Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/flow/tests/test_maxflow.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 """Maximum flow algorithms test suite. |
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2 """ |
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3 import pytest |
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4 |
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5 import networkx as nx |
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6 from networkx.algorithms.flow import build_flow_dict, build_residual_network |
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7 from networkx.algorithms.flow import boykov_kolmogorov |
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8 from networkx.algorithms.flow import edmonds_karp |
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9 from networkx.algorithms.flow import preflow_push |
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10 from networkx.algorithms.flow import shortest_augmenting_path |
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11 from networkx.algorithms.flow import dinitz |
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12 |
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13 flow_funcs = [ |
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14 boykov_kolmogorov, |
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15 dinitz, |
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16 edmonds_karp, |
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17 preflow_push, |
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18 shortest_augmenting_path, |
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19 ] |
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20 max_min_funcs = [nx.maximum_flow, nx.minimum_cut] |
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21 flow_value_funcs = [nx.maximum_flow_value, nx.minimum_cut_value] |
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22 interface_funcs = sum([max_min_funcs, flow_value_funcs], []) |
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23 all_funcs = sum([flow_funcs, interface_funcs], []) |
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24 |
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25 |
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26 def compute_cutset(G, partition): |
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27 reachable, non_reachable = partition |
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28 cutset = set() |
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29 for u, nbrs in ((n, G[n]) for n in reachable): |
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30 cutset.update((u, v) for v in nbrs if v in non_reachable) |
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31 return cutset |
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32 |
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33 |
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34 def validate_flows(G, s, t, flowDict, solnValue, capacity, flow_func): |
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35 errmsg = f"Assertion failed in function: {flow_func.__name__}" |
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36 assert set(G) == set(flowDict), errmsg |
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37 for u in G: |
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38 assert set(G[u]) == set(flowDict[u]), errmsg |
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39 excess = {u: 0 for u in flowDict} |
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40 for u in flowDict: |
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41 for v, flow in flowDict[u].items(): |
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42 if capacity in G[u][v]: |
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43 assert flow <= G[u][v][capacity] |
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44 assert flow >= 0, errmsg |
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45 excess[u] -= flow |
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46 excess[v] += flow |
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47 for u, exc in excess.items(): |
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48 if u == s: |
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49 assert exc == -solnValue, errmsg |
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50 elif u == t: |
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51 assert exc == solnValue, errmsg |
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52 else: |
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53 assert exc == 0, errmsg |
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54 |
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55 |
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56 def validate_cuts(G, s, t, solnValue, partition, capacity, flow_func): |
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57 errmsg = f"Assertion failed in function: {flow_func.__name__}" |
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58 assert all(n in G for n in partition[0]), errmsg |
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59 assert all(n in G for n in partition[1]), errmsg |
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60 cutset = compute_cutset(G, partition) |
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61 assert all(G.has_edge(u, v) for (u, v) in cutset), errmsg |
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62 assert solnValue == sum(G[u][v][capacity] for (u, v) in cutset), errmsg |
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63 H = G.copy() |
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64 H.remove_edges_from(cutset) |
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65 if not G.is_directed(): |
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66 assert not nx.is_connected(H), errmsg |
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67 else: |
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68 assert not nx.is_strongly_connected(H), errmsg |
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69 |
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70 |
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71 def compare_flows_and_cuts(G, s, t, solnFlows, solnValue, capacity="capacity"): |
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72 for flow_func in flow_funcs: |
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73 errmsg = f"Assertion failed in function: {flow_func.__name__}" |
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74 R = flow_func(G, s, t, capacity) |
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75 # Test both legacy and new implementations. |
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76 flow_value = R.graph["flow_value"] |
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77 flow_dict = build_flow_dict(G, R) |
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78 assert flow_value == solnValue, errmsg |
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79 validate_flows(G, s, t, flow_dict, solnValue, capacity, flow_func) |
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80 # Minimum cut |
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81 cut_value, partition = nx.minimum_cut( |
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82 G, s, t, capacity=capacity, flow_func=flow_func |
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83 ) |
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84 validate_cuts(G, s, t, solnValue, partition, capacity, flow_func) |
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85 |
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86 |
