1 /* -*- C++ -*- |
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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) 2003-2008 |
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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_HARTMANN_ORLIN_H |
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20 #define LEMON_HARTMANN_ORLIN_H |
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21 |
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22 /// \ingroup min_mean_cycle |
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23 /// |
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24 /// \file |
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25 /// \brief Hartmann-Orlin's algorithm for finding a minimum mean cycle. |
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26 |
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27 #include <vector> |
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28 #include <limits> |
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29 #include <lemon/core.h> |
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30 #include <lemon/path.h> |
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31 #include <lemon/tolerance.h> |
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32 #include <lemon/connectivity.h> |
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33 |
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34 namespace lemon { |
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35 |
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36 /// \brief Default traits class of HartmannOrlin algorithm. |
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37 /// |
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38 /// Default traits class of HartmannOrlin algorithm. |
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39 /// \tparam GR The type of the digraph. |
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40 /// \tparam LEN The type of the length map. |
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41 /// It must conform to the \ref concepts::Rea_data "Rea_data" concept. |
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42 #ifdef DOXYGEN |
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43 template <typename GR, typename LEN> |
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44 #else |
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45 template <typename GR, typename LEN, |
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46 bool integer = std::numeric_limits<typename LEN::Value>::is_integer> |
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47 #endif |
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48 struct HartmannOrlinDefaultTraits |
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49 { |
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50 /// The type of the digraph |
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51 typedef GR Digraph; |
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52 /// The type of the length map |
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53 typedef LEN LengthMap; |
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54 /// The type of the arc lengths |
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55 typedef typename LengthMap::Value Value; |
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56 |
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57 /// \brief The large value type used for internal computations |
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58 /// |
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59 /// The large value type used for internal computations. |
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60 /// It is \c long \c long if the \c Value type is integer, |
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61 /// otherwise it is \c double. |
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62 /// \c Value must be convertible to \c LargeValue. |
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63 typedef double LargeValue; |
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64 |
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65 /// The tolerance type used for internal computations |
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66 typedef lemon::Tolerance<LargeValue> Tolerance; |
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67 |
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68 /// \brief The path type of the found cycles |
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69 /// |
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70 /// The path type of the found cycles. |
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71 /// It must conform to the \ref lemon::concepts::Path "Path" concept |
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72 /// and it must have an \c addFront() function. |
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73 typedef lemon::Path<Digraph> Path; |
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74 }; |
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75 |
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76 // Default traits class for integer value types |
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77 template <typename GR, typename LEN> |
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78 struct HartmannOrlinDefaultTraits<GR, LEN, true> |
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79 { |
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80 typedef GR Digraph; |
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81 typedef LEN LengthMap; |
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82 typedef typename LengthMap::Value Value; |
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83 #ifdef LEMON_HAVE_LONG_LONG |
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84 typedef long long LargeValue; |
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85 #else |
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86 typedef long LargeValue; |
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87 #endif |
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88 typedef lemon::Tolerance<LargeValue> Tolerance; |
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89 typedef lemon::Path<Digraph> Path; |
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90 }; |
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91 |
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92 |
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93 /// \addtogroup min_mean_cycle |
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94 /// @{ |
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95 |
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96 /// \brief Implementation of the Hartmann-Orlin algorithm for finding |
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97 /// a minimum mean cycle. |
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98 /// |
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99 /// This class implements the Hartmann-Orlin algorithm for finding |
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100 /// a directed cycle of minimum mean length (cost) in a digraph |
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101 /// \ref amo93networkflows, \ref dasdan98minmeancycle. |
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102 /// It is an improved version of \ref Karp "Karp"'s original algorithm, |
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103 /// it applies an efficient early termination scheme. |
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104 /// It runs in time O(ne) and uses space O(n<sup>2</sup>+e). |
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105 /// |
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106 /// \tparam GR The type of the digraph the algorithm runs on. |
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107 /// \tparam LEN The type of the length map. The default |
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108 /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
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109 /// \tparam TR The traits class that defines various types used by the |
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110 /// algorithm. By default, it is \ref HartmannOrlinDefaultTraits |
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111 /// "HartmannOrlinDefaultTraits<GR, LEN>". |
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112 /// In most cases, this parameter should not be set directly, |
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113 /// consider to use the named template parameters instead. |
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114 #ifdef DOXYGEN |
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115 template <typename GR, typename LEN, typename TR> |
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116 #else |
