345 | { |
---|
1346 | ++eps_phase_cnt; |
---|
1347 | |
---|
1348 | // Price refinement heuristic |
---|
1349 | if (eps_phase_cnt >= PRICE_REFINEMENT_LIMIT) { |
---|
1350 | if (priceRefinement()) continue; |
---|
1351 | } |
---|
1352 | |
---|
1353 | // Initialize current phase |
---|
1354 | initPhase(); |
---|
1355 | |
---|
1356 | // Perform partial augment and relabel operations |
---|
1357 | while (true) { |
---|
1358 | // Select an active node (FIFO selection) |
---|
1359 | while (_active_nodes.size() > 0 && |
---|
1360 | _excess[_active_nodes.front()] <= 0) { |
---|
1361 | _active_nodes.pop_front(); |
---|
1362 | } |
---|
1363 | if (_active_nodes.size() == 0) break; |
---|
1364 | int start = _active_nodes.front(); |
---|
1365 | |
---|
1366 | // Find an augmenting path from the start node |
---|
1367 | int tip = start; |
---|
1368 | while (int(path.size()) < max_length && _excess[tip] >= 0) { |
---|
1369 | int u; |
---|
1370 | LargeCost rc, min_red_cost = std::numeric_limits<LargeCost>::max(); |
---|
1371 | LargeCost pi_tip = _pi[tip]; |
---|
1372 | int last_out = _first_out[tip+1]; |
---|
1373 | for (int a = _next_out[tip]; a != last_out; ++a) { |
---|
1374 | if (_res_cap[a] > 0) { |
---|
1375 | u = _target[a]; |
---|
1376 | rc = _cost[a] + pi_tip - _pi[u]; |
---|
1377 | if (rc < 0) { |
---|
1378 | path.push_back(a); |
---|
1379 | _next_out[tip] = a; |
---|
1380 | if (path_arc[a]) { |
---|
1381 | goto augment; // a cycle is found, stop path search |
---|
1382 | } |
---|
1383 | tip = u; |
---|
1384 | path_arc[a] = true; |
---|
1385 | goto next_step; |
---|
1386 | } |
---|
1387 | else if (rc < min_red_cost) { |
---|
1388 | min_red_cost = rc; |
---|
1389 | } |
---|
1390 | } |
---|
1391 | } |
---|
1392 | |
---|
1393 | // Relabel tip node |
---|
1394 | if (tip != start) { |
---|
1395 | int ra = _reverse[path.back()]; |
---|
1396 | min_red_cost = |
---|
1397 | std::min(min_red_cost, _cost[ra] + pi_tip - _pi[_target[ra]]); |
---|
1398 | } |
---|
1399 | last_out = _next_out[tip]; |
---|
1400 | for (int a = _first_out[tip]; a != last_out; ++a) { |
---|
1401 | if (_res_cap[a] > 0) { |
---|
1402 | rc = _cost[a] + pi_tip - _pi[_target[a]]; |
---|
1403 | if (rc < min_red_cost) { |
---|
1404 | min_red_cost = rc; |
---|
1405 | } |
---|
1406 | } |
---|
1407 | } |
---|
1408 | _pi[tip] -= min_red_cost + _epsilon; |
---|
1409 | _next_out[tip] = _first_out[tip]; |
---|
1410 | ++relabel_cnt; |
---|
1411 | |
---|
1412 | // Step back |
---|
1413 | if (tip != start) { |
---|
1414 | int pa = path.back(); |
---|
1415 | path_arc[pa] = false; |
---|
1416 | tip = _source[pa]; |
---|
1417 | path.pop_back(); |
---|
1418 | } |
---|
1419 | |
---|
1420 | next_step: ; |
---|
1421 | } |
---|
1422 | |
---|
1423 | // Augment along the found path (as much flow as possible) |
---|
1424 | augment: |
---|
1425 | Value delta; |
---|
1426 | int pa, u, v = start; |
---|
