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_GOMORY_HU_TREE_H |
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20 | #define LEMON_GOMORY_HU_TREE_H |
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21 | |
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22 | #include <limits> |
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23 | |
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24 | #include <lemon/preflow.h> |
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25 | #include <lemon/concept_check.h> |
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26 | #include <lemon/concepts/maps.h> |
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27 | |
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28 | /// \ingroup min_cut |
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29 | /// \file |
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30 | /// \brief Gomory-Hu cut tree in graphs. |
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31 | |
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32 | namespace lemon { |
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33 | |
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34 | /// \ingroup min_cut |
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35 | /// |
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36 | /// \brief Gomory-Hu cut tree algorithm |
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37 | /// |
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38 | /// The Gomory-Hu tree is a tree on the nodeset of the digraph, but it |
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39 | /// may contain arcs which are not in the original digraph. It helps |
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40 | /// to calculate the minimum cut between all pairs of nodes, because |
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41 | /// the minimum capacity arc on the tree path between two nodes has |
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42 | /// the same weight as the minimum cut in the digraph between these |
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43 | /// nodes. Moreover this arc separates the nodes to two parts which |
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44 | /// determine this minimum cut. |
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45 | /// |
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46 | /// The algorithm calculates \e n-1 distinict minimum cuts with |
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47 | /// preflow algorithm, therefore the algorithm has |
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48 | /// \f$(O(n^3\sqrt{e})\f$ overall time complexity. It calculates a |
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49 | /// rooted Gomory-Hu tree, the structure of the tree and the weights |
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50 | /// can be obtained with \c predNode() and \c predValue() |
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51 | /// functions. The \c minCutValue() and \c minCutMap() calculates |
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52 | /// the minimum cut and the minimum cut value between any two node |
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53 | /// in the digraph. |
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54 | template <typename _Graph, |
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55 | typename _Capacity = typename _Graph::template EdgeMap<int> > |
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56 | class GomoryHuTree { |
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57 | public: |
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58 | |
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59 | /// The graph type |
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60 | typedef _Graph Graph; |
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61 | /// The capacity on edges |
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62 | typedef _Capacity Capacity; |
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63 | /// The value type of capacities |
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64 | typedef typename Capacity::Value Value; |
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65 | |
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66 | private: |
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67 | |
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68 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
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69 | |
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70 | const Graph& _graph; |
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71 | const Capacity& _capacity; |
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72 | |
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73 | Node _root; |
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74 | typename Graph::template NodeMap<Node>* _pred; |
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75 | typename Graph::template NodeMap<Value>* _weight; |
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76 | typename Graph::template NodeMap<int>* _order; |
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77 | |
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78 | void createStructures() { |
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79 | if (!_pred) { |
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80 | _pred = new typename Graph::template NodeMap<Node>(_graph); |
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81 | } |
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82 | if (!_weight) { |
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83 | _weight = new typename Graph::template NodeMap<Value>(_graph); |
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84 | } |
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85 | if (!_order) { |
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86 | _order = new typename Graph::template NodeMap<int>(_graph); |
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87 | } |
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88 | } |
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89 | |
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90 | void destroyStructures() { |
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91 | if (_pred) { |
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92 | delete _pred; |
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93 | } |
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94 | if (_weight) { |
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95 | delete _weight; |
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96 | } |
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97 | if (_order) { |
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98 | delete _order; |
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99 | } |
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100 | } |
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101 | |
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102 | public: |
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103 | |
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104 | /// \brief Constructor |
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105 | /// |
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106 | /// Constructor |
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107 | /// \param graph The graph type. |
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108 | /// \param capacity The capacity map. |
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109 | GomoryHuTree(const Graph& graph, const Capacity& capacity) |
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110 | : _graph(graph), _capacity(capacity), |
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111 | _pred(0), _weight(0), _order(0) |
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112 | { |
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113 | checkConcept<concepts::ReadMap<Edge, Value>, Capacity>(); |
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114 | } |
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115 | |
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116 | |
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117 | /// \brief Destructor |
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118 | /// |
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119 | /// Destructor |
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120 | ~GomoryHuTree() { |
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121 | destroyStructures(); |
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122 | } |
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123 | |
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124 | /// \brief Initializes the internal data structures. |
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125 | /// |
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126 | /// Initializes the internal data structures. |
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127 | /// |
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128 | void init() { |
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129 | createStructures(); |
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130 | |
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131 | _root = NodeIt(_graph); |
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132 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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133 | _pred->set(n, _root); |
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134 | _order->set(n, -1); |
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135 | } |
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136 | _pred->set(_root, INVALID); |
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137 | _weight->set(_root, std::numeric_limits<Value>::max()); |
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138 | } |
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139 | |
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140 | |
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141 | /// \brief Starts the algorithm |
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142 | /// |
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143 | /// Starts the algorithm. |
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144 | void start() { |
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145 | Preflow<Graph, Capacity> fa(_graph, _capacity, _root, INVALID); |
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146 | |
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147 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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148 | if (n == _root) continue; |
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149 | |
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150 | Node pn = (*_pred)[n]; |
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151 | fa.source(n); |
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152 | fa.target(pn); |
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153 | |
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154 | fa.runMinCut(); |
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155 | |
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156 | _weight->set(n, fa.flowValue()); |
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157 | |
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158 | for (NodeIt nn(_graph); nn != INVALID; ++nn) { |
