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) 2003-2013 |
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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_CYCLE_CANCELING_H |
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20 | #define LEMON_CYCLE_CANCELING_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 Cycle-canceling algorithms for finding a minimum cost flow. |
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25 | |
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26 | #include <vector> |
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27 | #include <limits> |
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28 | |
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29 | #include <lemon/core.h> |
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30 | #include <lemon/maps.h> |
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31 | #include <lemon/path.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/adaptors.h> |
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35 | #include <lemon/circulation.h> |
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36 | #include <lemon/bellman_ford.h> |
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37 | #include <lemon/howard_mmc.h> |
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38 | #include <lemon/hartmann_orlin_mmc.h> |
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39 | |
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40 | namespace lemon { |
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41 | |
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42 | /// \addtogroup min_cost_flow_algs |
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43 | /// @{ |
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44 | |
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45 | /// \brief Implementation of cycle-canceling algorithms for |
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46 | /// finding a \ref min_cost_flow "minimum cost flow". |
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47 | /// |
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48 | /// \ref CycleCanceling implements three different cycle-canceling |
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49 | /// algorithms for finding a \ref min_cost_flow "minimum cost flow" |
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50 | /// \cite amo93networkflows, \cite klein67primal, |
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51 | /// \cite goldberg89cyclecanceling. |
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52 | /// The most efficent one is the \ref CANCEL_AND_TIGHTEN |
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53 | /// "Cancel-and-Tighten" algorithm, thus it is the default method. |
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54 | /// It runs in strongly polynomial time \f$O(n^2 m^2 \log n)\f$, |
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55 | /// but in practice, it is typically orders of magnitude slower than |
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56 | /// the scaling algorithms and \ref NetworkSimplex. |
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57 | /// (For more information, see \ref min_cost_flow_algs "the module page".) |
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58 | /// |
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59 | /// Most of the parameters of the problem (except for the digraph) |
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60 | /// can be given using separate functions, and the algorithm can be |
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61 | /// executed using the \ref run() function. If some parameters are not |
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62 | /// specified, then default values will be used. |
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63 | /// |
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64 | /// \tparam GR The digraph type the algorithm runs on. |
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65 | /// \tparam V The number type used for flow amounts, capacity bounds |
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66 | /// and supply values in the algorithm. By default, it is \c int. |
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67 | /// \tparam C The number type used for costs and potentials in the |
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68 | /// algorithm. By default, it is the same as \c V. |
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69 | /// |
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70 | /// \warning Both \c V and \c C must be signed number types. |
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71 | /// \warning All input data (capacities, supply values, and costs) must |
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72 | /// be integer. |
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73 | /// \warning This algorithm does not support negative costs for |
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74 | /// arcs having infinite upper bound. |
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75 | /// |
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76 | /// \note For more information about the three available methods, |
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77 | /// see \ref Method. |
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78 | #ifdef DOXYGEN |
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79 | template <typename GR, typename V, typename C> |
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80 | #else |
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81 | template <typename GR, typename V = int, typename C = V> |
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82 | #endif |
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83 | class CycleCanceling |
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84 | { |
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85 | public: |
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86 | |
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87 | /// The type of the digraph |
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88 | typedef GR Digraph; |
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89 | /// The type of the flow amounts, capacity bounds and supply values |
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90 | typedef V Value; |
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91 | /// The type of the arc costs |
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92 | typedef C Cost; |
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93 | |
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94 | public: |
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95 | |
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96 | /// \brief Problem type constants for the \c run() function. |
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97 | /// |
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98 | /// Enum type containing the problem type constants that can be |
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99 | /// returned by the \ref run() function of the algorithm. |
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100 | enum ProblemType { |
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101 | /// The problem has no feasible solution (flow). |
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102 | INFEASIBLE, |
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103 | /// The problem has optimal solution (i.e. it is feasible and |
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104 | /// bounded), and the algorithm has found optimal flow and node |
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105 | /// potentials (primal and dual solutions). |
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106 | OPTIMAL, |
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107 | /// The digraph contains an arc of negative cost and infinite |
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108 | /// upper bound. It means that the objective function is unbounded |
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109 | /// on that arc, however, note that it could actually be bounded |
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110 | /// over the feasible flows, but this algroithm cannot handle |
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111 | /// these cases. |
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112 | UNBOUNDED |
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113 | }; |
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114 | |
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115 | /// \brief Constants for selecting the used method. |
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116 | /// |