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117 template < typename GR, |
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118 typename LEN = typename GR::template ArcMap<int>, |
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119 typename TR = HartmannOrlinDefaultTraits<GR, LEN> > |
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120 #endif |
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121 class HartmannOrlin |
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122 { |
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123 public: |
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124 |
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125 /// The type of the digraph |
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126 typedef typename TR::Digraph Digraph; |
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127 /// The type of the length map |
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128 typedef typename TR::LengthMap LengthMap; |
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129 /// The type of the arc lengths |
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130 typedef typename TR::Value Value; |
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131 |
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132 /// \brief The large value type |
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133 /// |
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134 /// The large value type used for internal computations. |
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135 /// By default, it is \c long \c long if the \c Value type is integer, |
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136 /// otherwise it is \c double. |
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137 typedef typename TR::LargeValue LargeValue; |
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138 |
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139 /// The tolerance type |
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140 typedef typename TR::Tolerance Tolerance; |
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141 |
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142 /// \brief The path type of the found cycles |
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143 /// |
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144 /// The path type of the found cycles. |
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145 /// Using the \ref HartmannOrlinDefaultTraits "default traits class", |
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146 /// it is \ref lemon::Path "Path<Digraph>". |
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147 typedef typename TR::Path Path; |
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148 |
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149 /// The \ref HartmannOrlinDefaultTraits "traits class" of the algorithm |
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150 typedef TR Traits; |
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151 |
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152 private: |
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153 |
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154 TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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155 |
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156 // Data sturcture for path data |
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157 struct PathData |
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158 { |
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159 LargeValue dist; |
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160 Arc pred; |
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161 PathData(LargeValue d, Arc p = INVALID) : |
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162 dist(d), pred(p) {} |
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163 }; |
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164 |
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165 typedef typename Digraph::template NodeMap<std::vector<PathData> > |
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166 PathDataNodeMap; |
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167 |
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168 private: |
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169 |
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170 // The digraph the algorithm runs on |
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171 const Digraph &_gr; |
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172 // The length of the arcs |
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173 const LengthMap &_length; |
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174 |
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175 // Data for storing the strongly connected components |
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176 int _comp_num; |
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177 typename Digraph::template NodeMap<int> _comp; |
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178 std::vector<std::vector<Node> > _comp_nodes; |
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179 std::vector<Node>* _nodes; |
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180 typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs; |
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181 |
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182 // Data for the found cycles |
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183 bool _curr_found, _best_found; |
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184 LargeValue _curr_length, _best_length; |
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185 int _curr_size, _best_size; |
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186 Node _curr_node, _best_node; |
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187 int _curr_level, _best_level; |
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188 |
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189 Path *_cycle_path; |
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190 bool _local_path; |
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191 |
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192 // Node map for storing path data |
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193 PathDataNodeMap _data; |
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194 // The processed nodes in the last round |
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195 std::vector<Node> _process; |
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196 |
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197 Tolerance _tolerance; |
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198 |
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199 // Infinite constant |
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200 const LargeValue INF; |
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201 |
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202 public: |
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203 |
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204 /// \name Named Template Parameters |
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205 /// @{ |
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206 |
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207 template <typename T> |
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208 struct SetLargeValueTraits : public Traits { |
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209 typedef T LargeValue; |
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210 typedef lemon::Tolerance<T> Tolerance; |
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211 }; |
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212 |
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213 /// \brief \ref named-templ-param "Named parameter" for setting |
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214 /// \c LargeValue type. |
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215 /// |
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216 /// \ref named-templ-param "Named parameter" for setting \c LargeValue |
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217 /// type. It is used for internal computations in the algorithm. |
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218 template <typename T> |
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219 struct SetLargeValue |
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220 : public HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > { |
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221 typedef HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > Create; |
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222 }; |
