Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/tests/test_matching.py @ 0:4f3585e2f14b draft default tip
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author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |
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1 from itertools import permutations |
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2 import math |
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3 |
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4 import networkx as nx |
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5 from networkx.algorithms.matching import matching_dict_to_set |
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6 from networkx.testing import assert_edges_equal |
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7 |
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8 |
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9 class TestMaxWeightMatching: |
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10 """Unit tests for the |
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11 :func:`~networkx.algorithms.matching.max_weight_matching` function. |
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12 |
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13 """ |
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14 |
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15 def test_trivial1(self): |
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16 """Empty graph""" |
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17 G = nx.Graph() |
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18 assert nx.max_weight_matching(G) == set() |
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19 |
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20 def test_trivial2(self): |
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21 """Self loop""" |
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22 G = nx.Graph() |
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23 G.add_edge(0, 0, weight=100) |
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24 assert nx.max_weight_matching(G) == set() |
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25 |
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26 def test_trivial3(self): |
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27 """Single edge""" |
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28 G = nx.Graph() |
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29 G.add_edge(0, 1) |
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30 assert_edges_equal( |
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31 nx.max_weight_matching(G), matching_dict_to_set({0: 1, 1: 0}) |
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32 ) |
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33 |
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34 def test_trivial4(self): |
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35 """Small graph""" |
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36 G = nx.Graph() |
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37 G.add_edge("one", "two", weight=10) |
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38 G.add_edge("two", "three", weight=11) |
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39 assert_edges_equal( |
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40 nx.max_weight_matching(G), |
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41 matching_dict_to_set({"three": "two", "two": "three"}), |
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42 ) |
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43 |
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44 def test_trivial5(self): |
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45 """Path""" |
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46 G = nx.Graph() |
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47 G.add_edge(1, 2, weight=5) |
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48 G.add_edge(2, 3, weight=11) |
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49 G.add_edge(3, 4, weight=5) |
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50 assert_edges_equal( |
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51 nx.max_weight_matching(G), matching_dict_to_set({2: 3, 3: 2}) |
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52 ) |
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53 assert_edges_equal( |
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54 nx.max_weight_matching(G, 1), matching_dict_to_set({1: 2, 2: 1, 3: 4, 4: 3}) |
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55 ) |
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56 |
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57 def test_trivial6(self): |
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58 """Small graph with arbitrary weight attribute""" |
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59 G = nx.Graph() |
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60 G.add_edge("one", "two", weight=10, abcd=11) |
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61 G.add_edge("two", "three", weight=11, abcd=10) |
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62 assert_edges_equal( |
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63 nx.max_weight_matching(G, weight="abcd"), |
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64 matching_dict_to_set({"one": "two", "two": "one"}), |
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65 ) |
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66 |
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67 def test_floating_point_weights(self): |
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68 """Floating point weights""" |
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69 G = nx.Graph() |
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70 G.add_edge(1, 2, weight=math.pi) |
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71 G.add_edge(2, 3, weight=math.exp(1)) |
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72 G.add_edge(1, 3, weight=3.0) |
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73 G.add_edge(1, 4, weight=math.sqrt(2.0)) |
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74 assert_edges_equal( |
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75 nx.max_weight_matching(G), matching_dict_to_set({1: 4, 2: 3, 3: 2, 4: 1}) |
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76 ) |
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77 |
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78 def test_negative_weights(self): |
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79 """Negative weights""" |
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80 G = nx.Graph() |
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81 G.add_edge(1, 2, weight=2) |
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82 G.add_edge(1, 3, weight=-2) |
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83 G.add_edge(2, 3, weight=1) |
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84 G.add_edge(2, 4, weight=-1) |
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85 G.add_edge(3, 4, weight=-6) |
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86 assert_edges_equal( |
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87 nx.max_weight_matching(G), matching_dict_to_set({1: 2, 2: 1}) |
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88 ) |
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89 assert_edges_equal( |
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90 nx.max_weight_matching(G, 1), matching_dict_to_set({1: 3, 2: 4, 3: 1, 4: 2}) |
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91 ) |
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92 |
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93 def test_s_blossom(self): |
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94 """Create S-blossom and use it for augmentation:""" |
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95 G = nx.Graph() |
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96 G.add_weighted_edges_from([(1, 2, 8), (1, 3, 9), (2, 3, 10), (3, 4, 7)]) |