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117 | /// Enum type containing constants for selecting the used method |
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118 | /// for the \ref run() function. |
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119 | /// |
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120 | /// \ref CycleCanceling provides three different cycle-canceling |
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121 | /// methods. By default, \ref CANCEL_AND_TIGHTEN "Cancel-and-Tighten" |
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122 | /// is used, which is by far the most efficient and the most robust. |
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123 | /// However, the other methods can be selected using the \ref run() |
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124 | /// function with the proper parameter. |
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125 | enum Method { |
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126 | /// A simple cycle-canceling method, which uses the |
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127 | /// \ref BellmanFord "Bellman-Ford" algorithm for detecting negative |
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128 | /// cycles in the residual network. |
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129 | /// The number of Bellman-Ford iterations is bounded by a successively |
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130 | /// increased limit. |
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131 | SIMPLE_CYCLE_CANCELING, |
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132 | /// The "Minimum Mean Cycle-Canceling" algorithm, which is a |
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133 | /// well-known strongly polynomial method |
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134 | /// \cite goldberg89cyclecanceling. It improves along a |
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135 | /// \ref min_mean_cycle "minimum mean cycle" in each iteration. |
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136 | /// Its running time complexity is \f$O(n^2 m^3 \log n)\f$. |
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137 | MINIMUM_MEAN_CYCLE_CANCELING, |
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138 | /// The "Cancel-and-Tighten" algorithm, which can be viewed as an |
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139 | /// improved version of the previous method |
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140 | /// \cite goldberg89cyclecanceling. |
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141 | /// It is faster both in theory and in practice, its running time |
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142 | /// complexity is \f$O(n^2 m^2 \log n)\f$. |
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143 | CANCEL_AND_TIGHTEN |
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144 | }; |
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145 | |
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146 | private: |
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147 | |
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148 | TEMPLATE_DIGRAPH_TYPEDEFS(GR); |
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149 | |
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150 | typedef std::vector<int> IntVector; |
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151 | typedef std::vector<double> DoubleVector; |
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152 | typedef std::vector<Value> ValueVector; |
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153 | typedef std::vector<Cost> CostVector; |
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154 | typedef std::vector<char> BoolVector; |
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155 | // Note: vector<char> is used instead of vector<bool> for efficiency reasons |
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156 | |
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157 | private: |
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158 | |
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159 | template <typename KT, typename VT> |
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160 | class StaticVectorMap { |
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161 | public: |
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162 | typedef KT Key; |
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163 | typedef VT Value; |
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164 | |
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165 | StaticVectorMap(std::vector<Value>& v) : _v(v) {} |
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166 | |
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167 | const Value& operator[](const Key& key) const { |
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168 | return _v[StaticDigraph::id(key)]; |
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169 | } |
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170 | |
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171 | Value& operator[](const Key& key) { |
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172 | return _v[StaticDigraph::id(key)]; |
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173 | } |
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174 | |
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175 | void set(const Key& key, const Value& val) { |
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176 | _v[StaticDigraph::id(key)] = val; |
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177 | } |
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178 | |
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179 | private: |
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180 | std::vector<Value>& _v; |
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181 | }; |
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182 | |
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183 | typedef StaticVectorMap<StaticDigraph::Node, Cost> CostNodeMap; |
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184 | typedef StaticVectorMap<StaticDigraph::Arc, Cost> CostArcMap; |
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185 | |
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186 | private: |
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187 | |
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188 | |
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189 | // Data related to the underlying digraph |
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190 | const GR &_graph; |
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191 | int _node_num; |
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192 | int _arc_num; |
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193 | int _res_node_num; |
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194 | int _res_arc_num; |
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195 | int _root; |
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196 | |
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197 | // Parameters of the problem |
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198 | bool _have_lower; |
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199 | Value _sum_supply; |
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200 | |
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201 | // Data structures for storing the digraph |
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202 | IntNodeMap _node_id; |
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203 | IntArcMap _arc_idf; |
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204 | IntArcMap _arc_idb; |
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205 | IntVector _first_out; |
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206 | BoolVector _forward; |
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207 | IntVector _source; |
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208 | IntVector _target; |
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209 | IntVector _reverse; |
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210 | |
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211 | // Node and arc data |
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212 | ValueVector _lower; |
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213 | ValueVector _upper; |
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214 | CostVector _cost; |
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215 | ValueVector _supply; |
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216 | |
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217 | ValueVector _res_cap; |
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218 | CostVector _pi; |
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219 | |