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87 class TestMaxflowMinCutCommon: |
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88 def test_graph1(self): |
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89 # Trivial undirected graph |
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90 G = nx.Graph() |
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91 G.add_edge(1, 2, capacity=1.0) |
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92 |
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93 solnFlows = {1: {2: 1.0}, 2: {1: 1.0}} |
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94 |
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95 compare_flows_and_cuts(G, 1, 2, solnFlows, 1.0) |
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96 |
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97 def test_graph2(self): |
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98 # A more complex undirected graph |
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99 # adapted from www.topcoder.com/tc?module=Statc&d1=tutorials&d2=maxFlow |
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100 G = nx.Graph() |
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101 G.add_edge("x", "a", capacity=3.0) |
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102 G.add_edge("x", "b", capacity=1.0) |
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103 G.add_edge("a", "c", capacity=3.0) |
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104 G.add_edge("b", "c", capacity=5.0) |
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105 G.add_edge("b", "d", capacity=4.0) |
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106 G.add_edge("d", "e", capacity=2.0) |
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107 G.add_edge("c", "y", capacity=2.0) |
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108 G.add_edge("e", "y", capacity=3.0) |
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109 |
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110 H = { |
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111 "x": {"a": 3, "b": 1}, |
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112 "a": {"c": 3, "x": 3}, |
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113 "b": {"c": 1, "d": 2, "x": 1}, |
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114 "c": {"a": 3, "b": 1, "y": 2}, |
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115 "d": {"b": 2, "e": 2}, |
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116 "e": {"d": 2, "y": 2}, |
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117 "y": {"c": 2, "e": 2}, |
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118 } |
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119 |
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120 compare_flows_and_cuts(G, "x", "y", H, 4.0) |
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121 |
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122 def test_digraph1(self): |
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123 # The classic directed graph example |
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124 G = nx.DiGraph() |
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125 G.add_edge("a", "b", capacity=1000.0) |
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126 G.add_edge("a", "c", capacity=1000.0) |
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127 G.add_edge("b", "c", capacity=1.0) |
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128 G.add_edge("b", "d", capacity=1000.0) |
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129 G.add_edge("c", "d", capacity=1000.0) |
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130 |
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131 H = { |
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132 "a": {"b": 1000.0, "c": 1000.0}, |
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133 "b": {"c": 0, "d": 1000.0}, |
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134 "c": {"d": 1000.0}, |
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135 "d": {}, |
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136 } |
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137 |
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138 compare_flows_and_cuts(G, "a", "d", H, 2000.0) |
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139 |
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140 def test_digraph2(self): |
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141 # An example in which some edges end up with zero flow. |
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142 G = nx.DiGraph() |
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143 G.add_edge("s", "b", capacity=2) |
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144 G.add_edge("s", "c", capacity=1) |
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145 G.add_edge("c", "d", capacity=1) |
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146 G.add_edge("d", "a", capacity=1) |
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147 G.add_edge("b", "a", capacity=2) |
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148 G.add_edge("a", "t", capacity=2) |
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149 |
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150 H = { |
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151 "s": {"b": 2, "c": 0}, |
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152 "c": {"d": 0}, |
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153 "d": {"a": 0}, |
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154 "b": {"a": 2}, |
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155 "a": {"t": 2}, |
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156 "t": {}, |
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157 } |
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158 |
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159 compare_flows_and_cuts(G, "s", "t", H, 2) |
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160 |
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161 def test_digraph3(self): |
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162 # A directed graph example from Cormen et al. |
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163 G = nx.DiGraph() |
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164 G.add_edge("s", "v1", capacity=16.0) |
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165 G.add_edge("s", "v2", capacity=13.0) |
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166 G.add_edge("v1", "v2", capacity=10.0) |
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167 G.add_edge("v2", "v1", capacity=4.0) |
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168 G.add_edge("v1", "v3", capacity=12.0) |
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169 G.add_edge("v3", "v2", capacity=9.0) |
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170 G.add_edge("v2", "v4", capacity=14.0) |
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171 G.add_edge("v4", "v3", capacity=7.0) |
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172 G.add_edge("v3", "t", capacity=20.0) |
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173 G.add_edge("v4", "t", capacity=4.0) |
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174 |
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175 H = { |
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176 "s": {"v1": 12.0, "v2": 11.0}, |
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177 "v2": {"v1": 0, "v4": 11.0}, |
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178 "v1": {"v2": 0, "v3": 12.0}, |
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179 "v3": {"v2": 0, "t": 19.0}, |
