Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/connectivity/tests/test_edge_augmentation.py @ 0:4f3585e2f14b draft default tip
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |
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1 import random |
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2 import networkx as nx |
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3 import itertools as it |
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4 from networkx.utils import pairwise |
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5 import pytest |
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6 from networkx.algorithms.connectivity import k_edge_augmentation |
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7 from networkx.algorithms.connectivity.edge_augmentation import ( |
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8 collapse, |
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9 complement_edges, |
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10 is_locally_k_edge_connected, |
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11 is_k_edge_connected, |
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12 _unpack_available_edges, |
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13 ) |
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14 |
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15 # This should be set to the largest k for which an efficient algorithm is |
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16 # explicitly defined. |
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17 MAX_EFFICIENT_K = 2 |
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18 |
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19 |
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20 def tarjan_bridge_graph(): |
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21 # graph from tarjan paper |
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22 # RE Tarjan - "A note on finding the bridges of a graph" |
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23 # Information Processing Letters, 1974 - Elsevier |
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24 # doi:10.1016/0020-0190(74)90003-9. |
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25 # define 2-connected components and bridges |
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26 ccs = [ |
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27 (1, 2, 4, 3, 1, 4), |
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28 (5, 6, 7, 5), |
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29 (8, 9, 10, 8), |
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30 (17, 18, 16, 15, 17), |
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31 (11, 12, 14, 13, 11, 14), |
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32 ] |
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33 bridges = [(4, 8), (3, 5), (3, 17)] |
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34 G = nx.Graph(it.chain(*(pairwise(path) for path in ccs + bridges))) |
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35 return G |
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36 |
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37 |
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38 def test_weight_key(): |
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39 G = nx.Graph() |
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40 G.add_nodes_from([1, 2, 3, 4, 5, 6, 7, 8, 9]) |
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41 G.add_edges_from([(3, 8), (1, 2), (2, 3)]) |
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42 impossible = {(3, 6), (3, 9)} |
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43 rng = random.Random(0) |
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44 avail_uv = list(set(complement_edges(G)) - impossible) |
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45 avail = [(u, v, {"cost": rng.random()}) for u, v in avail_uv] |
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46 |
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47 _augment_and_check(G, k=1) |
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48 _augment_and_check(G, k=1, avail=avail_uv) |
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49 _augment_and_check(G, k=1, avail=avail, weight="cost") |
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50 |
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51 _check_augmentations(G, avail, weight="cost") |
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52 |
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53 |
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54 def test_is_locally_k_edge_connected_exceptions(): |
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55 pytest.raises(nx.NetworkXNotImplemented, is_k_edge_connected, nx.DiGraph(), k=0) |
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56 pytest.raises(nx.NetworkXNotImplemented, is_k_edge_connected, nx.MultiGraph(), k=0) |
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57 pytest.raises(ValueError, is_k_edge_connected, nx.Graph(), k=0) |
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58 |
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59 |
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60 def test_is_k_edge_connected(): |
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61 G = nx.barbell_graph(10, 0) |
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62 assert is_k_edge_connected(G, k=1) |
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63 assert not is_k_edge_connected(G, k=2) |
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64 |
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65 G = nx.Graph() |
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66 G.add_nodes_from([5, 15]) |
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67 assert not is_k_edge_connected(G, k=1) |
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68 assert not is_k_edge_connected(G, k=2) |
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69 |
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70 G = nx.complete_graph(5) |
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71 assert is_k_edge_connected(G, k=1) |
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72 assert is_k_edge_connected(G, k=2) |
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73 assert is_k_edge_connected(G, k=3) |
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74 assert is_k_edge_connected(G, k=4) |
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75 |
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76 |
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77 def test_is_k_edge_connected_exceptions(): |
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78 pytest.raises( |
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79 nx.NetworkXNotImplemented, is_locally_k_edge_connected, nx.DiGraph(), 1, 2, k=0 |
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80 ) |
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81 pytest.raises( |
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82 nx.NetworkXNotImplemented, |
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83 is_locally_k_edge_connected, |
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84 nx.MultiGraph(), |
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85 1, |
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86 2, |
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87 k=0, |
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88 ) |
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89 pytest.raises(ValueError, is_locally_k_edge_connected, nx.Graph(), 1, 2, k=0) |
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90 |
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91 |
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92 def test_is_locally_k_edge_connected(): |
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93 G = nx.barbell_graph(10, 0) |
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94 assert is_locally_k_edge_connected(G, 5, 15, k=1) |
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95 assert not is_locally_k_edge_connected(G, 5, 15, k=2) |
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96 |
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97 G = nx.Graph() |