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220 | // Data for a StaticDigraph structure |
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221 | typedef std::pair<int, int> IntPair; |
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222 | StaticDigraph _sgr; |
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223 | std::vector<IntPair> _arc_vec; |
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224 | std::vector<Cost> _cost_vec; |
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225 | IntVector _id_vec; |
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226 | CostArcMap _cost_map; |
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227 | CostNodeMap _pi_map; |
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228 | |
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229 | public: |
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230 | |
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231 | /// \brief Constant for infinite upper bounds (capacities). |
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232 | /// |
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233 | /// Constant for infinite upper bounds (capacities). |
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234 | /// It is \c std::numeric_limits<Value>::infinity() if available, |
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235 | /// \c std::numeric_limits<Value>::max() otherwise. |
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236 | const Value INF; |
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237 | |
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238 | public: |
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239 | |
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240 | /// \brief Constructor. |
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241 | /// |
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242 | /// The constructor of the class. |
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243 | /// |
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244 | /// \param graph The digraph the algorithm runs on. |
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245 | CycleCanceling(const GR& graph) : |
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246 | _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph), |
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247 | _cost_map(_cost_vec), _pi_map(_pi), |
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248 | INF(std::numeric_limits<Value>::has_infinity ? |
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249 | std::numeric_limits<Value>::infinity() : |
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250 | std::numeric_limits<Value>::max()) |
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251 | { |
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252 | // Check the number types |
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253 | LEMON_ASSERT(std::numeric_limits<Value>::is_signed, |
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254 | "The flow type of CycleCanceling must be signed"); |
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255 | LEMON_ASSERT(std::numeric_limits<Cost>::is_signed, |
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256 | "The cost type of CycleCanceling must be signed"); |
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257 | |
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258 | // Reset data structures |
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259 | reset(); |
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260 | } |
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261 | |
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262 | /// \name Parameters |
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263 | /// The parameters of the algorithm can be specified using these |
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264 | /// functions. |
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265 | |
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266 | /// @{ |
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267 | |
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268 | /// \brief Set the lower bounds on the arcs. |
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269 | /// |
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270 | /// This function sets the lower bounds on the arcs. |
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271 | /// If it is not used before calling \ref run(), the lower bounds |
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272 | /// will be set to zero on all arcs. |
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273 | /// |
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274 | /// \param map An arc map storing the lower bounds. |
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275 | /// Its \c Value type must be convertible to the \c Value type |
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276 | /// of the algorithm. |
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277 | /// |
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278 | /// \return <tt>(*this)</tt> |
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279 | template <typename LowerMap> |
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280 | CycleCanceling& lowerMap(const LowerMap& map) { |
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281 | _have_lower = true; |
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282 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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283 | _lower[_arc_idf[a]] = map[a]; |
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284 | _lower[_arc_idb[a]] = map[a]; |
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285 | } |
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286 | return *this; |
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287 | } |
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288 | |
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289 | /// \brief Set the upper bounds (capacities) on the arcs. |
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290 | /// |
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291 | /// This function sets the upper bounds (capacities) on the arcs. |
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292 | /// If it is not used before calling \ref run(), the upper bounds |
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293 | /// will be set to \ref INF on all arcs (i.e. the flow value will be |
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294 | /// unbounded from above). |
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295 | /// |
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296 | /// \param map An arc map storing the upper bounds. |
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297 | /// Its \c Value type must be convertible to the \c Value type |
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298 | /// of the algorithm. |
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299 | /// |
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300 | /// \return <tt>(*this)</tt> |
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301 | template<typename UpperMap> |
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302 | CycleCanceling& upperMap(const UpperMap& map) { |
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303 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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304 | _upper[_arc_idf[a]] = map[a]; |
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305 | } |
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306 | return *this; |
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307 | } |
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308 | |
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309 | /// \brief Set the costs of the arcs. |
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310 | /// |
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311 | /// This function sets the costs of the arcs. |
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312 | /// If it is not used before calling \ref run(), the costs |
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313 | /// will be set to \c 1 on all arcs. |
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314 | /// |
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315 | /// \param map An arc map storing the costs. |
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316 | /// Its \c Value type must be convertible to the \c Cost type |
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317 | /// of the algorithm. |
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318 | /// |
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319 | /// \return <tt>(*this)</tt> |
