Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/bipartite/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 """Unit tests for the :mod:`networkx.algorithms.bipartite.matching` module.""" |
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2 import itertools |
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3 |
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4 import networkx as nx |
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5 |
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6 import pytest |
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7 |
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8 from networkx.algorithms.bipartite.matching import eppstein_matching |
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9 from networkx.algorithms.bipartite.matching import hopcroft_karp_matching |
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10 from networkx.algorithms.bipartite.matching import maximum_matching |
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11 from networkx.algorithms.bipartite.matching import minimum_weight_full_matching |
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12 from networkx.algorithms.bipartite.matching import to_vertex_cover |
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13 |
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14 |
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15 class TestMatching: |
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16 """Tests for bipartite matching algorithms.""" |
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17 |
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18 def setup(self): |
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19 """Creates a bipartite graph for use in testing matching algorithms. |
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20 |
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21 The bipartite graph has a maximum cardinality matching that leaves |
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22 vertex 1 and vertex 10 unmatched. The first six numbers are the left |
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23 vertices and the next six numbers are the right vertices. |
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24 |
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25 """ |
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26 self.simple_graph = nx.complete_bipartite_graph(2, 3) |
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27 self.simple_solution = {0: 2, 1: 3, 2: 0, 3: 1} |
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28 |
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29 edges = [(0, 7), (0, 8), (2, 6), (2, 9), (3, 8), (4, 8), (4, 9), (5, 11)] |
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30 self.top_nodes = set(range(6)) |
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31 self.graph = nx.Graph() |
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32 self.graph.add_nodes_from(range(12)) |
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33 self.graph.add_edges_from(edges) |
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34 |
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35 # Example bipartite graph from issue 2127 |
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36 G = nx.Graph() |
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37 G.add_nodes_from( |
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38 [ |
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39 (1, "C"), |
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40 (1, "B"), |
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41 (0, "G"), |
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42 (1, "F"), |
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43 (1, "E"), |
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44 (0, "C"), |
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45 (1, "D"), |
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46 (1, "I"), |
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47 (0, "A"), |
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48 (0, "D"), |
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49 (0, "F"), |
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50 (0, "E"), |
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51 (0, "H"), |
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52 (1, "G"), |
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53 (1, "A"), |
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54 (0, "I"), |
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55 (0, "B"), |
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56 (1, "H"), |
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57 ] |
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58 ) |
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59 G.add_edge((1, "C"), (0, "A")) |
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60 G.add_edge((1, "B"), (0, "A")) |
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61 G.add_edge((0, "G"), (1, "I")) |
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62 G.add_edge((0, "G"), (1, "H")) |
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63 G.add_edge((1, "F"), (0, "A")) |
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64 G.add_edge((1, "F"), (0, "C")) |
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65 G.add_edge((1, "F"), (0, "E")) |
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66 G.add_edge((1, "E"), (0, "A")) |
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67 G.add_edge((1, "E"), (0, "C")) |
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68 G.add_edge((0, "C"), (1, "D")) |
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69 G.add_edge((0, "C"), (1, "I")) |
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70 G.add_edge((0, "C"), (1, "G")) |
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71 G.add_edge((0, "C"), (1, "H")) |
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72 G.add_edge((1, "D"), (0, "A")) |
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73 G.add_edge((1, "I"), (0, "A")) |
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74 G.add_edge((1, "I"), (0, "E")) |
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75 G.add_edge((0, "A"), (1, "G")) |
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76 G.add_edge((0, "A"), (1, "H")) |
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77 G.add_edge((0, "E"), (1, "G")) |
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78 G.add_edge((0, "E"), (1, "H")) |
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79 self.disconnected_graph = G |
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80 |
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81 def check_match(self, matching): |
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82 """Asserts that the matching is what we expect from the bipartite graph |
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83 constructed in the :meth:`setup` fixture. |