1427 | for (int i = 0; i != int(path.size()); ++i) { |
---|
1428 | pa = path[i]; |
---|
1429 | u = v; |
---|
1430 | v = _target[pa]; |
---|
1431 | path_arc[pa] = false; |
---|
1432 | delta = std::min(_res_cap[pa], _excess[u]); |
---|
1433 | _res_cap[pa] -= delta; |
---|
1434 | _res_cap[_reverse[pa]] += delta; |
---|
1435 | _excess[u] -= delta; |
---|
1436 | _excess[v] += delta; |
---|
1437 | if (_excess[v] > 0 && _excess[v] <= delta) { |
---|
1438 | _active_nodes.push_back(v); |
---|
1439 | } |
---|
1440 | } |
---|
1441 | path.clear(); |
---|
1442 | |
---|
1443 | // Global update heuristic |
---|
1444 | if (relabel_cnt >= next_global_update_limit) { |
---|
1445 | globalUpdate(); |
---|
1446 | next_global_update_limit += global_update_skip; |
---|
1447 | } |
---|
1448 | } |
---|
1449 | |
---|
1450 | } |
---|
1451 | |
---|
1452 | } |
---|
1453 | |
---|
1454 | /// Execute the algorithm performing push and relabel operations |
---|
1455 | void startPush() { |
---|
1456 | // Paramters for heuristics |
---|
1457 | const int PRICE_REFINEMENT_LIMIT = 2; |
---|
1458 | const double GLOBAL_UPDATE_FACTOR = 2.0; |
---|
1459 | |
---|
1460 | const int global_update_skip = static_cast<int>(GLOBAL_UPDATE_FACTOR * |
---|
1461 | (_res_node_num + _sup_node_num * _sup_node_num)); |
---|
1462 | int next_global_update_limit = global_update_skip; |
---|
1463 | |
---|
1464 | // Perform cost scaling phases |
---|
1465 | BoolVector hyper(_res_node_num, false); |
---|
1466 | LargeCostVector hyper_cost(_res_node_num); |
---|
1467 | int relabel_cnt = 0; |
---|
1468 | int eps_phase_cnt = 0; |
---|
1469 | for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ? |
---|
1470 | 1 : _epsilon / _alpha ) |
---|
1471 | { |
---|
1472 | ++eps_phase_cnt; |
---|
1473 | |
---|
1474 | // Price refinement heuristic |
---|
1475 | if (eps_phase_cnt >= PRICE_REFINEMENT_LIMIT) { |
---|
1476 | if (priceRefinement()) continue; |
---|
1477 | } |
---|
1478 | |
---|
1479 | // Initialize current phase |
---|
1480 | initPhase(); |
---|
1481 | |
---|
1482 | // Perform push and relabel operations |
---|
1483 | while (_active_nodes.size() > 0) { |
---|
1484 | LargeCost min_red_cost, rc, pi_n; |
---|
1485 | Value delta; |
---|
1486 | int n, t, a, last_out = _res_arc_num; |
---|
1487 | |
---|
1488 | next_node: |
---|
1489 | // Select an active node (FIFO selection) |
---|
1490 | n = _active_nodes.front(); |
---|
1491 | last_out = _first_out[n+1]; |
---|
1492 | pi_n = _pi[n]; |
---|
1493 | |
---|
1494 | // Perform push operations if there are admissible arcs |
---|
1495 | if (_excess[n] > 0) { |
---|
1496 | for (a = _next_out[n]; a != last_out; ++a) { |
---|
1497 | if (_res_cap[a] > 0 && |
---|
1498 | _cost[a] + pi_n - _pi[_target[a]] < 0) { |
---|
1499 | delta = std::min(_res_cap[a], _excess[n]); |
---|
1500 | t = _target[a]; |
---|
1501 | |
---|
1502 | // Push-look-ahead heuristic |
---|
1503 | Value ahead = -_excess[t]; |