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180 "v4": {"v3": 7.0, "t": 4.0}, |
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181 "t": {}, |
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182 } |
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183 |
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184 compare_flows_and_cuts(G, "s", "t", H, 23.0) |
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185 |
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186 def test_digraph4(self): |
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187 # A more complex directed graph |
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188 # from www.topcoder.com/tc?module=Statc&d1=tutorials&d2=maxFlow |
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189 G = nx.DiGraph() |
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190 G.add_edge("x", "a", capacity=3.0) |
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191 G.add_edge("x", "b", capacity=1.0) |
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192 G.add_edge("a", "c", capacity=3.0) |
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193 G.add_edge("b", "c", capacity=5.0) |
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194 G.add_edge("b", "d", capacity=4.0) |
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195 G.add_edge("d", "e", capacity=2.0) |
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196 G.add_edge("c", "y", capacity=2.0) |
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197 G.add_edge("e", "y", capacity=3.0) |
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198 |
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199 H = { |
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200 "x": {"a": 2.0, "b": 1.0}, |
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201 "a": {"c": 2.0}, |
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202 "b": {"c": 0, "d": 1.0}, |
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203 "c": {"y": 2.0}, |
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204 "d": {"e": 1.0}, |
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205 "e": {"y": 1.0}, |
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206 "y": {}, |
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207 } |
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208 |
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209 compare_flows_and_cuts(G, "x", "y", H, 3.0) |
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210 |
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211 def test_wikipedia_dinitz_example(self): |
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212 # Nice example from https://en.wikipedia.org/wiki/Dinic's_algorithm |
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213 G = nx.DiGraph() |
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214 G.add_edge("s", 1, capacity=10) |
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215 G.add_edge("s", 2, capacity=10) |
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216 G.add_edge(1, 3, capacity=4) |
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217 G.add_edge(1, 4, capacity=8) |
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218 G.add_edge(1, 2, capacity=2) |
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219 G.add_edge(2, 4, capacity=9) |
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220 G.add_edge(3, "t", capacity=10) |
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221 G.add_edge(4, 3, capacity=6) |
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222 G.add_edge(4, "t", capacity=10) |
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223 |
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224 solnFlows = { |
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225 1: {2: 0, 3: 4, 4: 6}, |
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226 2: {4: 9}, |
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227 3: {"t": 9}, |
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228 4: {3: 5, "t": 10}, |
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229 "s": {1: 10, 2: 9}, |
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230 "t": {}, |
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231 } |
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232 |
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233 compare_flows_and_cuts(G, "s", "t", solnFlows, 19) |
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234 |
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235 def test_optional_capacity(self): |
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236 # Test optional capacity parameter. |
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237 G = nx.DiGraph() |
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238 G.add_edge("x", "a", spam=3.0) |
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239 G.add_edge("x", "b", spam=1.0) |
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240 G.add_edge("a", "c", spam=3.0) |
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241 G.add_edge("b", "c", spam=5.0) |
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242 G.add_edge("b", "d", spam=4.0) |
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243 G.add_edge("d", "e", spam=2.0) |
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244 G.add_edge("c", "y", spam=2.0) |
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245 G.add_edge("e", "y", spam=3.0) |
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246 |
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247 solnFlows = { |
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248 "x": {"a": 2.0, "b": 1.0}, |
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249 "a": {"c": 2.0}, |
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250 "b": {"c": 0, "d": 1.0}, |
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251 "c": {"y": 2.0}, |
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252 "d": {"e": 1.0}, |
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253 "e": {"y": 1.0}, |
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254 "y": {}, |
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255 } |
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256 solnValue = 3.0 |
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257 s = "x" |
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258 t = "y" |
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259 |
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260 compare_flows_and_cuts(G, s, t, solnFlows, solnValue, capacity="spam") |
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261 |
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262 def test_digraph_infcap_edges(self): |
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263 # DiGraph with infinite capacity edges |
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264 G = nx.DiGraph() |
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265 G.add_edge("s", "a") |
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266 G.add_edge("s", "b", capacity=30) |
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267 G.add_edge("a", "c", capacity=25) |
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268 G.add_edge("b", "c", capacity=12) |
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269 G.add_edge("a", "t", capacity=60) |
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270 G.add_edge("c", "t") |
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271 |
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272 H = { |
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273 "s": {"a": 85, "b": 12}, |
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274 "a": {"c": 25, "t": 60}, |
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275 "b": {"c": 12}, |