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98 G.add_nodes_from([5, 15]) |
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99 assert not is_locally_k_edge_connected(G, 5, 15, k=2) |
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100 |
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101 |
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102 def test_null_graph(): |
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103 G = nx.Graph() |
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104 _check_augmentations(G, max_k=MAX_EFFICIENT_K + 2) |
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105 |
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106 |
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107 def test_cliques(): |
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108 for n in range(1, 10): |
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109 G = nx.complete_graph(n) |
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110 _check_augmentations(G, max_k=MAX_EFFICIENT_K + 2) |
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111 |
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112 |
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113 def test_clique_and_node(): |
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114 for n in range(1, 10): |
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115 G = nx.complete_graph(n) |
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116 G.add_node(n + 1) |
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117 _check_augmentations(G, max_k=MAX_EFFICIENT_K + 2) |
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118 |
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119 |
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120 def test_point_graph(): |
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121 G = nx.Graph() |
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122 G.add_node(1) |
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123 _check_augmentations(G, max_k=MAX_EFFICIENT_K + 2) |
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124 |
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125 |
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126 def test_edgeless_graph(): |
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127 G = nx.Graph() |
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128 G.add_nodes_from([1, 2, 3, 4]) |
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129 _check_augmentations(G) |
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130 |
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131 |
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132 def test_invalid_k(): |
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133 G = nx.Graph() |
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134 pytest.raises(ValueError, list, k_edge_augmentation(G, k=-1)) |
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135 pytest.raises(ValueError, list, k_edge_augmentation(G, k=0)) |
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136 |
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137 |
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138 def test_unfeasible(): |
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139 G = tarjan_bridge_graph() |
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140 pytest.raises(nx.NetworkXUnfeasible, list, k_edge_augmentation(G, k=1, avail=[])) |
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141 |
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142 pytest.raises(nx.NetworkXUnfeasible, list, k_edge_augmentation(G, k=2, avail=[])) |
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143 |
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144 pytest.raises( |
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145 nx.NetworkXUnfeasible, list, k_edge_augmentation(G, k=2, avail=[(7, 9)]) |
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146 ) |
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147 |
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148 # partial solutions should not error if real solutions are infeasible |
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149 aug_edges = list(k_edge_augmentation(G, k=2, avail=[(7, 9)], partial=True)) |
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150 assert aug_edges == [(7, 9)] |
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151 |
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152 _check_augmentations(G, avail=[], max_k=MAX_EFFICIENT_K + 2) |
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153 |
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154 _check_augmentations(G, avail=[(7, 9)], max_k=MAX_EFFICIENT_K + 2) |
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155 |
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156 |
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157 def test_tarjan(): |
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158 G = tarjan_bridge_graph() |
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159 |
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160 aug_edges = set(_augment_and_check(G, k=2)[0]) |
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161 print(f"aug_edges = {aug_edges!r}") |
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162 # can't assert edge exactly equality due to non-determinant edge order |
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163 # but we do know the size of the solution must be 3 |
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164 assert len(aug_edges) == 3 |
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165 |
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166 avail = [ |
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167 (9, 7), |
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168 (8, 5), |
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169 (2, 10), |
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170 (6, 13), |
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171 (11, 18), |
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172 (1, 17), |
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173 (2, 3), |
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174 (16, 17), |
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175 (18, 14), |
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176 (15, 14), |
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177 ] |
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178 aug_edges = set(_augment_and_check(G, avail=avail, k=2)[0]) |
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179 |
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180 # Can't assert exact length since approximation depends on the order of a |
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181 # dict traversal. |
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182 assert len(aug_edges) <= 3 * 2 |
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183 |
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184 _check_augmentations(G, avail) |
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185 |
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186 |
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187 def test_configuration(): |
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188 # seeds = [2718183590, 2470619828, 1694705158, 3001036531, 2401251497] |
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189 seeds = [1001, 1002, 1003, 1004] |
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190 for seed in seeds: |
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191 deg_seq = nx.random_powerlaw_tree_sequence(20, seed=seed, tries=5000) |
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192 G = nx.Graph(nx.configuration_model(deg_seq, seed=seed)) |
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193 G.remove_edges_from(nx.selfloop_edges(G)) |
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194 _check_augmentations(G) |
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195 |
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196 |
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197 def test_shell(): |
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198 # seeds = [2057382236, 3331169846, 1840105863, 476020778, 2247498425] |
