1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library. |
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4 | * |
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5 | * Copyright (C) 2003-2009 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #include <iostream> |
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20 | #include <sstream> |
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21 | #include <vector> |
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22 | #include <queue> |
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23 | #include <cstdlib> |
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24 | |
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25 | #include <lemon/fractional_matching.h> |
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26 | #include <lemon/smart_graph.h> |
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27 | #include <lemon/concepts/graph.h> |
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28 | #include <lemon/concepts/maps.h> |
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29 | #include <lemon/lgf_reader.h> |
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30 | #include <lemon/math.h> |
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31 | |
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32 | #include "test_tools.h" |
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33 | |
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34 | using namespace std; |
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35 | using namespace lemon; |
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36 | |
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37 | GRAPH_TYPEDEFS(SmartGraph); |
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38 | |
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39 | |
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40 | const int lgfn = 4; |
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41 | const std::string lgf[lgfn] = { |
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42 | "@nodes\n" |
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43 | "label\n" |
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44 | "0\n" |
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45 | "1\n" |
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46 | "2\n" |
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47 | "3\n" |
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48 | "4\n" |
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49 | "5\n" |
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50 | "6\n" |
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51 | "7\n" |
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52 | "@edges\n" |
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53 | " label weight\n" |
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54 | "7 4 0 984\n" |
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55 | "0 7 1 73\n" |
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56 | "7 1 2 204\n" |
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57 | "2 3 3 583\n" |
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58 | "2 7 4 565\n" |
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59 | "2 1 5 582\n" |
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60 | "0 4 6 551\n" |
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61 | "2 5 7 385\n" |
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62 | "1 5 8 561\n" |
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63 | "5 3 9 484\n" |
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64 | "7 5 10 904\n" |
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65 | "3 6 11 47\n" |
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66 | "7 6 12 888\n" |
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67 | "3 0 13 747\n" |
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68 | "6 1 14 310\n", |
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69 | |
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70 | "@nodes\n" |
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71 | "label\n" |
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72 | "0\n" |
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73 | "1\n" |
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74 | "2\n" |
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75 | "3\n" |
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76 | "4\n" |
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77 | "5\n" |
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78 | "6\n" |
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79 | "7\n" |
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80 | "@edges\n" |
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81 | " label weight\n" |
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82 | "2 5 0 710\n" |
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83 | "0 5 1 241\n" |
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84 | "2 4 2 856\n" |
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85 | "2 6 3 762\n" |
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86 | "4 1 4 747\n" |
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87 | "6 1 5 962\n" |
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88 | "4 7 6 723\n" |
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89 | "1 7 7 661\n" |
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90 | "2 3 8 376\n" |
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91 | "1 0 9 416\n" |
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92 | "6 7 10 391\n", |
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93 | |
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94 | "@nodes\n" |
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95 | "label\n" |
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96 | "0\n" |
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97 | "1\n" |
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98 | "2\n" |
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99 | "3\n" |
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100 | "4\n" |
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101 | "5\n" |
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102 | "6\n" |
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103 | "7\n" |
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104 | "@edges\n" |
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105 | " label weight\n" |
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106 | "6 2 0 553\n" |
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107 | "0 7 1 653\n" |
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108 | "6 3 2 22\n" |
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109 | "4 7 3 846\n" |
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110 | "7 2 4 981\n" |
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111 | "7 6 5 250\n" |
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112 | "5 2 6 539\n", |
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113 | |
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114 | "@nodes\n" |
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115 | "label\n" |
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116 | "0\n" |
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117 | "@edges\n" |
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118 | " label weight\n" |
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119 | "0 0 0 100\n" |
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120 | }; |
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121 | |
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122 | void checkMaxFractionalMatchingCompile() |
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123 | { |
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124 | typedef concepts::Graph Graph; |
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125 | typedef Graph::Node Node; |
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126 | typedef Graph::Edge Edge; |
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127 | |
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128 | Graph g; |
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129 | Node n; |
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130 | Edge e; |
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131 | |
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132 | MaxFractionalMatching<Graph> mat_test(g); |