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97 assert_edges_equal( |
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98 nx.max_weight_matching(G), matching_dict_to_set({1: 2, 2: 1, 3: 4, 4: 3}) |
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99 ) |
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100 |
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101 G.add_weighted_edges_from([(1, 6, 5), (4, 5, 6)]) |
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102 assert_edges_equal( |
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103 nx.max_weight_matching(G), |
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104 matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 5, 5: 4, 6: 1}), |
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105 ) |
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106 |
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107 def test_s_t_blossom(self): |
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108 """Create S-blossom, relabel as T-blossom, use for augmentation:""" |
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109 G = nx.Graph() |
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110 G.add_weighted_edges_from( |
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111 [(1, 2, 9), (1, 3, 8), (2, 3, 10), (1, 4, 5), (4, 5, 4), (1, 6, 3)] |
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112 ) |
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113 assert_edges_equal( |
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114 nx.max_weight_matching(G), |
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115 matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 5, 5: 4, 6: 1}), |
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116 ) |
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117 G.add_edge(4, 5, weight=3) |
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118 G.add_edge(1, 6, weight=4) |
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119 assert_edges_equal( |
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120 nx.max_weight_matching(G), |
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121 matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 5, 5: 4, 6: 1}), |
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122 ) |
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123 G.remove_edge(1, 6) |
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124 G.add_edge(3, 6, weight=4) |
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125 assert_edges_equal( |
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126 nx.max_weight_matching(G), |
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127 matching_dict_to_set({1: 2, 2: 1, 3: 6, 4: 5, 5: 4, 6: 3}), |
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128 ) |
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129 |
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130 def test_nested_s_blossom(self): |
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131 """Create nested S-blossom, use for augmentation:""" |
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132 |
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133 G = nx.Graph() |
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134 G.add_weighted_edges_from( |
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135 [ |
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136 (1, 2, 9), |
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137 (1, 3, 9), |
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138 (2, 3, 10), |
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139 (2, 4, 8), |
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140 (3, 5, 8), |
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141 (4, 5, 10), |
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142 (5, 6, 6), |
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143 ] |
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144 ) |
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145 dict_format = {1: 3, 2: 4, 3: 1, 4: 2, 5: 6, 6: 5} |
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146 expected = {frozenset(e) for e in matching_dict_to_set(dict_format)} |
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147 answer = {frozenset(e) for e in nx.max_weight_matching(G)} |
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148 assert answer == expected |
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149 |
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150 def test_nested_s_blossom_relabel(self): |
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151 """Create S-blossom, relabel as S, include in nested S-blossom:""" |
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152 G = nx.Graph() |
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153 G.add_weighted_edges_from( |
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154 [ |
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155 (1, 2, 10), |
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156 (1, 7, 10), |
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157 (2, 3, 12), |
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158 (3, 4, 20), |
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159 (3, 5, 20), |
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160 (4, 5, 25), |
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161 (5, 6, 10), |
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162 (6, 7, 10), |
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163 (7, 8, 8), |
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164 ] |
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165 ) |
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166 assert_edges_equal( |
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167 nx.max_weight_matching(G), |
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168 matching_dict_to_set({1: 2, 2: 1, 3: 4, 4: 3, 5: 6, 6: 5, 7: 8, 8: 7}), |
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169 ) |
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170 |
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171 def test_nested_s_blossom_expand(self): |
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172 """Create nested S-blossom, augment, expand recursively:""" |
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173 G = nx.Graph() |
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174 G.add_weighted_edges_from( |
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175 [ |
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176 (1, 2, 8), |
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177 (1, 3, 8), |
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178 (2, 3, 10), |
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179 (2, 4, 12), |
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180 (3, 5, 12), |
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181 (4, 5, 14), |
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182 (4, 6, 12), |
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183 (5, 7, 12), |
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184 (6, 7, 14), |
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185 (7, 8, 12), |
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186 ] |
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187 ) |
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188 assert_edges_equal( |
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189 nx.max_weight_matching(G), |
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190 matching_dict_to_set({1: 2, 2: 1, 3: 5, 4: 6, 5: 3, 6: 4, 7: 8, 8: 7}), |
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191 ) |
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192 |
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193 def test_s_blossom_relabel_expand(self): |
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194 """Create S-blossom, relabel as T, expand:""" |
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195 G = nx.Graph() |
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196 G.add_weighted_edges_from( |