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199 seeds = [18] |
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200 for seed in seeds: |
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201 constructor = [(12, 70, 0.8), (15, 40, 0.6)] |
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202 G = nx.random_shell_graph(constructor, seed=seed) |
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203 _check_augmentations(G) |
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204 |
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205 |
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206 def test_karate(): |
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207 G = nx.karate_club_graph() |
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208 _check_augmentations(G) |
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209 |
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210 |
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211 def test_star(): |
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212 G = nx.star_graph(3) |
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213 _check_augmentations(G) |
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214 |
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215 G = nx.star_graph(5) |
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216 _check_augmentations(G) |
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217 |
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218 G = nx.star_graph(10) |
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219 _check_augmentations(G) |
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220 |
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221 |
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222 def test_barbell(): |
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223 G = nx.barbell_graph(5, 0) |
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224 _check_augmentations(G) |
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225 |
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226 G = nx.barbell_graph(5, 2) |
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227 _check_augmentations(G) |
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228 |
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229 G = nx.barbell_graph(5, 3) |
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230 _check_augmentations(G) |
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231 |
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232 G = nx.barbell_graph(5, 4) |
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233 _check_augmentations(G) |
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234 |
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235 |
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236 def test_bridge(): |
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237 G = nx.Graph([(2393, 2257), (2393, 2685), (2685, 2257), (1758, 2257)]) |
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238 _check_augmentations(G) |
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239 |
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240 |
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241 def test_gnp_augmentation(): |
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242 rng = random.Random(0) |
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243 G = nx.gnp_random_graph(30, 0.005, seed=0) |
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244 # Randomly make edges available |
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245 avail = { |
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246 (u, v): 1 + rng.random() for u, v in complement_edges(G) if rng.random() < 0.25 |
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247 } |
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248 _check_augmentations(G, avail) |
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249 |
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250 |
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251 def _assert_solution_properties(G, aug_edges, avail_dict=None): |
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252 """ Checks that aug_edges are consistently formatted """ |
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253 if avail_dict is not None: |
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254 assert all( |
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255 e in avail_dict for e in aug_edges |
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256 ), "when avail is specified aug-edges should be in avail" |
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257 |
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258 unique_aug = set(map(tuple, map(sorted, aug_edges))) |
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259 unique_aug = list(map(tuple, map(sorted, aug_edges))) |
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260 assert len(aug_edges) == len(unique_aug), "edges should be unique" |
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261 |
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262 assert not any(u == v for u, v in unique_aug), "should be no self-edges" |
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263 |
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264 assert not any( |
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265 G.has_edge(u, v) for u, v in unique_aug |
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266 ), "aug edges and G.edges should be disjoint" |
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267 |
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268 |
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269 def _augment_and_check( |
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270 G, k, avail=None, weight=None, verbose=False, orig_k=None, max_aug_k=None |
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271 ): |
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272 """ |
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273 Does one specific augmentation and checks for properties of the result |
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274 """ |
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275 if orig_k is None: |
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276 try: |
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277 orig_k = nx.edge_connectivity(G) |
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278 except nx.NetworkXPointlessConcept: |
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279 orig_k = 0 |
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280 info = {} |
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281 try: |
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282 if avail is not None: |
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283 # ensure avail is in dict form |
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284 avail_dict = dict(zip(*_unpack_available_edges(avail, weight=weight))) |
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285 else: |
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286 avail_dict = None |
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287 try: |
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288 # Find the augmentation if possible |
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289 generator = nx.k_edge_augmentation(G, k=k, weight=weight, avail=avail) |
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290 assert not isinstance(generator, list), "should always return an iter" |
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291 aug_edges = [] |
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292 for edge in generator: |
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293 aug_edges.append(edge) |
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294 except nx.NetworkXUnfeasible: |
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295 infeasible = True |
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296 info["infeasible"] = True |
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297 assert len(aug_edges) == 0, "should not generate anything if unfeasible" |
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298 |