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133 | const MaxFractionalMatching<Graph>& |
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134 | const_mat_test = mat_test; |
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135 | |
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136 | mat_test.init(); |
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137 | mat_test.start(); |
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138 | mat_test.start(true); |
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139 | mat_test.startPerfect(); |
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140 | mat_test.startPerfect(true); |
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141 | mat_test.run(); |
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142 | mat_test.run(true); |
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143 | mat_test.runPerfect(); |
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144 | mat_test.runPerfect(true); |
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145 | |
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146 | const_mat_test.matchingSize(); |
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147 | const_mat_test.matching(e); |
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148 | const_mat_test.matching(n); |
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149 | const MaxFractionalMatching<Graph>::MatchingMap& mmap = |
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150 | const_mat_test.matchingMap(); |
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151 | e = mmap[n]; |
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152 | |
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153 | const_mat_test.barrier(n); |
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154 | } |
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155 | |
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156 | void checkMaxWeightedFractionalMatchingCompile() |
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157 | { |
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158 | typedef concepts::Graph Graph; |
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159 | typedef Graph::Node Node; |
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160 | typedef Graph::Edge Edge; |
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161 | typedef Graph::EdgeMap<int> WeightMap; |
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162 | |
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163 | Graph g; |
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164 | Node n; |
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165 | Edge e; |
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166 | WeightMap w(g); |
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167 | |
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168 | MaxWeightedFractionalMatching<Graph> mat_test(g, w); |
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169 | const MaxWeightedFractionalMatching<Graph>& |
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170 | const_mat_test = mat_test; |
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171 | |
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172 | mat_test.init(); |
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173 | mat_test.start(); |
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174 | mat_test.run(); |
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175 | |
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176 | const_mat_test.matchingWeight(); |
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177 | const_mat_test.matchingSize(); |
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178 | const_mat_test.matching(e); |
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179 | const_mat_test.matching(n); |
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180 | const MaxWeightedFractionalMatching<Graph>::MatchingMap& mmap = |
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181 | const_mat_test.matchingMap(); |
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182 | e = mmap[n]; |
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183 | |
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184 | const_mat_test.dualValue(); |
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185 | const_mat_test.nodeValue(n); |
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186 | } |
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187 | |
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188 | void checkMaxWeightedPerfectFractionalMatchingCompile() |
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189 | { |
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190 | typedef concepts::Graph Graph; |
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191 | typedef Graph::Node Node; |
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192 | typedef Graph::Edge Edge; |
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193 | typedef Graph::EdgeMap<int> WeightMap; |
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194 | |
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195 | Graph g; |
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196 | Node n; |
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197 | Edge e; |
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198 | WeightMap w(g); |
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199 | |
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200 | MaxWeightedPerfectFractionalMatching<Graph> mat_test(g, w); |
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201 | const MaxWeightedPerfectFractionalMatching<Graph>& |
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202 | const_mat_test = mat_test; |
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203 | |
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204 | mat_test.init(); |
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205 | mat_test.start(); |
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206 | mat_test.run(); |
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207 | |
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208 | const_mat_test.matchingWeight(); |
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209 | const_mat_test.matching(e); |
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210 | const_mat_test.matching(n); |
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211 | const MaxWeightedPerfectFractionalMatching<Graph>::MatchingMap& mmap = |
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212 | const_mat_test.matchingMap(); |
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213 | e = mmap[n]; |
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214 | |
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215 | const_mat_test.dualValue(); |
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216 | const_mat_test.nodeValue(n); |
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217 | } |
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218 | |
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219 | void checkFractionalMatching(const SmartGraph& graph, |
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220 | const MaxFractionalMatching<SmartGraph>& mfm, |
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221 | bool allow_loops = true) { |
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222 | int pv = 0; |
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223 | for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) { |
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224 | int indeg = 0; |
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225 | for (InArcIt a(graph, n); a != INVALID; ++a) { |
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226 | if (mfm.matching(graph.source(a)) == a) { |
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227 | ++indeg; |
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228 | } |
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229 | } |
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230 | if (mfm.matching(n) != INVALID) { |
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231 | check(indeg == 1, "Invalid matching"); |
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232 | ++pv; |
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233 | } else { |
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234 | check(indeg == 0, "Invalid matching"); |