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197 [ |
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198 (1, 2, 23), |
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199 (1, 5, 22), |
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200 (1, 6, 15), |
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201 (2, 3, 25), |
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202 (3, 4, 22), |
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203 (4, 5, 25), |
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204 (4, 8, 14), |
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205 (5, 7, 13), |
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206 ] |
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207 ) |
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208 assert_edges_equal( |
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209 nx.max_weight_matching(G), |
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210 matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 8, 5: 7, 6: 1, 7: 5, 8: 4}), |
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211 ) |
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212 |
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213 def test_nested_s_blossom_relabel_expand(self): |
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214 """Create nested S-blossom, relabel as T, expand:""" |
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215 G = nx.Graph() |
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216 G.add_weighted_edges_from( |
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217 [ |
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218 (1, 2, 19), |
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219 (1, 3, 20), |
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220 (1, 8, 8), |
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221 (2, 3, 25), |
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222 (2, 4, 18), |
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223 (3, 5, 18), |
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224 (4, 5, 13), |
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225 (4, 7, 7), |
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226 (5, 6, 7), |
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227 ] |
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228 ) |
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229 assert_edges_equal( |
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230 nx.max_weight_matching(G), |
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231 matching_dict_to_set({1: 8, 2: 3, 3: 2, 4: 7, 5: 6, 6: 5, 7: 4, 8: 1}), |
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232 ) |
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233 |
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234 def test_nasty_blossom1(self): |
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235 """Create blossom, relabel as T in more than one way, expand, |
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236 augment: |
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237 """ |
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238 G = nx.Graph() |
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239 G.add_weighted_edges_from( |
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240 [ |
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241 (1, 2, 45), |
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242 (1, 5, 45), |
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243 (2, 3, 50), |
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244 (3, 4, 45), |
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245 (4, 5, 50), |
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246 (1, 6, 30), |
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247 (3, 9, 35), |
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248 (4, 8, 35), |
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249 (5, 7, 26), |
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250 (9, 10, 5), |
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251 ] |
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252 ) |
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253 assert_edges_equal( |
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254 nx.max_weight_matching(G), |
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255 matching_dict_to_set( |
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256 {1: 6, 2: 3, 3: 2, 4: 8, 5: 7, 6: 1, 7: 5, 8: 4, 9: 10, 10: 9} |
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257 ), |
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258 ) |
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259 |
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260 def test_nasty_blossom2(self): |
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261 """Again but slightly different:""" |
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262 G = nx.Graph() |
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263 G.add_weighted_edges_from( |
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264 [ |
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265 (1, 2, 45), |
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266 (1, 5, 45), |
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267 (2, 3, 50), |
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268 (3, 4, 45), |
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269 (4, 5, 50), |
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270 (1, 6, 30), |
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271 (3, 9, 35), |
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272 (4, 8, 26), |
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273 (5, 7, 40), |
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274 (9, 10, 5), |
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275 ] |
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276 ) |
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277 assert_edges_equal( |
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278 nx.max_weight_matching(G), |
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279 matching_dict_to_set( |
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280 {1: 6, 2: 3, 3: 2, 4: 8, 5: 7, 6: 1, 7: 5, 8: 4, 9: 10, 10: 9} |
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281 ), |
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282 ) |
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283 |
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284 def test_nasty_blossom_least_slack(self): |
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285 """Create blossom, relabel as T, expand such that a new |
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286 least-slack S-to-free dge is produced, augment: |
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287 """ |
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288 G = nx.Graph() |
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289 G.add_weighted_edges_from( |
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290 [ |
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291 (1, 2, 45), |
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292 (1, 5, 45), |
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293 (2, 3, 50), |
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294 (3, 4, 45), |
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295 (4, 5, 50), |
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296 (1, 6, 30), |
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297 (3, 9, 35), |
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298 (4, 8, 28), |
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299 (5, 7, 26), |
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300 (9, 10, 5), |
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301 ] |
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302 ) |
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303 assert_edges_equal( |
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304 nx.max_weight_matching(G), |
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305 matching_dict_to_set( |