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299 if avail is None: |
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300 n_nodes = G.number_of_nodes() |
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301 assert n_nodes <= k, ( |
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302 "unconstrained cases are only unfeasible if |V| <= k. " |
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303 f"Got |V|={n_nodes} and k={k}" |
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304 ) |
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305 else: |
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306 if max_aug_k is None: |
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307 G_aug_all = G.copy() |
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308 G_aug_all.add_edges_from(avail_dict.keys()) |
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309 try: |
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310 max_aug_k = nx.edge_connectivity(G_aug_all) |
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311 except nx.NetworkXPointlessConcept: |
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312 max_aug_k = 0 |
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313 |
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314 assert max_aug_k < k, ( |
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315 "avail should only be unfeasible if using all edges " |
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316 "does not achieve k-edge-connectivity" |
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317 ) |
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318 |
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319 # Test for a partial solution |
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320 partial_edges = list( |
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321 nx.k_edge_augmentation(G, k=k, weight=weight, partial=True, avail=avail) |
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322 ) |
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323 |
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324 info["n_partial_edges"] = len(partial_edges) |
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325 |
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326 if avail_dict is None: |
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327 assert set(partial_edges) == set( |
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328 complement_edges(G) |
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329 ), "unweighted partial solutions should be the complement" |
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330 elif len(avail_dict) > 0: |
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331 H = G.copy() |
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332 |
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333 # Find the partial / full augmented connectivity |
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334 H.add_edges_from(partial_edges) |
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335 partial_conn = nx.edge_connectivity(H) |
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336 |
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337 H.add_edges_from(set(avail_dict.keys())) |
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338 full_conn = nx.edge_connectivity(H) |
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339 |
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340 # Full connectivity should be no better than our partial |
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341 # solution. |
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342 assert ( |
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343 partial_conn == full_conn |
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344 ), "adding more edges should not increase k-conn" |
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345 |
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346 # Find the new edge-connectivity after adding the augmenting edges |
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347 aug_edges = partial_edges |
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348 else: |
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349 infeasible = False |
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350 |
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351 # Find the weight of the augmentation |
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352 num_edges = len(aug_edges) |
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353 if avail is not None: |
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354 total_weight = sum([avail_dict[e] for e in aug_edges]) |
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355 else: |
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356 total_weight = num_edges |
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357 |
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358 info["total_weight"] = total_weight |
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359 info["num_edges"] = num_edges |
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360 |
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361 # Find the new edge-connectivity after adding the augmenting edges |
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362 G_aug = G.copy() |
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363 G_aug.add_edges_from(aug_edges) |
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364 try: |
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365 aug_k = nx.edge_connectivity(G_aug) |
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366 except nx.NetworkXPointlessConcept: |
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367 aug_k = 0 |
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368 info["aug_k"] = aug_k |
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369 |
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370 # Do checks |
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371 if not infeasible and orig_k < k: |
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372 assert info["aug_k"] >= k, f"connectivity should increase to k={k} or more" |
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373 |
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374 assert info["aug_k"] >= orig_k, "augmenting should never reduce connectivity" |
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375 |
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376 _assert_solution_properties(G, aug_edges, avail_dict) |
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377 |
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378 except Exception: |
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379 info["failed"] = True |
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380 print(f"edges = {list(G.edges())}") |
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381 print(f"nodes = {list(G.nodes())}") |
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382 print(f"aug_edges = {list(aug_edges)}") |
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383 print(f"info = {info}") |
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384 raise |
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385 else: |
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386 if verbose: |
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387 print(f"info = {info}") |
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388 |
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389 if infeasible: |
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390 aug_edges = None |
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391 return aug_edges, info |
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392 |
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393 |
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394 def _check_augmentations(G, avail=None, max_k=None, weight=None, verbose=False): |
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395 """ Helper to check weighted/unweighted cases with multiple values of k """ |
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396 # Using all available edges, find the maximum edge-connectivity |
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397 try: |