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223 |
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224 template <typename T> |
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225 struct SetPathTraits : public Traits { |
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226 typedef T Path; |
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227 }; |
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228 |
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229 /// \brief \ref named-templ-param "Named parameter" for setting |
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230 /// \c %Path type. |
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231 /// |
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232 /// \ref named-templ-param "Named parameter" for setting the \c %Path |
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233 /// type of the found cycles. |
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234 /// It must conform to the \ref lemon::concepts::Path "Path" concept |
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235 /// and it must have an \c addFront() function. |
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236 template <typename T> |
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237 struct SetPath |
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238 : public HartmannOrlin<GR, LEN, SetPathTraits<T> > { |
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239 typedef HartmannOrlin<GR, LEN, SetPathTraits<T> > Create; |
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240 }; |
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241 |
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242 /// @} |
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243 |
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244 protected: |
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245 |
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246 HartmannOrlin() {} |
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247 |
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248 public: |
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249 |
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250 /// \brief Constructor. |
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251 /// |
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252 /// The constructor of the class. |
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253 /// |
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254 /// \param digraph The digraph the algorithm runs on. |
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255 /// \param length The lengths (costs) of the arcs. |
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256 HartmannOrlin( const Digraph &digraph, |
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257 const LengthMap &length ) : |
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258 _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph), |
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259 _best_found(false), _best_length(0), _best_size(1), |
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260 _cycle_path(NULL), _local_path(false), _data(digraph), |
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261 INF(std::numeric_limits<LargeValue>::has_infinity ? |
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262 std::numeric_limits<LargeValue>::infinity() : |
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263 std::numeric_limits<LargeValue>::max()) |
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264 {} |
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265 |
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266 /// Destructor. |
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267 ~HartmannOrlin() { |
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268 if (_local_path) delete _cycle_path; |
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269 } |
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270 |
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271 /// \brief Set the path structure for storing the found cycle. |
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272 /// |
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273 /// This function sets an external path structure for storing the |
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274 /// found cycle. |
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275 /// |
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276 /// If you don't call this function before calling \ref run() or |
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277 /// \ref findMinMean(), it will allocate a local \ref Path "path" |
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278 /// structure. The destuctor deallocates this automatically |
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279 /// allocated object, of course. |
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280 /// |
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281 /// \note The algorithm calls only the \ref lemon::Path::addFront() |
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282 /// "addFront()" function of the given path structure. |
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283 /// |
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284 /// \return <tt>(*this)</tt> |
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285 HartmannOrlin& cycle(Path &path) { |
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286 if (_local_path) { |
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287 delete _cycle_path; |
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288 _local_path = false; |
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289 } |
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290 _cycle_path = &path; |
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291 return *this; |
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292 } |
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293 |
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294 /// \brief Set the tolerance used by the algorithm. |
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295 /// |
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296 /// This function sets the tolerance object used by the algorithm. |
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297 /// |
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298 /// \return <tt>(*this)</tt> |
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299 HartmannOrlin& tolerance(const Tolerance& tolerance) { |
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300 _tolerance = tolerance; |
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301 return *this; |
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302 } |
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303 |
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304 /// \brief Return a const reference to the tolerance. |
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305 /// |
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306 /// This function returns a const reference to the tolerance object |
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307 /// used by the algorithm. |
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308 const Tolerance& tolerance() const { |
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309 return _tolerance; |
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310 } |
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311 |
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312 /// \name Execution control |
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313 /// The simplest way to execute the algorithm is to call the \ref run() |
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314 /// function.\n |
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315 /// If you only need the minimum mean length, you may call |
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316 /// \ref findMinMean(). |
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317 |
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318 /// @{ |
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319 |
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320 /// \brief Run the algorithm. |
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321 /// |
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322 /// This function runs the algorithm. |
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323 /// It can be called more than once (e.g. if the underlying digraph |
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324 /// and/or the arc lengths have been modified). |
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325 /// |
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326 /// \return \c true if a directed cycle exists in the digraph. |