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306 {1: 6, 2: 3, 3: 2, 4: 8, 5: 7, 6: 1, 7: 5, 8: 4, 9: 10, 10: 9} |
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307 ), |
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308 ) |
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309 |
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310 def test_nasty_blossom_augmenting(self): |
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311 """Create nested blossom, relabel as T in more than one way""" |
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312 # expand outer blossom such that inner blossom ends up on an |
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313 # augmenting path: |
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314 G = nx.Graph() |
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315 G.add_weighted_edges_from( |
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316 [ |
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317 (1, 2, 45), |
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318 (1, 7, 45), |
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319 (2, 3, 50), |
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320 (3, 4, 45), |
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321 (4, 5, 95), |
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322 (4, 6, 94), |
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323 (5, 6, 94), |
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324 (6, 7, 50), |
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325 (1, 8, 30), |
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326 (3, 11, 35), |
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327 (5, 9, 36), |
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328 (7, 10, 26), |
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329 (11, 12, 5), |
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330 ] |
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331 ) |
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332 assert_edges_equal( |
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333 nx.max_weight_matching(G), |
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334 matching_dict_to_set( |
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335 { |
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336 1: 8, |
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337 2: 3, |
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338 3: 2, |
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339 4: 6, |
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340 5: 9, |
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341 6: 4, |
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342 7: 10, |
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343 8: 1, |
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344 9: 5, |
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345 10: 7, |
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346 11: 12, |
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347 12: 11, |
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348 } |
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349 ), |
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350 ) |
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351 |
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352 def test_nasty_blossom_expand_recursively(self): |
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353 """Create nested S-blossom, relabel as S, expand recursively:""" |
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354 G = nx.Graph() |
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355 G.add_weighted_edges_from( |
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356 [ |
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357 (1, 2, 40), |
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358 (1, 3, 40), |
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359 (2, 3, 60), |
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360 (2, 4, 55), |
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361 (3, 5, 55), |
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362 (4, 5, 50), |
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363 (1, 8, 15), |
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364 (5, 7, 30), |
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365 (7, 6, 10), |
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366 (8, 10, 10), |
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367 (4, 9, 30), |
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368 ] |
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369 ) |
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370 assert_edges_equal( |
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371 nx.max_weight_matching(G), |
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372 matching_dict_to_set( |
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373 {1: 2, 2: 1, 3: 5, 4: 9, 5: 3, 6: 7, 7: 6, 8: 10, 9: 4, 10: 8} |
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374 ), |
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375 ) |
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376 |
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377 |
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378 class TestIsMatching: |
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379 """Unit tests for the |
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380 :func:`~networkx.algorithms.matching.is_matching` function. |
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381 |
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382 """ |
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383 |
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384 def test_dict(self): |
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385 G = nx.path_graph(4) |
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386 assert nx.is_matching(G, {0: 1, 1: 0, 2: 3, 3: 2}) |
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387 |
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388 def test_empty_matching(self): |
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389 G = nx.path_graph(4) |
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390 assert nx.is_matching(G, set()) |
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391 |
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392 def test_single_edge(self): |
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393 G = nx.path_graph(4) |
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394 assert nx.is_matching(G, {(1, 2)}) |
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395 |
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396 def test_edge_order(self): |
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397 G = nx.path_graph(4) |
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398 assert nx.is_matching(G, {(0, 1), (2, 3)}) |
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399 assert nx.is_matching(G, {(1, 0), (2, 3)}) |
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400 assert nx.is_matching(G, {(0, 1), (3, 2)}) |
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401 assert nx.is_matching(G, {(1, 0), (3, 2)}) |
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402 |
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403 def test_valid(self): |
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404 G = nx.path_graph(4) |
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405 assert nx.is_matching(G, {(0, 1), (2, 3)}) |
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406 |
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407 def test_invalid(self): |
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408 G = nx.path_graph(4) |
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409 assert not nx.is_matching(G, {(0, 1), (1, 2), (2, 3)}) |
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410 |
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411 |
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412 class TestIsMaximalMatching: |
