Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/isomorphism/isomorphvf2.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 """ |
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2 ************* |
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3 VF2 Algorithm |
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4 ************* |
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5 |
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6 An implementation of VF2 algorithm for graph ismorphism testing. |
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7 |
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8 The simplest interface to use this module is to call networkx.is_isomorphic(). |
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9 |
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10 Introduction |
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11 ------------ |
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12 |
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13 The GraphMatcher and DiGraphMatcher are responsible for matching |
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14 graphs or directed graphs in a predetermined manner. This |
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15 usually means a check for an isomorphism, though other checks |
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16 are also possible. For example, a subgraph of one graph |
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17 can be checked for isomorphism to a second graph. |
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18 |
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19 Matching is done via syntactic feasibility. It is also possible |
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20 to check for semantic feasibility. Feasibility, then, is defined |
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21 as the logical AND of the two functions. |
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22 |
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23 To include a semantic check, the (Di)GraphMatcher class should be |
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24 subclassed, and the semantic_feasibility() function should be |
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25 redefined. By default, the semantic feasibility function always |
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26 returns True. The effect of this is that semantics are not |
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27 considered in the matching of G1 and G2. |
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28 |
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29 Examples |
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30 -------- |
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31 |
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32 Suppose G1 and G2 are isomorphic graphs. Verification is as follows: |
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33 |
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34 >>> from networkx.algorithms import isomorphism |
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35 >>> G1 = nx.path_graph(4) |
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36 >>> G2 = nx.path_graph(4) |
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37 >>> GM = isomorphism.GraphMatcher(G1, G2) |
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38 >>> GM.is_isomorphic() |
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39 True |
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40 |
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41 GM.mapping stores the isomorphism mapping from G1 to G2. |
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42 |
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43 >>> GM.mapping |
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44 {0: 0, 1: 1, 2: 2, 3: 3} |
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45 |
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46 |
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47 Suppose G1 and G2 are isomorphic directed graphs |
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48 graphs. Verification is as follows: |
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49 |
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50 >>> G1 = nx.path_graph(4, create_using=nx.DiGraph()) |
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51 >>> G2 = nx.path_graph(4, create_using=nx.DiGraph()) |
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52 >>> DiGM = isomorphism.DiGraphMatcher(G1, G2) |
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53 >>> DiGM.is_isomorphic() |
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54 True |
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55 |
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56 DiGM.mapping stores the isomorphism mapping from G1 to G2. |
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57 |
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58 >>> DiGM.mapping |
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59 {0: 0, 1: 1, 2: 2, 3: 3} |
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60 |
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61 |
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62 |
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63 Subgraph Isomorphism |
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64 -------------------- |
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65 Graph theory literature can be ambiguous about the meaning of the |
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66 above statement, and we seek to clarify it now. |
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67 |
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68 In the VF2 literature, a mapping M is said to be a graph-subgraph |
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69 isomorphism iff M is an isomorphism between G2 and a subgraph of G1. |
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70 Thus, to say that G1 and G2 are graph-subgraph isomorphic is to say |
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71 that a subgraph of G1 is isomorphic to G2. |
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72 |
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73 Other literature uses the phrase 'subgraph isomorphic' as in 'G1 does |
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74 not have a subgraph isomorphic to G2'. Another use is as an in adverb |
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75 for isomorphic. Thus, to say that G1 and G2 are subgraph isomorphic |
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76 is to say that a subgraph of G1 is isomorphic to G2. |
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77 |
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78 Finally, the term 'subgraph' can have multiple meanings. In this |
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79 context, 'subgraph' always means a 'node-induced subgraph'. Edge-induced |
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80 subgraph isomorphisms are not directly supported, but one should be |
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81 able to perform the check by making use of nx.line_graph(). For |
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82 subgraphs which are not induced, the term 'monomorphism' is preferred |
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83 over 'isomorphism'. |
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84 |
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85 Let G=(N,E) be a graph with a set of nodes N and set of edges E. |
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86 |
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87 If G'=(N',E') is a subgraph, then: |
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88 N' is a subset of N |
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89 E' is a subset of E |
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90 |
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91 If G'=(N',E') is a node-induced subgraph, then: |
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92 N' is a subset of N |
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93 E' is the subset of edges in E relating nodes in N' |
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94 |
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95 If G'=(N',E') is an edge-induced subgraph, then: |
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96 N' is the subset of nodes in N related by edges in E' |
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97 E' is a subset of E |
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98 |
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99 If G'=(N',E') is a monomorphism, then: |
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100 N' is a subset of N |
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101 E' is a subset of the set of edges in E relating nodes in N' |
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102 |
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103 Note that if G' is a node-induced subgraph of G, then it is always a |
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104 subgraph monomorphism of G, but the opposite is not always true, as a |
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105 monomorphism can have fewer edges. |
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106 |