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276 "c": {"t": 37}, |
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277 "t": {}, |
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278 } |
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279 |
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280 compare_flows_and_cuts(G, "s", "t", H, 97) |
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281 |
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282 # DiGraph with infinite capacity digon |
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283 G = nx.DiGraph() |
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284 G.add_edge("s", "a", capacity=85) |
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285 G.add_edge("s", "b", capacity=30) |
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286 G.add_edge("a", "c") |
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287 G.add_edge("c", "a") |
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288 G.add_edge("b", "c", capacity=12) |
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289 G.add_edge("a", "t", capacity=60) |
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290 G.add_edge("c", "t", capacity=37) |
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291 |
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292 H = { |
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293 "s": {"a": 85, "b": 12}, |
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294 "a": {"c": 25, "t": 60}, |
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295 "c": {"a": 0, "t": 37}, |
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296 "b": {"c": 12}, |
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297 "t": {}, |
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298 } |
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299 |
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300 compare_flows_and_cuts(G, "s", "t", H, 97) |
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301 |
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302 def test_digraph_infcap_path(self): |
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303 # Graph with infinite capacity (s, t)-path |
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304 G = nx.DiGraph() |
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305 G.add_edge("s", "a") |
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306 G.add_edge("s", "b", capacity=30) |
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307 G.add_edge("a", "c") |
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308 G.add_edge("b", "c", capacity=12) |
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309 G.add_edge("a", "t", capacity=60) |
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310 G.add_edge("c", "t") |
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311 |
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312 for flow_func in all_funcs: |
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313 pytest.raises(nx.NetworkXUnbounded, flow_func, G, "s", "t") |
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314 |
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315 def test_graph_infcap_edges(self): |
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316 # Undirected graph with infinite capacity edges |
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317 G = nx.Graph() |
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318 G.add_edge("s", "a") |
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319 G.add_edge("s", "b", capacity=30) |
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320 G.add_edge("a", "c", capacity=25) |
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321 G.add_edge("b", "c", capacity=12) |
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322 G.add_edge("a", "t", capacity=60) |
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323 G.add_edge("c", "t") |
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324 |
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325 H = { |
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326 "s": {"a": 85, "b": 12}, |
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327 "a": {"c": 25, "s": 85, "t": 60}, |
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328 "b": {"c": 12, "s": 12}, |
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329 "c": {"a": 25, "b": 12, "t": 37}, |
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330 "t": {"a": 60, "c": 37}, |
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331 } |
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332 |
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333 compare_flows_and_cuts(G, "s", "t", H, 97) |
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334 |
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335 def test_digraph5(self): |
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336 # From ticket #429 by mfrasca. |
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337 G = nx.DiGraph() |
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338 G.add_edge("s", "a", capacity=2) |
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339 G.add_edge("s", "b", capacity=2) |
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340 G.add_edge("a", "b", capacity=5) |
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341 G.add_edge("a", "t", capacity=1) |
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342 G.add_edge("b", "a", capacity=1) |
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343 G.add_edge("b", "t", capacity=3) |
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344 flowSoln = { |
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345 "a": {"b": 1, "t": 1}, |
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346 "b": {"a": 0, "t": 3}, |
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347 "s": {"a": 2, "b": 2}, |
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348 "t": {}, |
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349 } |
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350 compare_flows_and_cuts(G, "s", "t", flowSoln, 4) |
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351 |
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352 def test_disconnected(self): |
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353 G = nx.Graph() |
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354 G.add_weighted_edges_from([(0, 1, 1), (1, 2, 1), (2, 3, 1)], weight="capacity") |
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355 G.remove_node(1) |
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356 assert nx.maximum_flow_value(G, 0, 3) == 0 |
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357 flowSoln = {0: {}, 2: {3: 0}, 3: {2: 0}} |
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358 compare_flows_and_cuts(G, 0, 3, flowSoln, 0) |
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359 |
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360 def test_source_target_not_in_graph(self): |
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361 G = nx.Graph() |
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362 G.add_weighted_edges_from([(0, 1, 1), (1, 2, 1), (2, 3, 1)], weight="capacity") |
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363 G.remove_node(0) |
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364 for flow_func in all_funcs: |
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365 pytest.raises(nx.NetworkXError, flow_func, G, 0, 3) |
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366 G.add_weighted_edges_from([(0, 1, 1), (1, 2, 1), (2, 3, 1)], weight="capacity") |
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367 G.remove_node(3) |