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327 /// |
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328 /// \note <tt>mmc.run()</tt> is just a shortcut of the following code. |
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329 /// \code |
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330 /// return mmc.findMinMean() && mmc.findCycle(); |
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331 /// \endcode |
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332 bool run() { |
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333 return findMinMean() && findCycle(); |
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334 } |
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335 |
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336 /// \brief Find the minimum cycle mean. |
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337 /// |
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338 /// This function finds the minimum mean length of the directed |
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339 /// cycles in the digraph. |
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340 /// |
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341 /// \return \c true if a directed cycle exists in the digraph. |
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342 bool findMinMean() { |
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343 // Initialization and find strongly connected components |
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344 init(); |
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345 findComponents(); |
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346 |
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347 // Find the minimum cycle mean in the components |
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348 for (int comp = 0; comp < _comp_num; ++comp) { |
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349 if (!initComponent(comp)) continue; |
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350 processRounds(); |
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351 |
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352 // Update the best cycle (global minimum mean cycle) |
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353 if ( _curr_found && (!_best_found || |
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354 _curr_length * _best_size < _best_length * _curr_size) ) { |
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355 _best_found = true; |
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356 _best_length = _curr_length; |
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357 _best_size = _curr_size; |
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358 _best_node = _curr_node; |
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359 _best_level = _curr_level; |
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360 } |
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361 } |
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362 return _best_found; |
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363 } |
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364 |
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365 /// \brief Find a minimum mean directed cycle. |
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366 /// |
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367 /// This function finds a directed cycle of minimum mean length |
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368 /// in the digraph using the data computed by findMinMean(). |
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369 /// |
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370 /// \return \c true if a directed cycle exists in the digraph. |
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371 /// |
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372 /// \pre \ref findMinMean() must be called before using this function. |
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373 bool findCycle() { |
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374 if (!_best_found) return false; |
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375 IntNodeMap reached(_gr, -1); |
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376 int r = _best_level + 1; |
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377 Node u = _best_node; |
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378 while (reached[u] < 0) { |
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379 reached[u] = --r; |
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380 u = _gr.source(_data[u][r].pred); |
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381 } |
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382 r = reached[u]; |
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383 Arc e = _data[u][r].pred; |
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384 _cycle_path->addFront(e); |
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385 _best_length = _length[e]; |
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386 _best_size = 1; |
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387 Node v; |
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388 while ((v = _gr.source(e)) != u) { |
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389 e = _data[v][--r].pred; |
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390 _cycle_path->addFront(e); |
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391 _best_length += _length[e]; |
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392 ++_best_size; |
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393 } |
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394 return true; |
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395 } |
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396 |
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397 /// @} |
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398 |
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399 /// \name Query Functions |
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400 /// The results of the algorithm can be obtained using these |
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401 /// functions.\n |
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402 /// The algorithm should be executed before using them. |
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403 |
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404 /// @{ |
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405 |
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406 /// \brief Return the total length of the found cycle. |
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407 /// |
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408 /// This function returns the total length of the found cycle. |
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409 /// |
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410 /// \pre \ref run() or \ref findMinMean() must be called before |
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411 /// using this function. |
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412 Value cycleLength() const { |
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413 return static_cast<Value>(_best_length); |
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414 } |
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415 |
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416 /// \brief Return the number of arcs on the found cycle. |
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417 /// |
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418 /// This function returns the number of arcs on the found cycle. |
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419 /// |
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420 /// \pre \ref run() or \ref findMinMean() must be called before |
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421 /// using this function. |
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422 int cycleArcNum() const { |
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423 return _best_size; |
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424 } |
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425 |
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426 /// \brief Return the mean length of the found cycle. |
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427 /// |
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428 /// This function returns the mean length of the found cycle. |
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429 /// |
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430 /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the |
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431 /// following code. |
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432 /// \code |