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107 References |
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108 ---------- |
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109 [1] Luigi P. Cordella, Pasquale Foggia, Carlo Sansone, Mario Vento, |
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110 "A (Sub)Graph Isomorphism Algorithm for Matching Large Graphs", |
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111 IEEE Transactions on Pattern Analysis and Machine Intelligence, |
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112 vol. 26, no. 10, pp. 1367-1372, Oct., 2004. |
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113 http://ieeexplore.ieee.org/iel5/34/29305/01323804.pdf |
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114 |
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115 [2] L. P. Cordella, P. Foggia, C. Sansone, M. Vento, "An Improved |
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116 Algorithm for Matching Large Graphs", 3rd IAPR-TC15 Workshop |
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117 on Graph-based Representations in Pattern Recognition, Cuen, |
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118 pp. 149-159, 2001. |
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119 http://amalfi.dis.unina.it/graph/db/papers/vf-algorithm.pdf |
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120 |
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121 See Also |
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122 -------- |
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123 syntactic_feasibility(), semantic_feasibility() |
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124 |
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125 Notes |
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126 ----- |
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127 |
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128 The implementation handles both directed and undirected graphs as well |
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129 as multigraphs. |
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130 |
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131 In general, the subgraph isomorphism problem is NP-complete whereas the |
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132 graph isomorphism problem is most likely not NP-complete (although no |
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133 polynomial-time algorithm is known to exist). |
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134 |
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135 """ |
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136 |
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137 # This work was originally coded by Christopher Ellison |
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138 # as part of the Computational Mechanics Python (CMPy) project. |
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139 # James P. Crutchfield, principal investigator. |
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140 # Complexity Sciences Center and Physics Department, UC Davis. |
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141 |
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142 import sys |
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143 |
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144 __all__ = ["GraphMatcher", "DiGraphMatcher"] |
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145 |
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146 |
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147 class GraphMatcher: |
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148 """Implementation of VF2 algorithm for matching undirected graphs. |
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149 |
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150 Suitable for Graph and MultiGraph instances. |
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151 """ |
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152 |
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153 def __init__(self, G1, G2): |
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154 """Initialize GraphMatcher. |
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155 |
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156 Parameters |
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157 ---------- |
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158 G1,G2: NetworkX Graph or MultiGraph instances. |
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159 The two graphs to check for isomorphism or monomorphism. |
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160 |
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161 Examples |
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162 -------- |
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163 To create a GraphMatcher which checks for syntactic feasibility: |
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164 |
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165 >>> from networkx.algorithms import isomorphism |
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166 >>> G1 = nx.path_graph(4) |
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167 >>> G2 = nx.path_graph(4) |
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168 >>> GM = isomorphism.GraphMatcher(G1, G2) |
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169 """ |
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170 self.G1 = G1 |
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171 self.G2 = G2 |
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172 self.G1_nodes = set(G1.nodes()) |
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173 self.G2_nodes = set(G2.nodes()) |
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174 self.G2_node_order = {n: i for i, n in enumerate(G2)} |
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175 |
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176 # Set recursion limit. |
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177 self.old_recursion_limit = sys.getrecursionlimit() |
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178 expected_max_recursion_level = len(self.G2) |
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179 if self.old_recursion_limit < 1.5 * expected_max_recursion_level: |
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180 # Give some breathing room. |
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181 sys.setrecursionlimit(int(1.5 * expected_max_recursion_level)) |
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182 |
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183 # Declare that we will be searching for a graph-graph isomorphism. |
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184 self.test = "graph" |
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185 |
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186 # Initialize state |
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187 self.initialize() |
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188 |
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189 def reset_recursion_limit(self): |
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190 """Restores the recursion limit.""" |
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191 # TODO: |
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192 # Currently, we use recursion and set the recursion level higher. |
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193 # It would be nice to restore the level, but because the |
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194 # (Di)GraphMatcher classes make use of cyclic references, garbage |
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195 # collection will never happen when we define __del__() to |
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196 # restore the recursion level. The result is a memory leak. |
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197 # So for now, we do not automatically restore the recursion level, |
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198 # and instead provide a method to do this manually. Eventually, |
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199 # we should turn this into a non-recursive implementation. |
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200 sys.setrecursionlimit(self.old_recursion_limit) |
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201 |
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202 def candidate_pairs_iter(self): |
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203 """Iterator over candidate pairs of nodes in G1 and G2.""" |
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204 |
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205 # All computations are done using the current state! |
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206 |
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207 G1_nodes = self.G1_nodes |
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208 G2_nodes = self.G2_nodes |
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209 min_key = self.G2_node_order.__getitem__ |
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210 |
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211 # First we compute the inout-terminal sets. |
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212 T1_inout = [node for node in self.inout_1 if node not in self.core_1] |
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213 T2_inout = [node for node in self.inout_2 if node not in self.core_2] |