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320 | template<typename CostMap> |
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321 | CycleCanceling& costMap(const CostMap& map) { |
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322 | for (ArcIt a(_graph); a != INVALID; ++a) { |
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323 | _cost[_arc_idf[a]] = map[a]; |
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324 | _cost[_arc_idb[a]] = -map[a]; |
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325 | } |
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326 | return *this; |
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327 | } |
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328 | |
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329 | /// \brief Set the supply values of the nodes. |
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330 | /// |
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331 | /// This function sets the supply values of the nodes. |
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332 | /// If neither this function nor \ref stSupply() is used before |
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333 | /// calling \ref run(), the supply of each node will be set to zero. |
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334 | /// |
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335 | /// \param map A node map storing the supply values. |
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336 | /// Its \c Value type must be convertible to the \c Value type |
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337 | /// of the algorithm. |
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338 | /// |
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339 | /// \return <tt>(*this)</tt> |
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340 | template<typename SupplyMap> |
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341 | CycleCanceling& supplyMap(const SupplyMap& map) { |
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342 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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343 | _supply[_node_id[n]] = map[n]; |
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344 | } |
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345 | return *this; |
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346 | } |
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347 | |
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348 | /// \brief Set single source and target nodes and a supply value. |
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349 | /// |
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350 | /// This function sets a single source node and a single target node |
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351 | /// and the required flow value. |
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352 | /// If neither this function nor \ref supplyMap() is used before |
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353 | /// calling \ref run(), the supply of each node will be set to zero. |
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354 | /// |
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355 | /// Using this function has the same effect as using \ref supplyMap() |
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356 | /// with a map in which \c k is assigned to \c s, \c -k is |
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357 | /// assigned to \c t and all other nodes have zero supply value. |
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358 | /// |
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359 | /// \param s The source node. |
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360 | /// \param t The target node. |
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361 | /// \param k The required amount of flow from node \c s to node \c t |
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362 | /// (i.e. the supply of \c s and the demand of \c t). |
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363 | /// |
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364 | /// \return <tt>(*this)</tt> |
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365 | CycleCanceling& stSupply(const Node& s, const Node& t, Value k) { |
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366 | for (int i = 0; i != _res_node_num; ++i) { |
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367 | _supply[i] = 0; |
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368 | } |
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369 | _supply[_node_id[s]] = k; |
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370 | _supply[_node_id[t]] = -k; |
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371 | return *this; |
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372 | } |
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373 | |
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374 | /// @} |
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375 | |
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376 | /// \name Execution control |
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377 | /// The algorithm can be executed using \ref run(). |
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378 | |
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379 | /// @{ |
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380 | |
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381 | /// \brief Run the algorithm. |
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382 | /// |
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383 | /// This function runs the algorithm. |
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384 | /// The paramters can be specified using functions \ref lowerMap(), |
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385 | /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(). |
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386 | /// For example, |
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387 | /// \code |
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388 | /// CycleCanceling<ListDigraph> cc(graph); |
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389 | /// cc.lowerMap(lower).upperMap(upper).costMap(cost) |
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390 | /// .supplyMap(sup).run(); |
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391 | /// \endcode |
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392 | /// |
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393 | /// This function can be called more than once. All the given parameters |
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394 | /// are kept for the next call, unless \ref resetParams() or \ref reset() |
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395 | /// is used, thus only the modified parameters have to be set again. |
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396 | /// If the underlying digraph was also modified after the construction |
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397 | /// of the class (or the last \ref reset() call), then the \ref reset() |
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398 | /// function must be called. |
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399 | /// |
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400 | /// \param method The cycle-canceling method that will be used. |
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401 | /// For more information, see \ref Method. |
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402 | /// |
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403 | /// \return \c INFEASIBLE if no feasible flow exists, |
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404 | /// \n \c OPTIMAL if the problem has optimal solution |
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405 | /// (i.e. it is feasible and bounded), and the algorithm has found |
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406 | /// optimal flow and node potentials (primal and dual solutions), |
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407 | /// \n \c UNBOUNDED if the digraph contains an arc of negative cost |
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408 | /// and infinite upper bound. It means that the objective function |
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409 | /// is unbounded on that arc, however, note that it could actually be |
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410 | /// bounded over the feasible flows, but this algroithm cannot handle |
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411 | /// these cases. |
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412 | /// |
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413 | /// \see ProblemType, Method |