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84 |
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85 """ |
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86 # For the sake of brevity, rename `matching` to `M`. |
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87 M = matching |
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88 matched_vertices = frozenset(itertools.chain(*M.items())) |
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89 # Assert that the maximum number of vertices (10) is matched. |
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90 assert matched_vertices == frozenset(range(12)) - {1, 10} |
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91 # Assert that no vertex appears in two edges, or in other words, that |
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92 # the matching (u, v) and (v, u) both appear in the matching |
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93 # dictionary. |
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94 assert all(u == M[M[u]] for u in range(12) if u in M) |
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95 |
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96 def check_vertex_cover(self, vertices): |
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97 """Asserts that the given set of vertices is the vertex cover we |
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98 expected from the bipartite graph constructed in the :meth:`setup` |
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99 fixture. |
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100 |
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101 """ |
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102 # By Konig's theorem, the number of edges in a maximum matching equals |
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103 # the number of vertices in a minimum vertex cover. |
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104 assert len(vertices) == 5 |
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105 # Assert that the set is truly a vertex cover. |
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106 for (u, v) in self.graph.edges(): |
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107 assert u in vertices or v in vertices |
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108 # TODO Assert that the vertices are the correct ones. |
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109 |
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110 def test_eppstein_matching(self): |
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111 """Tests that David Eppstein's implementation of the Hopcroft--Karp |
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112 algorithm produces a maximum cardinality matching. |
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113 |
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114 """ |
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115 self.check_match(eppstein_matching(self.graph, self.top_nodes)) |
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116 |
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117 def test_hopcroft_karp_matching(self): |
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118 """Tests that the Hopcroft--Karp algorithm produces a maximum |
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119 cardinality matching in a bipartite graph. |
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120 |
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121 """ |
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122 self.check_match(hopcroft_karp_matching(self.graph, self.top_nodes)) |
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123 |
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124 def test_to_vertex_cover(self): |
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125 """Test for converting a maximum matching to a minimum vertex cover.""" |
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126 matching = maximum_matching(self.graph, self.top_nodes) |
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127 vertex_cover = to_vertex_cover(self.graph, matching, self.top_nodes) |
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128 self.check_vertex_cover(vertex_cover) |
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129 |
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130 def test_eppstein_matching_simple(self): |
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131 match = eppstein_matching(self.simple_graph) |
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132 assert match == self.simple_solution |
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133 |
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134 def test_hopcroft_karp_matching_simple(self): |
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135 match = hopcroft_karp_matching(self.simple_graph) |
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136 assert match == self.simple_solution |
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137 |
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138 def test_eppstein_matching_disconnected(self): |
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139 with pytest.raises(nx.AmbiguousSolution): |
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140 match = eppstein_matching(self.disconnected_graph) |
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141 |
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142 def test_hopcroft_karp_matching_disconnected(self): |
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143 with pytest.raises(nx.AmbiguousSolution): |
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144 match = hopcroft_karp_matching(self.disconnected_graph) |
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145 |
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146 def test_issue_2127(self): |
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147 """Test from issue 2127""" |
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148 # Build the example DAG |
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149 G = nx.DiGraph() |
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150 G.add_edge("A", "C") |
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151 G.add_edge("A", "B") |
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152 G.add_edge("C", "E") |
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153 G.add_edge("C", "D") |
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154 G.add_edge("E", "G") |
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155 G.add_edge("E", "F") |
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156 G.add_edge("G", "I") |
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157 G.add_edge("G", "H") |
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158 |
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159 tc = nx.transitive_closure(G) |
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160 btc = nx.Graph() |