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413 """Unit tests for the |
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414 :func:`~networkx.algorithms.matching.is_maximal_matching` function. |
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415 |
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416 """ |
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417 |
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418 def test_dict(self): |
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419 G = nx.path_graph(4) |
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420 assert nx.is_maximal_matching(G, {0: 1, 1: 0, 2: 3, 3: 2}) |
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421 |
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422 def test_valid(self): |
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423 G = nx.path_graph(4) |
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424 assert nx.is_maximal_matching(G, {(0, 1), (2, 3)}) |
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425 |
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426 def test_not_matching(self): |
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427 G = nx.path_graph(4) |
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428 assert not nx.is_maximal_matching(G, {(0, 1), (1, 2), (2, 3)}) |
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429 |
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430 def test_not_maximal(self): |
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431 G = nx.path_graph(4) |
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432 assert not nx.is_maximal_matching(G, {(0, 1)}) |
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433 |
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434 |
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435 class TestIsPerfectMatching: |
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436 """Unit tests for the |
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437 :func:`~networkx.algorithms.matching.is_perfect_matching` function. |
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438 |
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439 """ |
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440 |
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441 def test_dict(self): |
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442 G = nx.path_graph(4) |
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443 assert nx.is_perfect_matching(G, {0: 1, 1: 0, 2: 3, 3: 2}) |
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444 |
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445 def test_valid(self): |
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446 G = nx.path_graph(4) |
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447 assert nx.is_perfect_matching(G, {(0, 1), (2, 3)}) |
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448 |
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449 def test_valid_not_path(self): |
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450 G = nx.cycle_graph(4) |
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451 G.add_edge(0, 4) |
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452 G.add_edge(1, 4) |
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453 G.add_edge(5, 2) |
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454 |
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455 assert nx.is_perfect_matching(G, {(1, 4), (0, 3), (5, 2)}) |
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456 |
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457 def test_not_matching(self): |
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458 G = nx.path_graph(4) |
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459 assert not nx.is_perfect_matching(G, {(0, 1), (1, 2), (2, 3)}) |
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460 |
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461 def test_maximal_but_not_perfect(self): |
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462 G = nx.cycle_graph(4) |
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463 G.add_edge(0, 4) |
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464 G.add_edge(1, 4) |
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465 |
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466 assert not nx.is_perfect_matching(G, {(1, 4), (0, 3)}) |
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467 |
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468 |
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469 class TestMaximalMatching: |
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470 """Unit tests for the |
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471 :func:`~networkx.algorithms.matching.maximal_matching`. |
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472 |
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473 """ |
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474 |
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475 def test_valid_matching(self): |
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476 edges = [(1, 2), (1, 5), (2, 3), (2, 5), (3, 4), (3, 6), (5, 6)] |
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477 G = nx.Graph(edges) |
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478 matching = nx.maximal_matching(G) |
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479 assert nx.is_maximal_matching(G, matching) |
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480 |
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481 def test_single_edge_matching(self): |
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482 # In the star graph, any maximal matching has just one edge. |
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483 G = nx.star_graph(5) |
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484 matching = nx.maximal_matching(G) |
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485 assert 1 == len(matching) |
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486 assert nx.is_maximal_matching(G, matching) |
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487 |
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488 def test_self_loops(self): |
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489 # Create the path graph with two self-loops. |
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490 G = nx.path_graph(3) |
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491 G.add_edges_from([(0, 0), (1, 1)]) |
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492 matching = nx.maximal_matching(G) |
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493 assert len(matching) == 1 |
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494 # The matching should never include self-loops. |
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495 assert not any(u == v for u, v in matching) |
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496 assert nx.is_maximal_matching(G, matching) |
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497 |
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498 def test_ordering(self): |
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499 """Tests that a maximal matching is computed correctly |
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500 regardless of the order in which nodes are added to the graph. |
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501 |
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502 """ |
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503 for nodes in permutations(range(3)): |
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504 G = nx.Graph() |
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505 G.add_nodes_from(nodes) |
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506 G.add_edges_from([(0, 1), (0, 2)]) |
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507 matching = nx.maximal_matching(G) |
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508 assert len(matching) == 1 |
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509 assert nx.is_maximal_matching(G, matching) |