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214 |
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215 # If T1_inout and T2_inout are both nonempty. |
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216 # P(s) = T1_inout x {min T2_inout} |
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217 if T1_inout and T2_inout: |
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218 node_2 = min(T2_inout, key=min_key) |
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219 for node_1 in T1_inout: |
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220 yield node_1, node_2 |
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221 |
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222 else: |
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223 # If T1_inout and T2_inout were both empty.... |
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224 # P(s) = (N_1 - M_1) x {min (N_2 - M_2)} |
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225 # if not (T1_inout or T2_inout): # as suggested by [2], incorrect |
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226 if 1: # as inferred from [1], correct |
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227 # First we determine the candidate node for G2 |
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228 other_node = min(G2_nodes - set(self.core_2), key=min_key) |
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229 for node in self.G1: |
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230 if node not in self.core_1: |
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231 yield node, other_node |
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232 |
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233 # For all other cases, we don't have any candidate pairs. |
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234 |
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235 def initialize(self): |
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236 """Reinitializes the state of the algorithm. |
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237 |
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238 This method should be redefined if using something other than GMState. |
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239 If only subclassing GraphMatcher, a redefinition is not necessary. |
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240 |
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241 """ |
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242 |
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243 # core_1[n] contains the index of the node paired with n, which is m, |
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244 # provided n is in the mapping. |
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245 # core_2[m] contains the index of the node paired with m, which is n, |
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246 # provided m is in the mapping. |
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247 self.core_1 = {} |
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248 self.core_2 = {} |
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249 |
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250 # See the paper for definitions of M_x and T_x^{y} |
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251 |
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252 # inout_1[n] is non-zero if n is in M_1 or in T_1^{inout} |
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253 # inout_2[m] is non-zero if m is in M_2 or in T_2^{inout} |
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254 # |
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255 # The value stored is the depth of the SSR tree when the node became |
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256 # part of the corresponding set. |
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257 self.inout_1 = {} |
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258 self.inout_2 = {} |
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259 # Practically, these sets simply store the nodes in the subgraph. |
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260 |
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261 self.state = GMState(self) |
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262 |
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263 # Provide a convenient way to access the isomorphism mapping. |
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264 self.mapping = self.core_1.copy() |
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265 |
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266 def is_isomorphic(self): |
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267 """Returns True if G1 and G2 are isomorphic graphs.""" |
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268 |
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269 # Let's do two very quick checks! |
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270 # QUESTION: Should we call faster_graph_could_be_isomorphic(G1,G2)? |
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271 # For now, I just copy the code. |
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272 |
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273 # Check global properties |
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274 if self.G1.order() != self.G2.order(): |
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275 return False |
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276 |
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277 # Check local properties |
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278 d1 = sorted(d for n, d in self.G1.degree()) |
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279 d2 = sorted(d for n, d in self.G2.degree()) |
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280 if d1 != d2: |
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281 return False |
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282 |
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283 try: |
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284 x = next(self.isomorphisms_iter()) |
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285 return True |
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286 except StopIteration: |
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287 return False |
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288 |
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289 def isomorphisms_iter(self): |
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290 """Generator over isomorphisms between G1 and G2.""" |
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291 # Declare that we are looking for a graph-graph isomorphism. |
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292 self.test = "graph" |
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293 self.initialize() |
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294 yield from self.match() |
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295 |
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296 def match(self): |
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297 """Extends the isomorphism mapping. |
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298 |
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299 This function is called recursively to determine if a complete |
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300 isomorphism can be found between G1 and G2. It cleans up the class |
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301 variables after each recursive call. If an isomorphism is found, |
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302 we yield the mapping. |
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303 |
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304 """ |
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305 if len(self.core_1) == len(self.G2): |
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306 # Save the final mapping, otherwise garbage collection deletes it. |
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307 self.mapping = self.core_1.copy() |
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308 # The mapping is complete. |
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309 yield self.mapping |
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310 else: |
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311 for G1_node, G2_node in self.candidate_pairs_iter(): |
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312 if self.syntactic_feasibility(G1_node, G2_node): |
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313 if self.semantic_feasibility(G1_node, G2_node): |
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314 # Recursive call, adding the feasible state. |
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315 newstate = self.state.__class__(self, G1_node, G2_node) |
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316 yield from self.match() |
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317 |
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318 # restore data structures |
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319 newstate.restore() |
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320 |
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321 def semantic_feasibility(self, G1_node, G2_node): |