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235 | } |
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236 | } |
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237 | check(pv == mfm.matchingSize(), "Wrong matching size"); |
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238 | |
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239 | for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) { |
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240 | check((e == mfm.matching(graph.u(e)) ? 1 : 0) + |
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241 | (e == mfm.matching(graph.v(e)) ? 1 : 0) == |
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242 | mfm.matching(e), "Invalid matching"); |
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243 | } |
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244 | |
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245 | SmartGraph::NodeMap<bool> processed(graph, false); |
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246 | for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) { |
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247 | if (processed[n]) continue; |
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248 | processed[n] = true; |
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249 | if (mfm.matching(n) == INVALID) continue; |
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250 | int num = 1; |
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251 | Node v = graph.target(mfm.matching(n)); |
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252 | while (v != n) { |
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253 | processed[v] = true; |
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254 | ++num; |
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255 | v = graph.target(mfm.matching(v)); |
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256 | } |
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257 | check(num == 2 || num % 2 == 1, "Wrong cycle size"); |
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258 | check(allow_loops || num != 1, "Wrong cycle size"); |
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259 | } |
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260 | |
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261 | int anum = 0, bnum = 0; |
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262 | SmartGraph::NodeMap<bool> neighbours(graph, false); |
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263 | for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) { |
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264 | if (!mfm.barrier(n)) continue; |
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265 | ++anum; |
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266 | for (SmartGraph::InArcIt a(graph, n); a != INVALID; ++a) { |
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267 | Node u = graph.source(a); |
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268 | if (!allow_loops && u == n) continue; |
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269 | if (!neighbours[u]) { |
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270 | neighbours[u] = true; |
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271 | ++bnum; |
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272 | } |
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273 | } |
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274 | } |
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275 | check(anum - bnum + mfm.matchingSize() == countNodes(graph), |
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276 | "Wrong barrier"); |
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277 | } |
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278 | |
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279 | void checkPerfectFractionalMatching(const SmartGraph& graph, |
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280 | const MaxFractionalMatching<SmartGraph>& mfm, |
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281 | bool perfect, bool allow_loops = true) { |
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282 | if (perfect) { |
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283 | for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) { |
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284 | int indeg = 0; |
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285 | for (InArcIt a(graph, n); a != INVALID; ++a) { |
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286 | if (mfm.matching(graph.source(a)) == a) { |
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287 | ++indeg; |
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288 | } |
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289 | } |
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290 | check(mfm.matching(n) != INVALID, "Invalid matching"); |
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291 | check(indeg == 1, "Invalid matching"); |
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292 | } |
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293 | for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) { |
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294 | check((e == mfm.matching(graph.u(e)) ? 1 : 0) + |
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295 | (e == mfm.matching(graph.v(e)) ? 1 : 0) == |
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296 | mfm.matching(e), "Invalid matching"); |
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297 | } |
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298 | } else { |
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299 | int anum = 0, bnum = 0; |
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300 | SmartGraph::NodeMap<bool> neighbours(graph, false); |
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301 | for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) { |
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302 | if (!mfm.barrier(n)) continue; |
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303 | ++anum; |
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304 | for (SmartGraph::InArcIt a(graph, n); a != INVALID; ++a) { |
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305 | Node u = graph.source(a); |
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306 | if (!allow_loops && u == n) continue; |
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307 | if (!neighbours[u]) { |
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308 | neighbours[u] = true; |
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309 | ++bnum; |
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310 | } |
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311 | } |
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312 | } |
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313 | check(anum - bnum > 0, "Wrong barrier"); |
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314 | } |
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315 | } |
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316 | |
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317 | void checkWeightedFractionalMatching(const SmartGraph& graph, |
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318 | const SmartGraph::EdgeMap<int>& weight, |
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319 | const MaxWeightedFractionalMatching<SmartGraph>& mwfm, |
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320 | bool allow_loops = true) { |
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321 | for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) { |
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322 | if (graph.u(e) == graph.v(e) && !allow_loops) continue; |
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323 | int rw = mwfm.nodeValue(graph.u(e)) + mwfm.nodeValue(graph.v(e)) |
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324 | - weight[e] * mwfm.dualScale; |
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325 | |
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326 | check(rw >= 0, "Negative reduced weight"); |
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327 | check(rw == 0 || !mwfm.matching(e), |
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328 | "Non-zero reduced weight on matching edge"); |
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329 | } |
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330 | |