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433 /// return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum(); |
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434 /// \endcode |
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435 /// |
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436 /// \pre \ref run() or \ref findMinMean() must be called before |
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437 /// using this function. |
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438 double cycleMean() const { |
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439 return static_cast<double>(_best_length) / _best_size; |
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440 } |
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441 |
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442 /// \brief Return the found cycle. |
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443 /// |
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444 /// This function returns a const reference to the path structure |
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445 /// storing the found cycle. |
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446 /// |
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447 /// \pre \ref run() or \ref findCycle() must be called before using |
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448 /// this function. |
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449 const Path& cycle() const { |
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450 return *_cycle_path; |
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451 } |
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452 |
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453 ///@} |
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454 |
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455 private: |
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456 |
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457 // Initialization |
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458 void init() { |
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459 if (!_cycle_path) { |
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460 _local_path = true; |
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461 _cycle_path = new Path; |
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462 } |
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463 _cycle_path->clear(); |
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464 _best_found = false; |
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465 _best_length = 0; |
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466 _best_size = 1; |
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467 _cycle_path->clear(); |
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468 for (NodeIt u(_gr); u != INVALID; ++u) |
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469 _data[u].clear(); |
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470 } |
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471 |
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472 // Find strongly connected components and initialize _comp_nodes |
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473 // and _out_arcs |
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474 void findComponents() { |
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475 _comp_num = stronglyConnectedComponents(_gr, _comp); |
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476 _comp_nodes.resize(_comp_num); |
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477 if (_comp_num == 1) { |
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478 _comp_nodes[0].clear(); |
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479 for (NodeIt n(_gr); n != INVALID; ++n) { |
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480 _comp_nodes[0].push_back(n); |
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481 _out_arcs[n].clear(); |
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482 for (OutArcIt a(_gr, n); a != INVALID; ++a) { |
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483 _out_arcs[n].push_back(a); |
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484 } |
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485 } |
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486 } else { |
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487 for (int i = 0; i < _comp_num; ++i) |
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488 _comp_nodes[i].clear(); |
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489 for (NodeIt n(_gr); n != INVALID; ++n) { |
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490 int k = _comp[n]; |
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491 _comp_nodes[k].push_back(n); |
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492 _out_arcs[n].clear(); |
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493 for (OutArcIt a(_gr, n); a != INVALID; ++a) { |
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494 if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a); |
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495 } |
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496 } |
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497 } |
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498 } |
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499 |
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500 // Initialize path data for the current component |
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501 bool initComponent(int comp) { |
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502 _nodes = &(_comp_nodes[comp]); |
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503 int n = _nodes->size(); |
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504 if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) { |
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505 return false; |
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506 } |
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507 for (int i = 0; i < n; ++i) { |
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508 _data[(*_nodes)[i]].resize(n + 1, PathData(INF)); |
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509 } |
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510 return true; |
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511 } |
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512 |
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513 // Process all rounds of computing path data for the current component. |
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514 // _data[v][k] is the length of a shortest directed walk from the root |
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515 // node to node v containing exactly k arcs. |
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516 void processRounds() { |
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517 Node start = (*_nodes)[0]; |
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518 _data[start][0] = PathData(0); |
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519 _process.clear(); |
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520 _process.push_back(start); |
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521 |
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522 int k, n = _nodes->size(); |
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523 int next_check = 4; |
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524 bool terminate = false; |
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525 for (k = 1; k <= n && int(_process.size()) < n && !terminate; ++k) { |
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526 processNextBuildRound(k); |
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527 if (k == next_check || k == n) { |
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528 terminate = checkTermination(k); |
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529 next_check = next_check * 3 / 2; |
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530 } |
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531 } |
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532 for ( ; k <= n && !terminate; ++k) { |
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533 processNextFullRound(k); |
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534 if (k == next_check || k == n) { |
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535 terminate = checkTermination(k); |
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536 next_check = next_check * 3 / 2; |
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537 } |
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538 } |
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539 } |
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540 |