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368 for flow_func in all_funcs: |
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369 pytest.raises(nx.NetworkXError, flow_func, G, 0, 3) |
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370 |
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371 def test_source_target_coincide(self): |
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372 G = nx.Graph() |
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373 G.add_node(0) |
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374 for flow_func in all_funcs: |
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375 pytest.raises(nx.NetworkXError, flow_func, G, 0, 0) |
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376 |
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377 def test_multigraphs_raise(self): |
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378 G = nx.MultiGraph() |
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379 M = nx.MultiDiGraph() |
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380 G.add_edges_from([(0, 1), (1, 0)], capacity=True) |
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381 for flow_func in all_funcs: |
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382 pytest.raises(nx.NetworkXError, flow_func, G, 0, 0) |
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383 |
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384 |
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385 class TestMaxFlowMinCutInterface: |
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386 def setup(self): |
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387 G = nx.DiGraph() |
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388 G.add_edge("x", "a", capacity=3.0) |
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389 G.add_edge("x", "b", capacity=1.0) |
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390 G.add_edge("a", "c", capacity=3.0) |
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391 G.add_edge("b", "c", capacity=5.0) |
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392 G.add_edge("b", "d", capacity=4.0) |
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393 G.add_edge("d", "e", capacity=2.0) |
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394 G.add_edge("c", "y", capacity=2.0) |
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395 G.add_edge("e", "y", capacity=3.0) |
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396 self.G = G |
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397 H = nx.DiGraph() |
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398 H.add_edge(0, 1, capacity=1.0) |
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399 H.add_edge(1, 2, capacity=1.0) |
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400 self.H = H |
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401 |
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402 def test_flow_func_not_callable(self): |
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403 elements = ["this_should_be_callable", 10, {1, 2, 3}] |
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404 G = nx.Graph() |
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405 G.add_weighted_edges_from([(0, 1, 1), (1, 2, 1), (2, 3, 1)], weight="capacity") |
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406 for flow_func in interface_funcs: |
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407 for element in elements: |
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408 pytest.raises(nx.NetworkXError, flow_func, G, 0, 1, flow_func=element) |
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409 pytest.raises(nx.NetworkXError, flow_func, G, 0, 1, flow_func=element) |
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410 |
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411 def test_flow_func_parameters(self): |
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412 G = self.G |
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413 fv = 3.0 |
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414 for interface_func in interface_funcs: |
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415 for flow_func in flow_funcs: |
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416 errmsg = ( |
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417 f"Assertion failed in function: {flow_func.__name__} " |
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418 f"in interface {interface_func.__name__}" |
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419 ) |
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420 result = interface_func(G, "x", "y", flow_func=flow_func) |
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421 if interface_func in max_min_funcs: |
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422 result = result[0] |
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423 assert fv == result, errmsg |
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424 |
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425 def test_minimum_cut_no_cutoff(self): |
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426 G = self.G |
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427 for flow_func in flow_funcs: |
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428 pytest.raises( |
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429 nx.NetworkXError, |
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430 nx.minimum_cut, |
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431 G, |
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432 "x", |
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433 "y", |
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434 flow_func=flow_func, |
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435 cutoff=1.0, |
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436 ) |
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437 pytest.raises( |
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438 nx.NetworkXError, |
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439 nx.minimum_cut_value, |
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440 G, |
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441 "x", |
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442 "y", |
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443 flow_func=flow_func, |
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444 cutoff=1.0, |
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445 ) |
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446 |
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447 def test_kwargs(self): |
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448 G = self.H |
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449 fv = 1.0 |
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450 to_test = ( |
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451 (shortest_augmenting_path, dict(two_phase=True)), |
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452 (preflow_push, dict(global_relabel_freq=5)), |
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453 ) |
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454 for interface_func in interface_funcs: |
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455 for flow_func, kwargs in to_test: |
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456 errmsg = ( |
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457 f"Assertion failed in function: {flow_func.__name__} " |
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458 f"in interface {interface_func.__name__}" |
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459 ) |
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460 result = interface_func(G, 0, 2, flow_func=flow_func, **kwargs) |