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398 orig_k = nx.edge_connectivity(G) |
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399 except nx.NetworkXPointlessConcept: |
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400 orig_k = 0 |
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401 |
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402 if avail is not None: |
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403 all_aug_edges = _unpack_available_edges(avail, weight=weight)[0] |
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404 G_aug_all = G.copy() |
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405 G_aug_all.add_edges_from(all_aug_edges) |
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406 try: |
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407 max_aug_k = nx.edge_connectivity(G_aug_all) |
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408 except nx.NetworkXPointlessConcept: |
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409 max_aug_k = 0 |
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410 else: |
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411 max_aug_k = G.number_of_nodes() - 1 |
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412 |
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413 if max_k is None: |
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414 max_k = min(4, max_aug_k) |
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415 |
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416 avail_uniform = {e: 1 for e in complement_edges(G)} |
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417 |
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418 if verbose: |
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419 print("\n=== CHECK_AUGMENTATION ===") |
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420 print(f"G.number_of_nodes = {G.number_of_nodes()!r}") |
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421 print(f"G.number_of_edges = {G.number_of_edges()!r}") |
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422 print(f"max_k = {max_k!r}") |
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423 print(f"max_aug_k = {max_aug_k!r}") |
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424 print(f"orig_k = {orig_k!r}") |
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425 |
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426 # check augmentation for multiple values of k |
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427 for k in range(1, max_k + 1): |
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428 if verbose: |
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429 print("---------------") |
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430 print(f"Checking k = {k}") |
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431 |
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432 # Check the unweighted version |
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433 if verbose: |
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434 print("unweighted case") |
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435 aug_edges1, info1 = _augment_and_check(G, k=k, verbose=verbose, orig_k=orig_k) |
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436 |
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437 # Check that the weighted version with all available edges and uniform |
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438 # weights gives a similar solution to the unweighted case. |
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439 if verbose: |
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440 print("weighted uniform case") |
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441 aug_edges2, info2 = _augment_and_check( |
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442 G, |
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443 k=k, |
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444 avail=avail_uniform, |
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445 verbose=verbose, |
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446 orig_k=orig_k, |
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447 max_aug_k=G.number_of_nodes() - 1, |
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448 ) |
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449 |
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450 # Check the weighted version |
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451 if avail is not None: |
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452 if verbose: |
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453 print("weighted case") |
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454 aug_edges3, info3 = _augment_and_check( |
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455 G, |
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456 k=k, |
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457 avail=avail, |
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458 weight=weight, |
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459 verbose=verbose, |
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460 max_aug_k=max_aug_k, |
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461 orig_k=orig_k, |
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462 ) |
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463 |
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464 if aug_edges1 is not None: |
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465 # Check approximation ratios |
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466 if k == 1: |
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467 # when k=1, both solutions should be optimal |
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468 assert info2["total_weight"] == info1["total_weight"] |
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469 if k == 2: |
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470 # when k=2, the weighted version is an approximation |
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471 if orig_k == 0: |
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472 # the approximation ratio is 3 if G is not connected |
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473 assert info2["total_weight"] <= info1["total_weight"] * 3 |
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474 else: |
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475 # the approximation ratio is 2 if G is was connected |
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476 assert info2["total_weight"] <= info1["total_weight"] * 2 |
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477 _check_unconstrained_bridge_property(G, info1) |
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478 |
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479 |
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480 def _check_unconstrained_bridge_property(G, info1): |
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481 # Check Theorem 5 from Eswaran and Tarjan. (1975) Augmentation problems |
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482 import math |
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483 |
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484 bridge_ccs = list(nx.connectivity.bridge_components(G)) |
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485 # condense G into an forest C |
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486 C = collapse(G, bridge_ccs) |
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487 |
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488 p = len([n for n, d in C.degree() if d == 1]) # leafs |
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489 q = len([n for n, d in C.degree() if d == 0]) # isolated |
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490 if p + q > 1: |
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491 size_target = int(math.ceil(p / 2.0)) + q |
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492 size_aug = info1["num_edges"] |
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493 assert ( |
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494 size_aug == size_target |
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495 ), "augmentation size is different from what theory predicts" |