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159 | if (nn != n && fa.minCut(nn) && (*_pred)[nn] == pn) { |
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160 | _pred->set(nn, n); |
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161 | } |
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162 | } |
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163 | if ((*_pred)[pn] != INVALID && fa.minCut((*_pred)[pn])) { |
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164 | _pred->set(n, (*_pred)[pn]); |
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165 | _pred->set(pn, n); |
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166 | _weight->set(n, (*_weight)[pn]); |
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167 | _weight->set(pn, fa.flowValue()); |
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168 | } |
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169 | } |
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170 | |
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171 | _order->set(_root, 0); |
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172 | int index = 1; |
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173 | |
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174 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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175 | std::vector<Node> st; |
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176 | Node nn = n; |
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177 | while ((*_order)[nn] == -1) { |
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178 | st.push_back(nn); |
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179 | nn = (*_pred)[nn]; |
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180 | } |
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181 | while (!st.empty()) { |
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182 | _order->set(st.back(), index++); |
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183 | st.pop_back(); |
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184 | } |
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185 | } |
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186 | } |
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187 | |
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188 | /// \brief Runs the Gomory-Hu algorithm. |
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189 | /// |
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190 | /// Runs the Gomory-Hu algorithm. |
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191 | /// \note gh.run() is just a shortcut of the following code. |
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192 | /// \code |
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193 | /// ght.init(); |
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194 | /// ght.start(); |
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195 | /// \endcode |
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196 | void run() { |
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197 | init(); |
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198 | start(); |
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199 | } |
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200 | |
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201 | /// \brief Returns the predecessor node in the Gomory-Hu tree. |
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202 | /// |
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203 | /// Returns the predecessor node in the Gomory-Hu tree. If the node is |
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204 | /// the root of the Gomory-Hu tree, then it returns \c INVALID. |
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205 | Node predNode(const Node& node) { |
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206 | return (*_pred)[node]; |
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207 | } |
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208 | |
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209 | /// \brief Returns the weight of the predecessor arc in the |
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210 | /// Gomory-Hu tree. |
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211 | /// |
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212 | /// Returns the weight of the predecessor arc in the Gomory-Hu |
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213 | /// tree. If the node is the root of the Gomory-Hu tree, the |
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214 | /// result is undefined. |
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215 | Value predValue(const Node& node) { |
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216 | return (*_weight)[node]; |
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217 | } |
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218 | |
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219 | /// \brief Returns the minimum cut value between two nodes |
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220 | /// |
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221 | /// Returns the minimum cut value between two nodes. The |
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222 | /// algorithm finds the nearest common ancestor in the Gomory-Hu |
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223 | /// tree and calculates the minimum weight arc on the paths to |
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224 | /// the ancestor. |
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225 | Value minCutValue(const Node& s, const Node& t) const { |
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226 | Node sn = s, tn = t; |
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227 | Value value = std::numeric_limits<Value>::max(); |
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228 | |
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229 | while (sn != tn) { |
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230 | if ((*_order)[sn] < (*_order)[tn]) { |
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231 | if ((*_weight)[tn] < value) value = (*_weight)[tn]; |
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232 | tn = (*_pred)[tn]; |
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233 | } else { |
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234 | if ((*_weight)[sn] < value) value = (*_weight)[sn]; |
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235 | sn = (*_pred)[sn]; |
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236 | } |
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237 | } |
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238 | return value; |
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239 | } |
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240 | |
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241 | /// \brief Returns the minimum cut between two nodes |
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242 | /// |
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243 | /// Returns the minimum cut value between two nodes. The |
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244 | /// algorithm finds the nearest common ancestor in the Gomory-Hu |
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245 | /// tree and calculates the minimum weight arc on the paths to |
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246 | /// the ancestor. Then it sets all nodes to the cut determined by |
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247 | /// this arc. The \c cutMap should be \ref concepts::ReadWriteMap |
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248 | /// "ReadWriteMap". |
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249 | template <typename CutMap> |
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250 | Value minCutMap(const Node& s, const Node& t, CutMap& cutMap) const { |
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251 | Node sn = s, tn = t; |
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252 | |
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253 | Node rn = INVALID; |
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254 | Value value = std::numeric_limits<Value>::max(); |
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255 | |
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256 | while (sn != tn) { |
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257 | if ((*_order)[sn] < (*_order)[tn]) { |
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258 | if ((*_weight)[tn] < value) { |
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259 | rn = tn; |
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260 | value = (*_weight)[tn]; |
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261 | } |
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262 | tn = (*_pred)[tn]; |
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263 | } else { |
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264 | if ((*_weight)[sn] < value) { |
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265 | rn = sn; |
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266 | value = (*_weight)[sn]; |
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267 | } |
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268 | sn = (*_pred)[sn]; |
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269 | } |
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270 | } |
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271 | |
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272 | typename Graph::template NodeMap<bool> reached(_graph, false); |
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273 | reached.set(_root, true); |
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274 | cutMap.set(_root, false); |
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275 | reached.set(rn, true); |
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276 | cutMap.set(rn, true); |
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277 | |
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278 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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279 | std::vector<Node> st; |
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280 | Node nn = n; |
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281 | while (!reached[nn]) { |
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282 | st.push_back(nn); |
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283 | nn = (*_pred)[nn]; |
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284 | } |
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285 | while (!st.empty()) { |
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286 | cutMap.set(st.back(), cutMap[nn]); |
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287 | st.pop_back(); |
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288 | } |
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289 | } |
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290 | |
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291 | return value; |
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292 | } |
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293 | |
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294 | }; |
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295 | |
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296 | } |
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297 | |
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298 | #endif |
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