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161 |
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162 # Create a bipartite graph based on the transitive closure of G |
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163 for v in tc.nodes(): |
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164 btc.add_node((0, v)) |
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165 btc.add_node((1, v)) |
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166 |
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167 for u, v in tc.edges(): |
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168 btc.add_edge((0, u), (1, v)) |
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169 |
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170 top_nodes = {n for n in btc if n[0] == 0} |
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171 matching = hopcroft_karp_matching(btc, top_nodes) |
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172 vertex_cover = to_vertex_cover(btc, matching, top_nodes) |
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173 independent_set = set(G) - {v for _, v in vertex_cover} |
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174 assert {"B", "D", "F", "I", "H"} == independent_set |
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175 |
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176 def test_vertex_cover_issue_2384(self): |
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177 G = nx.Graph([(0, 3), (1, 3), (1, 4), (2, 3)]) |
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178 matching = maximum_matching(G) |
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179 vertex_cover = to_vertex_cover(G, matching) |
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180 for u, v in G.edges(): |
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181 assert u in vertex_cover or v in vertex_cover |
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182 |
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183 def test_unorderable_nodes(self): |
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184 a = object() |
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185 b = object() |
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186 c = object() |
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187 d = object() |
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188 e = object() |
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189 G = nx.Graph([(a, d), (b, d), (b, e), (c, d)]) |
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190 matching = maximum_matching(G) |
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191 vertex_cover = to_vertex_cover(G, matching) |
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192 for u, v in G.edges(): |
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193 assert u in vertex_cover or v in vertex_cover |
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194 |
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195 |
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196 def test_eppstein_matching(): |
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197 """Test in accordance to issue #1927""" |
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198 G = nx.Graph() |
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199 G.add_nodes_from(["a", 2, 3, 4], bipartite=0) |
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200 G.add_nodes_from([1, "b", "c"], bipartite=1) |
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201 G.add_edges_from([("a", 1), ("a", "b"), (2, "b"), (2, "c"), (3, "c"), (4, 1)]) |
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202 matching = eppstein_matching(G) |
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203 assert len(matching) == len(maximum_matching(G)) |
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204 assert all(x in set(matching.keys()) for x in set(matching.values())) |
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205 |
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206 |
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207 class TestMinimumWeightFullMatching: |
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208 @classmethod |
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209 def setup_class(cls): |
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210 global scipy |
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211 scipy = pytest.importorskip("scipy") |
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212 |
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213 def test_minimum_weight_full_matching_incomplete_graph(self): |
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214 B = nx.Graph() |
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215 B.add_nodes_from([1, 2], bipartite=0) |
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216 B.add_nodes_from([3, 4], bipartite=1) |
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217 B.add_edge(1, 4, weight=100) |
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218 B.add_edge(2, 3, weight=100) |
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219 B.add_edge(2, 4, weight=50) |
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220 matching = minimum_weight_full_matching(B) |
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221 assert matching == {1: 4, 2: 3, 4: 1, 3: 2} |
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222 |
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223 def test_minimum_weight_full_matching_with_no_full_matching(self): |
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224 B = nx.Graph() |
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225 B.add_nodes_from([1, 2, 3], bipartite=0) |
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226 B.add_nodes_from([4, 5, 6], bipartite=1) |
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227 B.add_edge(1, 4, weight=100) |
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228 B.add_edge(2, 4, weight=100) |
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229 B.add_edge(3, 4, weight=50) |
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230 B.add_edge(3, 5, weight=50) |
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231 B.add_edge(3, 6, weight=50) |
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232 with pytest.raises(ValueError): |
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233 minimum_weight_full_matching(B) |
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234 |
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235 def test_minimum_weight_full_matching_square(self): |
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236 G = nx.complete_bipartite_graph(3, 3) |
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237 G.add_edge(0, 3, weight=400) |
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238 G.add_edge(0, 4, weight=150) |
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239 G.add_edge(0, 5, weight=400) |