---|
1504 | int last_out_t = _first_out[t+1]; |
---|
1505 | LargeCost pi_t = _pi[t]; |
---|
1506 | for (int ta = _next_out[t]; ta != last_out_t; ++ta) { |
---|
1507 | if (_res_cap[ta] > 0 && |
---|
1508 | _cost[ta] + pi_t - _pi[_target[ta]] < 0) |
---|
1509 | ahead += _res_cap[ta]; |
---|
1510 | if (ahead >= delta) break; |
---|
1511 | } |
---|
1512 | if (ahead < 0) ahead = 0; |
---|
1513 | |
---|
1514 | // Push flow along the arc |
---|
1515 | if (ahead < delta && !hyper[t]) { |
---|
1516 | _res_cap[a] -= ahead; |
---|
1517 | _res_cap[_reverse[a]] += ahead; |
---|
1518 | _excess[n] -= ahead; |
---|
1519 | _excess[t] += ahead; |
---|
1520 | _active_nodes.push_front(t); |
---|
1521 | hyper[t] = true; |
---|
1522 | hyper_cost[t] = _cost[a] + pi_n - pi_t; |
---|
1523 | _next_out[n] = a; |
---|
1524 | goto next_node; |
---|
1525 | } else { |
---|
1526 | _res_cap[a] -= delta; |
---|
1527 | _res_cap[_reverse[a]] += delta; |
---|
1528 | _excess[n] -= delta; |
---|
1529 | _excess[t] += delta; |
---|
1530 | if (_excess[t] > 0 && _excess[t] <= delta) |
---|
1531 | _active_nodes.push_back(t); |
---|
1532 | } |
---|
1533 | |
---|
1534 | if (_excess[n] == 0) { |
---|
1535 | _next_out[n] = a; |
---|
1536 | goto remove_nodes; |
---|
1537 | } |
---|
1538 | } |
---|
1539 | } |
---|
1540 | _next_out[n] = a; |
---|
1541 | } |
---|
1542 | |
---|
1543 | // Relabel the node if it is still active (or hyper) |
---|
1544 | if (_excess[n] > 0 || hyper[n]) { |
---|
1545 | min_red_cost = hyper[n] ? -hyper_cost[n] : |
---|
1546 | std::numeric_limits<LargeCost>::max(); |
---|
1547 | for (int a = _first_out[n]; a != last_out; ++a) { |
---|
1548 | if (_res_cap[a] > 0) { |
---|
1549 | rc = _cost[a] + pi_n - _pi[_target[a]]; |
---|
1550 | if (rc < min_red_cost) { |
---|
1551 | min_red_cost = rc; |
---|
1552 | } |
---|
1553 | } |
---|
1554 | } |
---|
1555 | _pi[n] -= min_red_cost + _epsilon; |
---|
1556 | _next_out[n] = _first_out[n]; |
---|
1557 | hyper[n] = false; |
---|
1558 | ++relabel_cnt; |
---|
1559 | } |
---|
1560 | |
---|
1561 | // Remove nodes that are not active nor hyper |
---|
1562 | remove_nodes: |
---|
1563 | while ( _active_nodes.size() > 0 && |
---|
1564 | _excess[_active_nodes.front()] <= 0 && |
---|
1565 | !hyper[_active_nodes.front()] ) { |
---|
1566 | _active_nodes.pop_front(); |
---|
1567 | } |
---|
1568 | |
---|
1569 | // Global update heuristic |
---|
1570 | if (relabel_cnt >= next_global_update_limit) { |
---|
1571 | globalUpdate(); |
---|
1572 | for (int u = 0; u != _res_node_num; ++u) |
---|
1573 | hyper[u] = false; |
---|
1574 | next_global_update_limit += global_update_skip; |
---|
1575 | } |
---|
1576 | } |
---|
1577 | } |
---|
1578 | } |
---|
1579 | |
---|
1580 | }; //class CostScaling |
---|
1581 | |
---|
1582 | ///@} |
---|
1583 | |
---|
1584 | } //namespace lemon |
---|
1585 | |
---|
1586 | #endif //LEMON_COST_SCALING_H |
---|