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541 // Process one round and rebuild _process |
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542 void processNextBuildRound(int k) { |
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543 std::vector<Node> next; |
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544 Node u, v; |
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545 Arc e; |
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546 LargeValue d; |
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547 for (int i = 0; i < int(_process.size()); ++i) { |
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548 u = _process[i]; |
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549 for (int j = 0; j < int(_out_arcs[u].size()); ++j) { |
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550 e = _out_arcs[u][j]; |
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551 v = _gr.target(e); |
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552 d = _data[u][k-1].dist + _length[e]; |
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553 if (_tolerance.less(d, _data[v][k].dist)) { |
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554 if (_data[v][k].dist == INF) next.push_back(v); |
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555 _data[v][k] = PathData(d, e); |
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556 } |
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557 } |
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558 } |
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559 _process.swap(next); |
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560 } |
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561 |
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562 // Process one round using _nodes instead of _process |
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563 void processNextFullRound(int k) { |
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564 Node u, v; |
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565 Arc e; |
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566 LargeValue d; |
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567 for (int i = 0; i < int(_nodes->size()); ++i) { |
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568 u = (*_nodes)[i]; |
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569 for (int j = 0; j < int(_out_arcs[u].size()); ++j) { |
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570 e = _out_arcs[u][j]; |
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571 v = _gr.target(e); |
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572 d = _data[u][k-1].dist + _length[e]; |
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573 if (_tolerance.less(d, _data[v][k].dist)) { |
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574 _data[v][k] = PathData(d, e); |
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575 } |
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576 } |
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577 } |
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578 } |
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579 |
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580 // Check early termination |
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581 bool checkTermination(int k) { |
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582 typedef std::pair<int, int> Pair; |
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583 typename GR::template NodeMap<Pair> level(_gr, Pair(-1, 0)); |
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584 typename GR::template NodeMap<LargeValue> pi(_gr); |
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585 int n = _nodes->size(); |
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586 LargeValue length; |
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587 int size; |
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588 Node u; |
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589 |
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590 // Search for cycles that are already found |
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591 _curr_found = false; |
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592 for (int i = 0; i < n; ++i) { |
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593 u = (*_nodes)[i]; |
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594 if (_data[u][k].dist == INF) continue; |
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595 for (int j = k; j >= 0; --j) { |
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596 if (level[u].first == i && level[u].second > 0) { |
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597 // A cycle is found |
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598 length = _data[u][level[u].second].dist - _data[u][j].dist; |
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599 size = level[u].second - j; |
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600 if (!_curr_found || length * _curr_size < _curr_length * size) { |
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601 _curr_length = length; |
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602 _curr_size = size; |
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603 _curr_node = u; |
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604 _curr_level = level[u].second; |
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605 _curr_found = true; |
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606 } |
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607 } |
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608 level[u] = Pair(i, j); |
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609 if (j != 0) { |
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610 u = _gr.source(_data[u][j].pred); |
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611 } |
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612 } |
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613 } |
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614 |
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615 // If at least one cycle is found, check the optimality condition |
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616 LargeValue d; |
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617 if (_curr_found && k < n) { |
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618 // Find node potentials |
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619 for (int i = 0; i < n; ++i) { |
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620 u = (*_nodes)[i]; |
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621 pi[u] = INF; |
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622 for (int j = 0; j <= k; ++j) { |
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623 if (_data[u][j].dist < INF) { |
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624 d = _data[u][j].dist * _curr_size - j * _curr_length; |
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625 if (_tolerance.less(d, pi[u])) pi[u] = d; |
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626 } |
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627 } |
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628 } |
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629 |
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630 // Check the optimality condition for all arcs |
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631 bool done = true; |
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632 for (ArcIt a(_gr); a != INVALID; ++a) { |
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633 if (_tolerance.less(_length[a] * _curr_size - _curr_length, |
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634 pi[_gr.target(a)] - pi[_gr.source(a)]) ) { |
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635 done = false; |
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636 break; |
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637 } |
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638 } |
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639 return done; |
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640 } |
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641 return (k == n); |
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642 } |
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643 |
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644 }; //class HartmannOrlin |
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645 |
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646 ///@} |
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647 |
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648 } //namespace lemon |
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649 |
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650 #endif //LEMON_HARTMANN_ORLIN_H |
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