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414 | /// \see resetParams(), reset() |
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415 | ProblemType run(Method method = CANCEL_AND_TIGHTEN) { |
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416 | ProblemType pt = init(); |
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417 | if (pt != OPTIMAL) return pt; |
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418 | start(method); |
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419 | return OPTIMAL; |
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420 | } |
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421 | |
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422 | /// \brief Reset all the parameters that have been given before. |
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423 | /// |
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424 | /// This function resets all the paramaters that have been given |
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425 | /// before using functions \ref lowerMap(), \ref upperMap(), |
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426 | /// \ref costMap(), \ref supplyMap(), \ref stSupply(). |
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427 | /// |
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428 | /// It is useful for multiple \ref run() calls. Basically, all the given |
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429 | /// parameters are kept for the next \ref run() call, unless |
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430 | /// \ref resetParams() or \ref reset() is used. |
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431 | /// If the underlying digraph was also modified after the construction |
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432 | /// of the class or the last \ref reset() call, then the \ref reset() |
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433 | /// function must be used, otherwise \ref resetParams() is sufficient. |
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434 | /// |
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435 | /// For example, |
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436 | /// \code |
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437 | /// CycleCanceling<ListDigraph> cs(graph); |
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438 | /// |
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439 | /// // First run |
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440 | /// cc.lowerMap(lower).upperMap(upper).costMap(cost) |
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441 | /// .supplyMap(sup).run(); |
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442 | /// |
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443 | /// // Run again with modified cost map (resetParams() is not called, |
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444 | /// // so only the cost map have to be set again) |
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445 | /// cost[e] += 100; |
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446 | /// cc.costMap(cost).run(); |
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447 | /// |
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448 | /// // Run again from scratch using resetParams() |
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449 | /// // (the lower bounds will be set to zero on all arcs) |
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450 | /// cc.resetParams(); |
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451 | /// cc.upperMap(capacity).costMap(cost) |
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452 | /// .supplyMap(sup).run(); |
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453 | /// \endcode |
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454 | /// |
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455 | /// \return <tt>(*this)</tt> |
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456 | /// |
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457 | /// \see reset(), run() |
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458 | CycleCanceling& resetParams() { |
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459 | for (int i = 0; i != _res_node_num; ++i) { |
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460 | _supply[i] = 0; |
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461 | } |
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462 | int limit = _first_out[_root]; |
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463 | for (int j = 0; j != limit; ++j) { |
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464 | _lower[j] = 0; |
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465 | _upper[j] = INF; |
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466 | _cost[j] = _forward[j] ? 1 : -1; |
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467 | } |
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468 | for (int j = limit; j != _res_arc_num; ++j) { |
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469 | _lower[j] = 0; |
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470 | _upper[j] = INF; |
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471 | _cost[j] = 0; |
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472 | _cost[_reverse[j]] = 0; |
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473 | } |
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474 | _have_lower = false; |
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475 | return *this; |
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476 | } |
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477 | |
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478 | /// \brief Reset the internal data structures and all the parameters |
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479 | /// that have been given before. |
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480 | /// |
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481 | /// This function resets the internal data structures and all the |
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482 | /// paramaters that have been given before using functions \ref lowerMap(), |
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483 | /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply(). |
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484 | /// |
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485 | /// It is useful for multiple \ref run() calls. Basically, all the given |
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486 | /// parameters are kept for the next \ref run() call, unless |
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487 | /// \ref resetParams() or \ref reset() is used. |
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488 | /// If the underlying digraph was also modified after the construction |
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489 | /// of the class or the last \ref reset() call, then the \ref reset() |
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490 | /// function must be used, otherwise \ref resetParams() is sufficient. |
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491 | /// |
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492 | /// See \ref resetParams() for examples. |
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493 | /// |
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494 | /// \return <tt>(*this)</tt> |
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495 | /// |
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496 | /// \see resetParams(), run() |
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497 | CycleCanceling& reset() { |
---|
498 | // Resize vectors |
---|
499 | _node_num = countNodes(_graph); |
---|
500 | _arc_num = countArcs(_graph); |
---|
501 | _res_node_num = _node_num + 1; |
---|
502 | _res_arc_num = 2 * (_arc_num + _node_num); |
---|
503 | _root = _node_num; |
---|
504 | |
---|
505 | _first_out.resize(_res_node_num + 1); |
---|
506 | _forward.resize(_res_arc_num); |
---|
507 | _source.resize(_res_arc_num); |
---|
508 | _target.resize(_res_arc_num); |
---|
509 | _reverse.resize(_res_arc_num); |
---|
510 | |
---|
511 | _lower.resize(_res_arc_num); |
---|
512 | _upper.resize(_res_arc_num); |
---|
513 | _cost.resize(_res_arc_num); |
---|
514 | _supply.resize(_res_node_num); |
---|
515 | |
---|
516 | _res_cap.resize(_res_arc_num); |
---|
517 | _pi.resize(_res_node_num); |
---|
518 | |
---|
519 | _arc_vec.reserve(_res_arc_num); |
---|
520 | _cost_vec.reserve(_res_arc_num); |
---|
521 | _id_vec.reserve(_res_arc_num); |
---|
522 | |
---|
523 | // Copy the graph |
---|
524 | int i = 0, j = 0, k = 2 * _arc_num + _node_num; |
---|
525 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
---|
526 | _node_id[n] = i; |
---|
527 | } |
---|
528 | i = 0; |
---|
529 | for (NodeIt n(_graph); n != INVALID; ++n, ++i) { |