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240 G.add_edge(1, 3, weight=400) |
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241 G.add_edge(1, 4, weight=450) |
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242 G.add_edge(1, 5, weight=600) |
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243 G.add_edge(2, 3, weight=300) |
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244 G.add_edge(2, 4, weight=225) |
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245 G.add_edge(2, 5, weight=300) |
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246 matching = minimum_weight_full_matching(G) |
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247 assert matching == {0: 4, 1: 3, 2: 5, 4: 0, 3: 1, 5: 2} |
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248 |
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249 def test_minimum_weight_full_matching_smaller_left(self): |
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250 G = nx.complete_bipartite_graph(3, 4) |
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251 G.add_edge(0, 3, weight=400) |
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252 G.add_edge(0, 4, weight=150) |
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253 G.add_edge(0, 5, weight=400) |
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254 G.add_edge(0, 6, weight=1) |
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255 G.add_edge(1, 3, weight=400) |
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256 G.add_edge(1, 4, weight=450) |
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257 G.add_edge(1, 5, weight=600) |
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258 G.add_edge(1, 6, weight=2) |
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259 G.add_edge(2, 3, weight=300) |
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260 G.add_edge(2, 4, weight=225) |
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261 G.add_edge(2, 5, weight=290) |
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262 G.add_edge(2, 6, weight=3) |
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263 matching = minimum_weight_full_matching(G) |
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264 assert matching == {0: 4, 1: 6, 2: 5, 4: 0, 5: 2, 6: 1} |
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265 |
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266 def test_minimum_weight_full_matching_smaller_top_nodes_right(self): |
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267 G = nx.complete_bipartite_graph(3, 4) |
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268 G.add_edge(0, 3, weight=400) |
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269 G.add_edge(0, 4, weight=150) |
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270 G.add_edge(0, 5, weight=400) |
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271 G.add_edge(0, 6, weight=1) |
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272 G.add_edge(1, 3, weight=400) |
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273 G.add_edge(1, 4, weight=450) |
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274 G.add_edge(1, 5, weight=600) |
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275 G.add_edge(1, 6, weight=2) |
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276 G.add_edge(2, 3, weight=300) |
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277 G.add_edge(2, 4, weight=225) |
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278 G.add_edge(2, 5, weight=290) |
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279 G.add_edge(2, 6, weight=3) |
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280 matching = minimum_weight_full_matching(G, top_nodes=[3, 4, 5, 6]) |
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281 assert matching == {0: 4, 1: 6, 2: 5, 4: 0, 5: 2, 6: 1} |
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282 |
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283 def test_minimum_weight_full_matching_smaller_right(self): |
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284 G = nx.complete_bipartite_graph(4, 3) |
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285 G.add_edge(0, 4, weight=400) |
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286 G.add_edge(0, 5, weight=400) |
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287 G.add_edge(0, 6, weight=300) |
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288 G.add_edge(1, 4, weight=150) |
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289 G.add_edge(1, 5, weight=450) |
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290 G.add_edge(1, 6, weight=225) |
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291 G.add_edge(2, 4, weight=400) |
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292 G.add_edge(2, 5, weight=600) |
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293 G.add_edge(2, 6, weight=290) |
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294 G.add_edge(3, 4, weight=1) |
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295 G.add_edge(3, 5, weight=2) |
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296 G.add_edge(3, 6, weight=3) |
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297 matching = minimum_weight_full_matching(G) |
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298 assert matching == {1: 4, 2: 6, 3: 5, 4: 1, 5: 3, 6: 2} |
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299 |
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300 def test_minimum_weight_full_matching_negative_weights(self): |
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301 G = nx.complete_bipartite_graph(2, 2) |
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302 G.add_edge(0, 2, weight=-2) |
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303 G.add_edge(0, 3, weight=0.2) |
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304 G.add_edge(1, 2, weight=-2) |
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305 G.add_edge(1, 3, weight=0.3) |
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306 matching = minimum_weight_full_matching(G) |
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307 assert matching == {0: 3, 1: 2, 2: 1, 3: 0} |
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308 |
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309 def test_minimum_weight_full_matching_different_weight_key(self): |
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310 G = nx.complete_bipartite_graph(2, 2) |
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311 G.add_edge(0, 2, mass=2) |
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312 G.add_edge(0, 3, mass=0.2) |
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313 G.add_edge(1, 2, mass=1) |
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314 G.add_edge(1, 3, mass=2) |
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315 matching = minimum_weight_full_matching(G, weight="mass") |
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316 assert matching == {0: 3, 1: 2, 2: 1, 3: 0} |