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322 """Returns True if adding (G1_node, G2_node) is symantically feasible. |
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323 |
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324 The semantic feasibility function should return True if it is |
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325 acceptable to add the candidate pair (G1_node, G2_node) to the current |
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326 partial isomorphism mapping. The logic should focus on semantic |
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327 information contained in the edge data or a formalized node class. |
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328 |
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329 By acceptable, we mean that the subsequent mapping can still become a |
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330 complete isomorphism mapping. Thus, if adding the candidate pair |
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331 definitely makes it so that the subsequent mapping cannot become a |
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332 complete isomorphism mapping, then this function must return False. |
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333 |
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334 The default semantic feasibility function always returns True. The |
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335 effect is that semantics are not considered in the matching of G1 |
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336 and G2. |
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337 |
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338 The semantic checks might differ based on the what type of test is |
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339 being performed. A keyword description of the test is stored in |
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340 self.test. Here is a quick description of the currently implemented |
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341 tests:: |
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342 |
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343 test='graph' |
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344 Indicates that the graph matcher is looking for a graph-graph |
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345 isomorphism. |
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346 |
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347 test='subgraph' |
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348 Indicates that the graph matcher is looking for a subgraph-graph |
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349 isomorphism such that a subgraph of G1 is isomorphic to G2. |
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350 |
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351 test='mono' |
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352 Indicates that the graph matcher is looking for a subgraph-graph |
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353 monomorphism such that a subgraph of G1 is monomorphic to G2. |
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354 |
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355 Any subclass which redefines semantic_feasibility() must maintain |
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356 the above form to keep the match() method functional. Implementations |
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357 should consider multigraphs. |
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358 """ |
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359 return True |
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360 |
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361 def subgraph_is_isomorphic(self): |
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362 """Returns True if a subgraph of G1 is isomorphic to G2.""" |
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363 try: |
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364 x = next(self.subgraph_isomorphisms_iter()) |
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365 return True |
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366 except StopIteration: |
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367 return False |
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368 |
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369 def subgraph_is_monomorphic(self): |
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370 """Returns True if a subgraph of G1 is monomorphic to G2.""" |
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371 try: |
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372 x = next(self.subgraph_monomorphisms_iter()) |
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373 return True |
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374 except StopIteration: |
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375 return False |
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376 |
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377 # subgraph_is_isomorphic.__doc__ += "\n" + subgraph.replace('\n','\n'+indent) |
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378 |
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379 def subgraph_isomorphisms_iter(self): |
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380 """Generator over isomorphisms between a subgraph of G1 and G2.""" |
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381 # Declare that we are looking for graph-subgraph isomorphism. |
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382 self.test = "subgraph" |
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383 self.initialize() |
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384 yield from self.match() |
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385 |
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386 def subgraph_monomorphisms_iter(self): |
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387 """Generator over monomorphisms between a subgraph of G1 and G2.""" |
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388 # Declare that we are looking for graph-subgraph monomorphism. |
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389 self.test = "mono" |
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390 self.initialize() |
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391 yield from self.match() |
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392 |
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393 # subgraph_isomorphisms_iter.__doc__ += "\n" + subgraph.replace('\n','\n'+indent) |
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394 |
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395 def syntactic_feasibility(self, G1_node, G2_node): |
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396 """Returns True if adding (G1_node, G2_node) is syntactically feasible. |
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397 |
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398 This function returns True if it is adding the candidate pair |
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399 to the current partial isomorphism/monomorphism mapping is allowable. |
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400 The addition is allowable if the inclusion of the candidate pair does |
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401 not make it impossible for an isomorphism/monomorphism to be found. |
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402 """ |
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403 |
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404 # The VF2 algorithm was designed to work with graphs having, at most, |
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405 # one edge connecting any two nodes. This is not the case when |
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406 # dealing with an MultiGraphs. |
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407 # |
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408 # Basically, when we test the look-ahead rules R_neighbor, we will |
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409 # make sure that the number of edges are checked. We also add |
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410 # a R_self check to verify that the number of selfloops is acceptable. |
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411 # |
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412 # Users might be comparing Graph instances with MultiGraph instances. |
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413 # So the generic GraphMatcher class must work with MultiGraphs. |
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414 # Care must be taken since the value in the innermost dictionary is a |
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415 # singlet for Graph instances. For MultiGraphs, the value in the |
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416 # innermost dictionary is a list. |
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417 |
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418 ### |
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419 # Test at each step to get a return value as soon as possible. |
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420 ### |
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421 |
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422 # Look ahead 0 |
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423 |