---|
530 | _first_out[i] = j; |
---|
531 | for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) { |
---|
532 | _arc_idf[a] = j; |
---|
533 | _forward[j] = true; |
---|
534 | _source[j] = i; |
---|
535 | _target[j] = _node_id[_graph.runningNode(a)]; |
---|
536 | } |
---|
537 | for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) { |
---|
538 | _arc_idb[a] = j; |
---|
539 | _forward[j] = false; |
---|
540 | _source[j] = i; |
---|
541 | _target[j] = _node_id[_graph.runningNode(a)]; |
---|
542 | } |
---|
543 | _forward[j] = false; |
---|
544 | _source[j] = i; |
---|
545 | _target[j] = _root; |
---|
546 | _reverse[j] = k; |
---|
547 | _forward[k] = true; |
---|
548 | _source[k] = _root; |
---|
549 | _target[k] = i; |
---|
550 | _reverse[k] = j; |
---|
551 | ++j; ++k; |
---|
552 | } |
---|
553 | _first_out[i] = j; |
---|
554 | _first_out[_res_node_num] = k; |
---|
555 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
556 | int fi = _arc_idf[a]; |
---|
557 | int bi = _arc_idb[a]; |
---|
558 | _reverse[fi] = bi; |
---|
559 | _reverse[bi] = fi; |
---|
560 | } |
---|
561 | |
---|
562 | // Reset parameters |
---|
563 | resetParams(); |
---|
564 | return *this; |
---|
565 | } |
---|
566 | |
---|
567 | /// @} |
---|
568 | |
---|
569 | /// \name Query Functions |
---|
570 | /// The results of the algorithm can be obtained using these |
---|
571 | /// functions.\n |
---|
572 | /// The \ref run() function must be called before using them. |
---|
573 | |
---|
574 | /// @{ |
---|
575 | |
---|
576 | /// \brief Return the total cost of the found flow. |
---|
577 | /// |
---|
578 | /// This function returns the total cost of the found flow. |
---|
579 | /// Its complexity is O(m). |
---|
580 | /// |
---|
581 | /// \note The return type of the function can be specified as a |
---|
582 | /// template parameter. For example, |
---|
583 | /// \code |
---|
584 | /// cc.totalCost<double>(); |
---|
585 | /// \endcode |
---|
586 | /// It is useful if the total cost cannot be stored in the \c Cost |
---|
587 | /// type of the algorithm, which is the default return type of the |
---|
588 | /// function. |
---|
589 | /// |
---|
590 | /// \pre \ref run() must be called before using this function. |
---|
591 | template <typename Number> |
---|
592 | Number totalCost() const { |
---|
593 | Number c = 0; |
---|
594 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
595 | int i = _arc_idb[a]; |
---|
596 | c += static_cast<Number>(_res_cap[i]) * |
---|
597 | (-static_cast<Number>(_cost[i])); |
---|
598 | } |
---|
599 | return c; |
---|
600 | } |
---|
601 | |
---|
602 | #ifndef DOXYGEN |
---|
603 | Cost totalCost() const { |
---|
604 | return totalCost<Cost>(); |
---|
605 | } |
---|
606 | #endif |
---|
607 | |
---|
608 | /// \brief Return the flow on the given arc. |
---|
609 | /// |
---|
610 | /// This function returns the flow on the given arc. |
---|
611 | /// |
---|
612 | /// \pre \ref run() must be called before using this function. |
---|
613 | Value flow(const Arc& a) const { |
---|
614 | return _res_cap[_arc_idb[a]]; |
---|
615 | } |
---|
616 | |
---|
617 | /// \brief Copy the flow values (the primal solution) into the |
---|
618 | /// given map. |
---|
619 | /// |
---|
620 | /// This function copies the flow value on each arc into the given |
---|
621 | /// map. The \c Value type of the algorithm must be convertible to |
---|
622 | /// the \c Value type of the map. |
---|
623 | /// |
---|
624 | /// \pre \ref run() must be called before using this function. |
---|
625 | template <typename FlowMap> |
---|
626 | void flowMap(FlowMap &map) const { |
---|
627 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
628 | map.set(a, _res_cap[_arc_idb[a]]); |
---|
629 | } |
---|
630 | } |
---|
631 | |
---|
632 | /// \brief Return the potential (dual value) of the given node. |
---|
633 | /// |
---|
634 | /// This function returns the potential (dual value) of the |
---|
635 | /// given node. |
---|
636 | /// |
---|
637 | /// \pre \ref run() must be called before using this function. |
---|
638 | Cost potential(const Node& n) const { |
---|
639 | return static_cast<Cost>(_pi[_node_id[n]]); |
---|
640 | } |
---|
641 | |
---|
642 | /// \brief Copy the potential values (the dual solution) into the |
---|
643 | /// given map. |
---|
644 | /// |
---|
645 | /// This function copies the potential (dual value) of each node |
---|
646 | /// into the given map. |
---|
647 | /// The \c Cost type of the algorithm must be convertible to the |
---|
648 | /// \c Value type of the map. |
---|
649 | /// |
---|
650 | /// \pre \ref run() must be called before using this function. |
---|
651 | template <typename PotentialMap> |
---|
652 | void potentialMap(PotentialMap &map) const { |
---|
653 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
654 | map.set(n, static_cast<Cost>(_pi[_node_id[n]])); |
---|
655 | } |
---|
656 | } |
---|
657 | |
---|
658 | /// @} |
---|
659 | |
---|
660 | private: |
---|
661 | |
---|
662 | // Initialize the algorithm |
---|
663 | ProblemType init() { |
---|
664 | if (_res_node_num <= 1) return INFEASIBLE; |
---|
665 | |
---|
666 | // Check the sum of supply values |
---|
667 | _sum_supply = 0; |
---|
668 | for (int i = 0; i != _root; ++i) { |
---|
669 | _sum_supply += _supply[i]; |
---|
670 | } |
---|
671 | if (_sum_supply > 0) return INFEASIBLE; |
---|
672 | |
---|
673 | // Check lower and upper bounds |
---|
674 | LEMON_DEBUG(checkBoundMaps(), |
---|
675 | "Upper bounds must be greater or equal to the lower bounds"); |
---|
676 | |
---|
677 | |
---|
678 | // Initialize vectors |
---|
679 | for (int i = 0; i != _res_node_num; ++i) { |
---|
680 | _pi[i] = 0; |
---|
681 | } |
---|
682 | ValueVector excess(_supply); |
---|
683 | |
---|
684 | // Remove infinite upper bounds and check negative arcs |
---|
685 | const Value MAX = std::numeric_limits<Value>::max(); |
---|
686 | int last_out; |
---|
687 | if (_have_lower) { |
---|
688 | for (int i = 0; i != _root; ++i) { |
---|
689 | last_out = _first_out[i+1]; |
---|
690 | for (int j = _first_out[i]; j != last_out; ++j) { |
---|
691 | if (_forward[j]) { |
---|
692 | Value c = _cost[j] < 0 ? _upper[j] : _lower[j]; |
---|
693 | if (c >= MAX) return UNBOUNDED; |
---|
694 | excess[i] -= c; |
---|
695 | excess[_target[j]] += c; |
---|
696 | } |
---|
697 | } |
---|
698 | } |
---|
699 | } else { |
---|
700 | for (int i = 0; i != _root; ++i) { |
---|
701 | last_out = _first_out[i+1]; |
---|
702 | for (int j = _first_out[i]; j != last_out; ++j) { |
---|
703 | if (_forward[j] && _cost[j] < 0) { |
---|
704 | Value c = _upper[j]; |
---|
705 | if (c >= MAX) return UNBOUNDED; |
---|
706 | excess[i] -= c; |
---|
707 | excess[_target[j]] += c; |
---|
708 | } |
---|
709 | } |
---|
710 | } |
---|
711 | } |
---|
712 | Value ex, max_cap = 0; |
---|
713 | for (int i = 0; i != _res_node_num; ++i) { |
---|
714 | ex = excess[i]; |
---|
715 | if (ex < 0) max_cap -= ex; |
---|
716 | } |
---|
717 | for (int j = 0; j != _res_arc_num; ++j) { |
---|
718 | if (_upper[j] >= MAX) _upper[j] = max_cap; |
---|
719 | } |
---|
720 | |
---|
721 | // Initialize maps for Circulation and remove non-zero lower bounds |
---|
722 | ConstMap<Arc, Value> low(0); |
---|
723 | typedef typename Digraph::template ArcMap<Value> ValueArcMap; |
---|
724 | typedef typename Digraph::template NodeMap<Value> ValueNodeMap; |
---|
725 | ValueArcMap cap(_graph), flow(_graph); |
---|
726 | ValueNodeMap sup(_graph); |
---|
727 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
728 | sup[n] = _supply[_node_id[n]]; |
---|
729 | } |
---|
730 | if (_have_lower) { |
---|
731 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
732 | int j = _arc_idf[a]; |
---|
733 | Value c = _lower[j]; |
---|
734 | cap[a] = _upper[j] - c; |
---|
735 | sup[_graph.source(a)] -= c; |
---|
736 | sup[_graph.target(a)] += c; |
---|
737 | } |
---|
738 | } else { |
---|
739 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
740 | cap[a] = _upper[_arc_idf[a]]; |
---|
741 | } |
---|
742 | } |
---|
743 | |
---|
744 | // Find a feasible flow using Circulation |
---|
745 | Circulation<Digraph, ConstMap<Arc, Value>, ValueArcMap, ValueNodeMap> |
---|
746 | circ(_graph, low, cap, sup); |
---|
747 | if (!circ.flowMap(flow).run()) return INFEASIBLE; |
---|
748 | |
---|
749 | // Set residual capacities and handle GEQ supply type |
---|
750 | if (_sum_supply < 0) { |
---|
751 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
752 | Value fa = flow[a]; |
---|
753 | _res_cap[_arc_idf[a]] = cap[a] - fa; |
---|
754 | _res_cap[_arc_idb[a]] = fa; |
---|
755 | sup[_graph.source(a)] -= fa; |
---|
756 | sup[_graph.target(a)] += fa; |
---|
757 | } |
---|
758 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
759 | excess[_node_id[n]] = sup[n]; |
---|
760 | } |
---|
761 | for (int a = _first_out[_root]; a != _res_arc_num; ++a) { |
---|
762 | int u = _target[a]; |
---|
763 | int ra = _reverse[a]; |
---|
764 | _res_cap[a] = -_sum_supply + 1; |