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461 if interface_func in max_min_funcs: |
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462 result = result[0] |
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463 assert fv == result, errmsg |
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464 |
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465 def test_kwargs_default_flow_func(self): |
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466 G = self.H |
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467 for interface_func in interface_funcs: |
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468 pytest.raises( |
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469 nx.NetworkXError, interface_func, G, 0, 1, global_relabel_freq=2 |
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470 ) |
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471 |
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472 def test_reusing_residual(self): |
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473 G = self.G |
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474 fv = 3.0 |
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475 s, t = "x", "y" |
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476 R = build_residual_network(G, "capacity") |
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477 for interface_func in interface_funcs: |
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478 for flow_func in flow_funcs: |
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479 errmsg = ( |
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480 f"Assertion failed in function: {flow_func.__name__} " |
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481 f"in interface {interface_func.__name__}" |
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482 ) |
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483 for i in range(3): |
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484 result = interface_func( |
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485 G, "x", "y", flow_func=flow_func, residual=R |
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486 ) |
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487 if interface_func in max_min_funcs: |
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488 result = result[0] |
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489 assert fv == result, errmsg |
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490 |
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491 |
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492 # Tests specific to one algorithm |
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493 def test_preflow_push_global_relabel_freq(): |
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494 G = nx.DiGraph() |
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495 G.add_edge(1, 2, capacity=1) |
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496 R = preflow_push(G, 1, 2, global_relabel_freq=None) |
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497 assert R.graph["flow_value"] == 1 |
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498 pytest.raises(nx.NetworkXError, preflow_push, G, 1, 2, global_relabel_freq=-1) |
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499 |
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500 |
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501 def test_preflow_push_makes_enough_space(): |
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502 # From ticket #1542 |
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503 G = nx.DiGraph() |
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504 nx.add_path(G, [0, 1, 3], capacity=1) |
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505 nx.add_path(G, [1, 2, 3], capacity=1) |
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506 R = preflow_push(G, 0, 3, value_only=False) |
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507 assert R.graph["flow_value"] == 1 |
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508 |
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509 |
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510 def test_shortest_augmenting_path_two_phase(): |
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511 k = 5 |
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512 p = 1000 |
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513 G = nx.DiGraph() |
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514 for i in range(k): |
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515 G.add_edge("s", (i, 0), capacity=1) |
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516 nx.add_path(G, ((i, j) for j in range(p)), capacity=1) |
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517 G.add_edge((i, p - 1), "t", capacity=1) |
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518 R = shortest_augmenting_path(G, "s", "t", two_phase=True) |
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519 assert R.graph["flow_value"] == k |
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520 R = shortest_augmenting_path(G, "s", "t", two_phase=False) |
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521 assert R.graph["flow_value"] == k |
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522 |
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523 |
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524 class TestCutoff: |
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525 def test_cutoff(self): |
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526 k = 5 |
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527 p = 1000 |
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528 G = nx.DiGraph() |
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529 for i in range(k): |
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530 G.add_edge("s", (i, 0), capacity=2) |
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531 nx.add_path(G, ((i, j) for j in range(p)), capacity=2) |
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532 G.add_edge((i, p - 1), "t", capacity=2) |
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533 R = shortest_augmenting_path(G, "s", "t", two_phase=True, cutoff=k) |
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534 assert k <= R.graph["flow_value"] <= (2 * k) |
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535 R = shortest_augmenting_path(G, "s", "t", two_phase=False, cutoff=k) |
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536 assert k <= R.graph["flow_value"] <= (2 * k) |
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537 R = edmonds_karp(G, "s", "t", cutoff=k) |
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538 assert k <= R.graph["flow_value"] <= (2 * k) |
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539 |
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540 def test_complete_graph_cutoff(self): |
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541 G = nx.complete_graph(5) |
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542 nx.set_edge_attributes(G, {(u, v): 1 for u, v in G.edges()}, "capacity") |
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543 for flow_func in [shortest_augmenting_path, edmonds_karp]: |
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544 for cutoff in [3, 2, 1]: |
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545 result = nx.maximum_flow_value( |
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546 G, 0, 4, flow_func=flow_func, cutoff=cutoff |
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547 ) |
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548 assert cutoff == result, f"cutoff error in {flow_func.__name__}" |