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331 | int pv = 0; |
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332 | for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) { |
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333 | int indeg = 0; |
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334 | for (InArcIt a(graph, n); a != INVALID; ++a) { |
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335 | if (mwfm.matching(graph.source(a)) == a) { |
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336 | ++indeg; |
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337 | } |
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338 | } |
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339 | check(indeg <= 1, "Invalid matching"); |
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340 | if (mwfm.matching(n) != INVALID) { |
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341 | check(mwfm.nodeValue(n) >= 0, "Invalid node value"); |
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342 | check(indeg == 1, "Invalid matching"); |
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343 | pv += weight[mwfm.matching(n)]; |
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344 | SmartGraph::Node o = graph.target(mwfm.matching(n)); |
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345 | } else { |
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346 | check(mwfm.nodeValue(n) == 0, "Invalid matching"); |
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347 | check(indeg == 0, "Invalid matching"); |
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348 | } |
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349 | } |
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350 | |
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351 | for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) { |
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352 | check((e == mwfm.matching(graph.u(e)) ? 1 : 0) + |
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353 | (e == mwfm.matching(graph.v(e)) ? 1 : 0) == |
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354 | mwfm.matching(e), "Invalid matching"); |
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355 | } |
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356 | |
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357 | int dv = 0; |
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358 | for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) { |
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359 | dv += mwfm.nodeValue(n); |
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360 | } |
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361 | |
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362 | check(pv * mwfm.dualScale == dv * 2, "Wrong duality"); |
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363 | |
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364 | SmartGraph::NodeMap<bool> processed(graph, false); |
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365 | for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) { |
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366 | if (processed[n]) continue; |
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367 | processed[n] = true; |
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368 | if (mwfm.matching(n) == INVALID) continue; |
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369 | int num = 1; |
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370 | Node v = graph.target(mwfm.matching(n)); |
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371 | while (v != n) { |
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372 | processed[v] = true; |
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373 | ++num; |
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374 | v = graph.target(mwfm.matching(v)); |
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375 | } |
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376 | check(num == 2 || num % 2 == 1, "Wrong cycle size"); |
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377 | check(allow_loops || num != 1, "Wrong cycle size"); |
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378 | } |
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379 | |
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380 | return; |
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381 | } |
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382 | |
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383 | void checkWeightedPerfectFractionalMatching(const SmartGraph& graph, |
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384 | const SmartGraph::EdgeMap<int>& weight, |
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385 | const MaxWeightedPerfectFractionalMatching<SmartGraph>& mwpfm, |
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386 | bool allow_loops = true) { |
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387 | for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) { |
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388 | if (graph.u(e) == graph.v(e) && !allow_loops) continue; |
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389 | int rw = mwpfm.nodeValue(graph.u(e)) + mwpfm.nodeValue(graph.v(e)) |
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390 | - weight[e] * mwpfm.dualScale; |
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391 | |
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392 | check(rw >= 0, "Negative reduced weight"); |
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393 | check(rw == 0 || !mwpfm.matching(e), |
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394 | "Non-zero reduced weight on matching edge"); |
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395 | } |
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396 | |
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397 | int pv = 0; |
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398 | for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) { |
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399 | int indeg = 0; |
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400 | for (InArcIt a(graph, n); a != INVALID; ++a) { |
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401 | if (mwpfm.matching(graph.source(a)) == a) { |
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402 | ++indeg; |
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403 | } |
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404 | } |
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405 | check(mwpfm.matching(n) != INVALID, "Invalid perfect matching"); |
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406 | check(indeg == 1, "Invalid perfect matching"); |
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407 | pv += weight[mwpfm.matching(n)]; |
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408 | SmartGraph::Node o = graph.target(mwpfm.matching(n)); |
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409 | } |
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410 | |
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411 | for (SmartGraph::EdgeIt e(graph); e != INVALID; ++e) { |
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412 | check((e == mwpfm.matching(graph.u(e)) ? 1 : 0) + |
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413 | (e == mwpfm.matching(graph.v(e)) ? 1 : 0) == |
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414 | mwpfm.matching(e), "Invalid matching"); |
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415 | } |
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416 | |
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417 | int dv = 0; |
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418 | for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) { |
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419 | dv += mwpfm.nodeValue(n); |
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420 | } |
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421 | |
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422 | check(pv * mwpfm.dualScale == dv * 2, "Wrong duality"); |
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423 | |
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424 | SmartGraph::NodeMap<bool> processed(graph, false); |
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425 | for (SmartGraph::NodeIt n(graph); n != INVALID; ++n) { |