---|
765 | _res_cap[ra] = -excess[u]; |
---|
766 | _cost[a] = 0; |
---|
767 | _cost[ra] = 0; |
---|
768 | } |
---|
769 | } else { |
---|
770 | for (ArcIt a(_graph); a != INVALID; ++a) { |
---|
771 | Value fa = flow[a]; |
---|
772 | _res_cap[_arc_idf[a]] = cap[a] - fa; |
---|
773 | _res_cap[_arc_idb[a]] = fa; |
---|
774 | } |
---|
775 | for (int a = _first_out[_root]; a != _res_arc_num; ++a) { |
---|
776 | int ra = _reverse[a]; |
---|
777 | _res_cap[a] = 1; |
---|
778 | _res_cap[ra] = 0; |
---|
779 | _cost[a] = 0; |
---|
780 | _cost[ra] = 0; |
---|
781 | } |
---|
782 | } |
---|
783 | |
---|
784 | return OPTIMAL; |
---|
785 | } |
---|
786 | |
---|
787 | // Check if the upper bound is greater or equal to the lower bound |
---|
788 | // on each arc. |
---|
789 | bool checkBoundMaps() { |
---|
790 | for (int j = 0; j != _res_arc_num; ++j) { |
---|
791 | if (_upper[j] < _lower[j]) return false; |
---|
792 | } |
---|
793 | return true; |
---|
794 | } |
---|
795 | |
---|
796 | // Build a StaticDigraph structure containing the current |
---|
797 | // residual network |
---|
798 | void buildResidualNetwork() { |
---|
799 | _arc_vec.clear(); |
---|
800 | _cost_vec.clear(); |
---|
801 | _id_vec.clear(); |
---|
802 | for (int j = 0; j != _res_arc_num; ++j) { |
---|
803 | if (_res_cap[j] > 0) { |
---|
804 | _arc_vec.push_back(IntPair(_source[j], _target[j])); |
---|
805 | _cost_vec.push_back(_cost[j]); |
---|
806 | _id_vec.push_back(j); |
---|
807 | } |
---|
808 | } |
---|
809 | _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end()); |
---|
810 | } |
---|
811 | |
---|
812 | // Execute the algorithm and transform the results |
---|
813 | void start(Method method) { |
---|
814 | // Execute the algorithm |
---|
815 | switch (method) { |
---|
816 | case SIMPLE_CYCLE_CANCELING: |
---|
817 | startSimpleCycleCanceling(); |
---|
818 | break; |
---|
819 | case MINIMUM_MEAN_CYCLE_CANCELING: |
---|
820 | startMinMeanCycleCanceling(); |
---|
821 | break; |
---|
822 | case CANCEL_AND_TIGHTEN: |
---|
823 | startCancelAndTighten(); |
---|
824 | break; |
---|
825 | } |
---|
826 | |
---|
827 | // Compute node potentials |
---|
828 | if (method != SIMPLE_CYCLE_CANCELING) { |
---|
829 | buildResidualNetwork(); |
---|
830 | typename BellmanFord<StaticDigraph, CostArcMap> |
---|
831 | ::template SetDistMap<CostNodeMap>::Create bf(_sgr, _cost_map); |
---|
832 | bf.distMap(_pi_map); |
---|
833 | bf.init(0); |
---|
834 | bf.start(); |
---|
835 | } |
---|
836 | |
---|
837 | // Handle non-zero lower bounds |
---|
838 | if (_have_lower) { |
---|
839 | int limit = _first_out[_root]; |
---|
840 | for (int j = 0; j != limit; ++j) { |
---|
841 | if (!_forward[j]) _res_cap[j] += _lower[j]; |
---|
842 | } |
---|
843 | } |
---|
844 | } |
---|
845 | |
---|
846 | // Execute the "Simple Cycle Canceling" method |
---|
847 | void startSimpleCycleCanceling() { |
---|
848 | // Constants for computing the iteration limits |
---|
849 | const int BF_FIRST_LIMIT = 2; |
---|
850 | const double BF_LIMIT_FACTOR = 1.5; |
---|
851 | |
---|
852 | typedef StaticVectorMap<StaticDigraph::Arc, Value> FilterMap; |
---|
853 | typedef FilterArcs<StaticDigraph, FilterMap> ResDigraph; |
---|
854 | typedef StaticVectorMap<StaticDigraph::Node, StaticDigraph::Arc> PredMap; |
---|
855 | typedef typename BellmanFord<ResDigraph, CostArcMap> |
---|
856 | ::template SetDistMap<CostNodeMap> |
---|
857 | ::template SetPredMap<PredMap>::Create BF; |
---|
858 | |
---|
859 | // Build the residual network |
---|
860 | _arc_vec.clear(); |
---|
861 | _cost_vec.clear(); |
---|
862 | for (int j = 0; j != _res_arc_num; ++j) { |
---|
863 | _arc_vec.push_back(IntPair(_source[j], _target[j])); |
---|
864 | _cost_vec.push_back(_cost[j]); |
---|
865 | } |
---|
866 | _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end()); |
---|
867 | |
---|
868 | FilterMap filter_map(_res_cap); |
---|
869 | ResDigraph rgr(_sgr, filter_map); |
---|
870 | std::vector<int> cycle; |
---|
871 | std::vector<StaticDigraph::Arc> pred(_res_arc_num); |
---|
872 | PredMap pred_map(pred); |
---|
873 | BF bf(rgr, _cost_map); |
---|
874 | bf.distMap(_pi_map).predMap(pred_map); |
---|
875 | |
---|
876 | int length_bound = BF_FIRST_LIMIT; |
---|
877 | bool optimal = false; |
---|
878 | while (!optimal) { |
---|
879 | bf.init(0); |
---|
880 | int iter_num = 0; |
---|
881 | bool cycle_found = false; |
---|
882 | while (!cycle_found) { |
---|
883 | // Perform some iterations of the Bellman-Ford algorithm |
---|
884 | int curr_iter_num = iter_num + length_bound <= _node_num ? |
---|
885 | length_bound : _node_num - iter_num; |
---|
886 | iter_num += curr_iter_num; |
---|
887 | int real_iter_num = curr_iter_num; |
---|
888 | for (int i = 0; i < curr_iter_num; ++i) { |
---|
889 | if (bf.processNextWeakRound()) { |
---|
890 | real_iter_num = i; |
---|
891 | break; |
---|
892 | } |
---|
893 | } |
---|
894 | if (real_iter_num < curr_iter_num) { |
---|
895 | // Optimal flow is found |
---|
896 | optimal = true; |
---|
897 | break; |
---|
898 | } else { |
---|
899 | // Search for node disjoint negative cycles |
---|
900 | std::vector<int> state(_res_node_num, 0); |
---|
901 | int id = 0; |
---|
902 | for (int u = 0; u != _res_node_num; ++u) { |
---|
903 | if (state[u] != 0) continue; |
---|
904 | ++id; |
---|
905 | int v = u; |
---|
906 | for (; v != -1 && state[v] == 0; v = pred[v] == INVALID ? |
---|
907 | -1 : rgr.id(rgr.source(pred[v]))) { |
---|
908 | state[v] = id; |
---|
909 | } |
---|
910 | if (v != -1 && state[v] == id) { |
---|
911 | // A negative cycle is found |
---|
912 | cycle_found = true; |
---|
913 | cycle.clear(); |
---|
914 | StaticDigraph::Arc a = pred[v]; |
---|
915 | Value d, delta = _res_cap[rgr.id(a)]; |
---|
916 | cycle.push_back(rgr.id(a)); |
---|
917 | while (rgr.id(rgr.source(a)) != v) { |
---|
918 | a = pred_map[rgr.source(a)]; |
---|
919 | d = _res_cap[rgr.id(a)]; |
---|
920 | if (d < delta) delta = d; |
---|
921 | cycle.push_back(rgr.id(a)); |
---|
922 | } |
---|
923 | |
---|
924 | // Augment along the cycle |
---|
925 | for (int i = 0; i < int(cycle.size()); ++i) { |
---|
926 | int j = cycle[i]; |
---|
927 | _res_cap[j] -= delta; |
---|
928 | _res_cap[_reverse[j]] += delta; |
---|
929 | } |
---|
930 | } |
---|
931 | } |
---|
932 | } |
---|
933 | |
---|
934 | // Increase iteration limit if no cycle is found |
---|
935 | if (!cycle_found) { |
---|
936 | length_bound = static_cast<int>(length_bound * BF_LIMIT_FACTOR); |
---|
937 | } |
---|
938 | } |
---|
939 | } |
---|
940 | } |
---|
941 | |
---|
942 | // Execute the "Minimum Mean Cycle Canceling" method |
---|
943 | void startMinMeanCycleCanceling() { |
---|
944 | typedef Path<StaticDigraph> SPath; |
---|
945 | typedef typename SPath::ArcIt SPathArcIt; |
---|
946 | typedef typename HowardMmc<StaticDigraph, CostArcMap> |
---|
947 | ::template SetPath<SPath>::Create HwMmc; |
---|
948 | typedef typename HartmannOrlinMmc<StaticDigraph, CostArcMap> |
---|
949 | ::template SetPath<SPath>::Create HoMmc; |
---|
950 | |
---|
951 | const double HW_ITER_LIMIT_FACTOR = 1.0; |
---|
952 | const int HW_ITER_LIMIT_MIN_VALUE = 5; |
---|
953 | |
---|
954 | const int hw_iter_limit = |
---|
955 | std::max(static_cast<int>(HW_ITER_LIMIT_FACTOR * _node_num), |
---|
956 | HW_ITER_LIMIT_MIN_VALUE); |
---|
957 | |
---|
958 | SPath cycle; |
---|
959 | HwMmc hw_mmc(_sgr, _cost_map); |
---|
960 | hw_mmc.cycle(cycle); |
---|
961 | buildResidualNetwork(); |
---|
962 | while (true) { |
---|
963 | |
---|
964 | typename HwMmc::TerminationCause hw_tc = |
---|
965 | hw_mmc.findCycleMean(hw_iter_limit); |
---|
966 | if (hw_tc == HwMmc::ITERATION_LIMIT) { |
---|
967 | // Howard's algorithm reached the iteration limit, start a |
---|
968 | // strongly polynomial algorithm instead |
---|
969 | HoMmc ho_mmc(_sgr, _cost_map); |
---|
970 | ho_mmc.cycle(cycle); |
---|
971 | // Find a minimum mean cycle (Hartmann-Orlin algorithm) |
---|
972 | if (!(ho_mmc.findCycleMean() && ho_mmc.cycleCost() < 0)) break; |
---|
973 | ho_mmc.findCycle(); |
---|
974 | } else { |
---|
975 | // Find a minimum mean cycle (Howard algorithm) |
---|
976 | if (!(hw_tc == HwMmc::OPTIMAL && hw_mmc.cycleCost() < 0)) break; |
---|
977 | hw_mmc.findCycle(); |
---|
978 | } |
---|
979 | |
---|
980 | // Compute delta value |
---|
981 | Value delta = INF; |
---|
982 | for (SPathArcIt a(cycle); a != INVALID; ++a) { |
---|
983 | Value d = _res_cap[_id_vec[_sgr.id(a)]]; |
---|
984 | if (d < delta) delta = d; |
---|
985 | } |
---|
986 | |
---|
987 | // Augment along the cycle |
---|
988 | for (SPathArcIt a(cycle); a != INVALID; ++a) { |
---|
989 | int j = _id_vec[_sgr.id(a)]; |
---|
990 | _res_cap[j] -= delta; |
---|
991 | _res_cap[_reverse[j]] += delta; |
---|
992 | } |
---|
993 | |
---|
994 | // Rebuild the residual network |
---|
995 | buildResidualNetwork(); |
---|
996 | } |
---|
997 | } |
---|
998 | |
---|
999 | // Execute the "Cancel-and-Tighten" method |
---|
1000 | void startCancelAndTighten() { |
---|
1001 | // Constants for the min mean cycle computations |
---|
1002 | const double LIMIT_FACTOR = 1.0; |
---|
1003 | const int MIN_LIMIT = 5; |
---|
1004 | const double HW_ITER_LIMIT_FACTOR = 1.0; |
---|
1005 | const int HW_ITER_LIMIT_MIN_VALUE = 5; |
---|
1006 | |
---|
1007 | const int hw_iter_limit = |
---|
1008 | std::max(static_cast<int>(HW_ITER_LIMIT_FACTOR * _node_num), |
---|
1009 | HW_ITER_LIMIT_MIN_VALUE); |
---|
1010 | |
---|
1011 | // Contruct auxiliary data vectors |
---|
1012 | DoubleVector pi(_res_node_num, 0.0); |
---|
1013 | IntVector level(_res_node_num); |
---|
1014 | BoolVector reached(_res_node_num); |
---|
1015 | BoolVector processed(_res_node_num); |
---|
1016 | IntVector pred_node(_res_node_num); |
---|
1017 | IntVector pred_arc(_res_node_num); |
---|
1018 | std::vector<int> stack(_res_node_num); |
---|
1019 | std::vector<int> proc_vector(_res_node_num); |
---|
1020 | |
---|
1021 | // Initialize epsilon |
---|
1022 | double epsilon = 0; |
---|
1023 | for (int a = 0; a != _res_arc_num; ++a) { |
---|
1024 | if (_res_cap[a] > 0 && -_cost[a] > epsilon) |
---|
1025 | epsilon = -_cost[a]; |
---|
1026 | } |
---|
1027 | |
---|
1028 | // Start phases |
---|
1029 | Tolerance<double> tol; |
---|
1030 | tol.epsilon(1e-6); |
---|
1031 | int limit = int(LIMIT_FACTOR * std::sqrt(double(_res_node_num))); |
---|
1032 | if (limit < MIN_LIMIT) limit = MIN_LIMIT; |
---|
1033 | int iter = limit; |
---|
1034 | while (epsilon * _res_node_num >= 1) { |
---|
1035 | // Find and cancel cycles in the admissible network using DFS |
---|
1036 | for (int u = 0; u != _res_node_num; ++u) { |
---|
1037 | reached[u] = false; |
---|
1038 | processed[u] = false; |
---|
1039 | } |
---|
1040 | int stack_head = -1; |
---|
1041 | int proc_head = -1; |
---|
1042 | for (int start = 0; start != _res_node_num; ++start) { |
---|
1043 | if (reached[start]) continue; |
---|
1044 | |
---|
1045 | // New start node |
---|
1046 | reached[start] = true; |
---|
1047 | pred_arc[start] = -1; |
---|
1048 | pred_node[start] = -1; |
---|
1049 | |
---|
1050 | // Find the first admissible outgoing arc |
---|
1051 | double p = pi[start]; |
---|
1052 | int a = _first_out[start]; |
---|
1053 | int last_out = _first_out[start+1]; |
---|
1054 | for (; a != last_out && (_res_cap[a] == 0 || |
---|
1055 | !tol.negative(_cost[a] + p - pi[_target[a]])); ++a) ; |
---|
1056 | if (a == last_out) { |
---|
1057 | processed[start] = true; |
---|
1058 | proc_vector[++proc_head] = start; |
---|
1059 | continue; |
---|
1060 | } |
---|
1061 | stack[++stack_head] = a; |
---|
1062 | |
---|
1063 | while (stack_head >= 0) { |
---|
1064 | int sa = stack[stack_head]; |
---|
1065 | int u = _source[sa]; |
---|
1066 | int v = _target[sa]; |
---|
1067 | |
---|
1068 | if (!reached[v]) { |
---|
1069 | // A new node is reached |
---|
1070 | reached[v] = true; |
---|
1071 | pred_node[v] = u; |
---|
1072 | pred_arc[v] = sa; |
---|
1073 | p = pi[v]; |
---|
1074 | a = _first_out[v]; |
---|
1075 | last_out = _first_out[v+1]; |
---|
1076 | for (; a != last_out && (_res_cap[a] == 0 || |
---|
1077 | !tol.negative(_cost[a] + p - pi[_target[a]])); ++a) ; |
---|
1078 | stack[++stack_head] = a == last_out ? -1 : a; |
---|
1079 | } else { |
---|
1080 | if (!processed[v]) { |
---|
1081 | // A cycle is found |
---|
1082 | int n, w = u; |
---|
1083 | Value d, delta = _res_cap[sa]; |
---|
1084 | for (n = u; n != v; n = pred_node[n]) { |
---|
1085 | d = _res_cap[pred_arc[n]]; |
---|
1086 | if (d <= delta) { |
---|
1087 | delta = d; |
---|
1088 | w = pred_node[n]; |
---|
1089 | } |
---|
1090 | } |
---|
1091 | |
---|
1092 | // Augment along the cycle |
---|
1093 | _res_cap[sa] -= delta; |
---|
1094 | _res_cap[_reverse[sa]] += delta; |
---|
1095 | for (n = u; n != v; n = pred_node[n]) { |
---|
1096 | int pa = pred_arc[n]; |
---|
1097 | _res_cap[pa] -= delta; |
---|
1098 | _res_cap[_reverse[pa]] += delta; |
---|
1099 | } |
---|
1100 | for (n = u; stack_head > 0 && n != w; n = pred_node[n]) { |
---|
1101 | --stack_head; |
---|
1102 | reached[n] = false; |
---|
1103 | } |
---|
1104 | u = w; |
---|
1105 | } |
---|
1106 | v = u; |
---|
1107 | |
---|
1108 | // Find the next admissible outgoing arc |
---|
1109 | p = pi[v]; |
---|
1110 | a = stack[stack_head] + 1; |
---|
1111 | last_out = _first_out[v+1]; |
---|
1112 | for (; a != last_out && (_res_cap[a] == 0 || |
---|
1113 | !tol.negative(_cost[a] + p - pi[_target[a]])); ++a) ; |
---|
1114 | stack[stack_head] = a == last_out ? -1 : a; |
---|
1115 | } |
---|
1116 | |
---|
1117 | while (stack_head >= 0 && stack[stack_head] == -1) { |
---|
1118 | processed[v] = true; |
---|
1119 | proc_vector[++proc_head] = v; |
---|
1120 | if (--stack_head >= 0) { |
---|
1121 | // Find the next admissible outgoing arc |
---|
1122 | v = _source[stack[stack_head]]; |
---|
1123 | p = pi[v]; |
---|
1124 | a = stack[stack_head] + 1; |
---|
1125 | last_out = _first_out[v+1]; |
---|
1126 | for (; a != last_out && (_res_cap[a] == 0 || |
---|
1127 | !tol.negative(_cost[a] + p - pi[_target[a]])); ++a) ; |
---|
1128 | stack[stack_head] = a == last_out ? -1 : a; |
---|
1129 | } |
---|
1130 | } |
---|
1131 | } |
---|
1132 | } |
---|
1133 | |
---|
1134 | // Tighten potentials and epsilon |
---|
1135 | if (--iter > 0) { |
---|
1136 | for (int u = 0; u != _res_node_num; ++u) { |
---|
1137 | level[u] = 0; |
---|
1138 | } |
---|
1139 | for (int i = proc_head; i > 0; --i) { |
---|
1140 | int u = proc_vector[i]; |
---|
1141 | double p = pi[u]; |
---|
1142 | int l = level[u] + 1; |
---|
1143 | int last_out = _first_out[u+1]; |
---|
1144 | for (int a = _first_out[u]; a != last_out; ++a) { |
---|
1145 | int v = _target[a]; |
---|
1146 | if (_res_cap[a] > 0 && tol.negative(_cost[a] + p - pi[v]) && |
---|
1147 | l > level[v]) level[v] = l; |
---|
1148 | } |
---|
1149 | } |
---|
1150 | |
---|
1151 | // Modify potentials |
---|
1152 | double q = std::numeric_limits<double>::max(); |
---|
1153 | for (int u = 0; u != _res_node_num; ++u) { |
---|
1154 | int lu = level[u]; |
---|
1155 | double p, pu = pi[u]; |
---|
1156 | int last_out = _first_out[u+1]; |
---|
1157 | for (int a = _first_out[u]; a != last_out; ++a) { |
---|
1158 | if (_res_cap[a] == 0) continue; |
---|
1159 | int v = _target[a]; |
---|
1160 | int ld = lu - level[v]; |
---|
1161 | if (ld > 0) { |
---|
1162 | p = (_cost[a] + pu - pi[v] + epsilon) / (ld + 1); |
---|
1163 | if (p < q) q = p; |
---|
1164 | } |
---|
1165 | } |
---|
1166 | } |
---|
1167 | for (int u = 0; u != _res_node_num; ++u) { |
---|
1168 | pi[u] -= q * level[u]; |
---|
1169 | } |
---|
1170 | |
---|
1171 | // Modify epsilon |
---|
1172 | epsilon = 0; |
---|
1173 | for (int u = 0; u != _res_node_num; ++u) { |
---|
1174 | double curr, pu = pi[u]; |
---|
1175 | int last_out = _first_out[u+1]; |
---|
1176 | for (int a = _first_out[u]; a != last_out; ++a) { |
---|
1177 | if (_res_cap[a] == 0) continue; |
---|
1178 | curr = _cost[a] + pu - pi[_target[a]]; |
---|
1179 | if (-curr > epsilon) epsilon = -curr; |
---|
1180 | } |
---|
1181 | } |
---|
1182 | } else { |
---|
1183 | typedef HowardMmc<StaticDigraph, CostArcMap> HwMmc; |
---|
1184 | typedef HartmannOrlinMmc<StaticDigraph, CostArcMap> HoMmc; |
---|
1185 | typedef typename BellmanFord<StaticDigraph, CostArcMap> |
---|
1186 | ::template SetDistMap<CostNodeMap>::Create BF; |
---|
1187 | |
---|
1188 | // Set epsilon to the minimum cycle mean |
---|
1189 | Cost cycle_cost = 0; |
---|
1190 | int cycle_size = 1; |
---|
1191 | buildResidualNetwork(); |
---|
1192 | HwMmc hw_mmc(_sgr, _cost_map); |
---|
1193 | if (hw_mmc.findCycleMean(hw_iter_limit) == HwMmc::ITERATION_LIMIT) { |
---|
1194 | // Howard's algorithm reached the iteration limit, start a |
---|
1195 | // strongly polynomial algorithm instead |
---|
1196 | HoMmc ho_mmc(_sgr, _cost_map); |
---|
1197 | ho_mmc.findCycleMean(); |
---|
1198 | epsilon = -ho_mmc.cycleMean(); |
---|
1199 | cycle_cost = ho_mmc.cycleCost(); |
---|
1200 | cycle_size = ho_mmc.cycleSize(); |
---|
1201 | } else { |
---|
1202 | // Set epsilon |
---|
1203 | epsilon = -hw_mmc.cycleMean(); |
---|
1204 | cycle_cost = hw_mmc.cycleCost(); |
---|
1205 | cycle_size = hw_mmc.cycleSize(); |
---|
1206 | } |
---|
1207 | |
---|
1208 | // Compute feasible potentials for the current epsilon |
---|
1209 | for (int i = 0; i != int(_cost_vec.size()); ++i) { |
---|
1210 | _cost_vec[i] = cycle_size * _cost_vec[i] - cycle_cost; |
---|
1211 | } |
---|
1212 | BF bf(_sgr, _cost_map); |
---|
1213 | bf.distMap(_pi_map); |
---|
1214 | bf.init(0); |
---|
1215 | bf.start(); |
---|
1216 | for (int u = 0; u != _res_node_num; ++u) { |
---|
1217 | pi[u] = static_cast<double>(_pi[u]) / cycle_size; |
---|
1218 | } |
---|
1219 | |
---|
1220 | iter = limit; |
---|
1221 | } |
---|
1222 | } |
---|
1223 | } |
---|
1224 | |
---|
1225 | }; //class CycleCanceling |
---|
1226 | |
---|
1227 | ///@} |
---|
1228 | |
---|
1229 | } //namespace lemon |
---|
1230 | |
---|
1231 | #endif //LEMON_CYCLE_CANCELING_H |
---|