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426 | if (processed[n]) continue; |
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427 | processed[n] = true; |
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428 | if (mwpfm.matching(n) == INVALID) continue; |
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429 | int num = 1; |
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430 | Node v = graph.target(mwpfm.matching(n)); |
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431 | while (v != n) { |
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432 | processed[v] = true; |
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433 | ++num; |
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434 | v = graph.target(mwpfm.matching(v)); |
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435 | } |
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436 | check(num == 2 || num % 2 == 1, "Wrong cycle size"); |
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437 | check(allow_loops || num != 1, "Wrong cycle size"); |
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438 | } |
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439 | |
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440 | return; |
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441 | } |
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442 | |
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443 | |
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444 | int main() { |
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445 | |
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446 | for (int i = 0; i < lgfn; ++i) { |
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447 | SmartGraph graph; |
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448 | SmartGraph::EdgeMap<int> weight(graph); |
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449 | |
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450 | istringstream lgfs(lgf[i]); |
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451 | graphReader(graph, lgfs). |
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452 | edgeMap("weight", weight).run(); |
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453 | |
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454 | bool perfect_with_loops; |
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455 | { |
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456 | MaxFractionalMatching<SmartGraph> mfm(graph, true); |
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457 | mfm.run(); |
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458 | checkFractionalMatching(graph, mfm, true); |
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459 | perfect_with_loops = mfm.matchingSize() == countNodes(graph); |
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460 | } |
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461 | |
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462 | bool perfect_without_loops; |
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463 | { |
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464 | MaxFractionalMatching<SmartGraph> mfm(graph, false); |
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465 | mfm.run(); |
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466 | checkFractionalMatching(graph, mfm, false); |
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467 | perfect_without_loops = mfm.matchingSize() == countNodes(graph); |
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468 | } |
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469 | |
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470 | { |
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471 | MaxFractionalMatching<SmartGraph> mfm(graph, true); |
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472 | bool result = mfm.runPerfect(); |
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473 | checkPerfectFractionalMatching(graph, mfm, result, true); |
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474 | check(result == perfect_with_loops, "Wrong perfect matching"); |
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475 | } |
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476 | |
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477 | { |
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478 | MaxFractionalMatching<SmartGraph> mfm(graph, false); |
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479 | bool result = mfm.runPerfect(); |
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480 | checkPerfectFractionalMatching(graph, mfm, result, false); |
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481 | check(result == perfect_without_loops, "Wrong perfect matching"); |
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482 | } |
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483 | |
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484 | { |
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485 | MaxWeightedFractionalMatching<SmartGraph> mwfm(graph, weight, true); |
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486 | mwfm.run(); |
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487 | checkWeightedFractionalMatching(graph, weight, mwfm, true); |
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488 | } |
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489 | |
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490 | { |
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491 | MaxWeightedFractionalMatching<SmartGraph> mwfm(graph, weight, false); |
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492 | mwfm.run(); |
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493 | checkWeightedFractionalMatching(graph, weight, mwfm, false); |
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494 | } |
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495 | |
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496 | { |
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497 | MaxWeightedPerfectFractionalMatching<SmartGraph> mwpfm(graph, weight, |
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498 | true); |
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499 | bool perfect = mwpfm.run(); |
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500 | check(perfect == (mwpfm.matchingSize() == countNodes(graph)), |
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501 | "Perfect matching found"); |
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502 | check(perfect == perfect_with_loops, "Wrong perfect matching"); |
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503 | |
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504 | if (perfect) { |
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505 | checkWeightedPerfectFractionalMatching(graph, weight, mwpfm, true); |
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506 | } |
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507 | } |
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508 | |
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509 | { |
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510 | MaxWeightedPerfectFractionalMatching<SmartGraph> mwpfm(graph, weight, |
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511 | false); |
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512 | bool perfect = mwpfm.run(); |
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513 | check(perfect == (mwpfm.matchingSize() == countNodes(graph)), |
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514 | "Perfect matching found"); |
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515 | check(perfect == perfect_without_loops, "Wrong perfect matching"); |
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516 | |
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517 | if (perfect) { |
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518 | checkWeightedPerfectFractionalMatching(graph, weight, mwpfm, false); |
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519 | } |
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520 | } |
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521 | |
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522 | } |
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523 | |
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524 | return 0; |
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525 | } |
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