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424 # R_self |
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425 |
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426 # The number of selfloops for G1_node must equal the number of |
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427 # self-loops for G2_node. Without this check, we would fail on |
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428 # R_neighbor at the next recursion level. But it is good to prune the |
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429 # search tree now. |
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430 |
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431 if self.test == "mono": |
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432 if self.G1.number_of_edges(G1_node, G1_node) < self.G2.number_of_edges( |
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433 G2_node, G2_node |
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434 ): |
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435 return False |
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436 else: |
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437 if self.G1.number_of_edges(G1_node, G1_node) != self.G2.number_of_edges( |
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438 G2_node, G2_node |
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439 ): |
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440 return False |
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441 |
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442 # R_neighbor |
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443 |
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444 # For each neighbor n' of n in the partial mapping, the corresponding |
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445 # node m' is a neighbor of m, and vice versa. Also, the number of |
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446 # edges must be equal. |
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447 if self.test != "mono": |
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changeset
|
448 for neighbor in self.G1[G1_node]: |
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parents:
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449 if neighbor in self.core_1: |
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parents:
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450 if not (self.core_1[neighbor] in self.G2[G2_node]): |
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parents:
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451 return False |
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parents:
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452 elif self.G1.number_of_edges( |
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parents:
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453 neighbor, G1_node |
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parents:
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454 ) != self.G2.number_of_edges(self.core_1[neighbor], G2_node): |
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parents:
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455 return False |
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parents:
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456 |
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parents:
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changeset
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457 for neighbor in self.G2[G2_node]: |
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parents:
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458 if neighbor in self.core_2: |
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parents:
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459 if not (self.core_2[neighbor] in self.G1[G1_node]): |
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parents:
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460 return False |
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parents:
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461 elif self.test == "mono": |
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parents:
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462 if self.G1.number_of_edges( |
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parents:
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463 self.core_2[neighbor], G1_node |
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464 ) < self.G2.number_of_edges(neighbor, G2_node): |
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465 return False |
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466 else: |
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467 if self.G1.number_of_edges( |
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468 self.core_2[neighbor], G1_node |
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469 ) != self.G2.number_of_edges(neighbor, G2_node): |
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parents:
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470 return False |
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parents:
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471 |
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parents:
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472 if self.test != "mono": |
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473 # Look ahead 1 |
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474 |
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parents:
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475 # R_terminout |
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476 # The number of neighbors of n in T_1^{inout} is equal to the |
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477 # number of neighbors of m that are in T_2^{inout}, and vice versa. |
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478 num1 = 0 |
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479 for neighbor in self.G1[G1_node]: |
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480 if (neighbor in self.inout_1) and (neighbor not in self.core_1): |
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481 num1 += 1 |
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482 num2 = 0 |
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483 for neighbor in self.G2[G2_node]: |
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parents:
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484 if (neighbor in self.inout_2) and (neighbor not in self.core_2): |
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parents:
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485 num2 += 1 |
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486 if self.test == "graph": |
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487 if not (num1 == num2): |
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488 return False |
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489 else: # self.test == 'subgraph' |
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490 if not (num1 >= num2): |
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491 return False |
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parents:
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492 |
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parents:
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493 # Look ahead 2 |
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494 |
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parents:
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495 # R_new |
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496 |
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497 # The number of neighbors of n that are neither in the core_1 nor |
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498 # T_1^{inout} is equal to the number of neighbors of m |
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499 # that are neither in core_2 nor T_2^{inout}. |
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500 num1 = 0 |
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501 for neighbor in self.G1[G1_node]: |
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parents:
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502 if neighbor not in self.inout_1: |
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parents:
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503 num1 += 1 |
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parents:
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504 num2 = 0 |
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505 for neighbor in self.G2[G2_node]: |
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parents:
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506 if neighbor not in self.inout_2: |
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parents:
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507 num2 += 1 |
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parents:
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508 if self.test == "graph": |
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parents:
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509 if not (num1 == num2): |
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parents:
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510 return False |
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parents:
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511 else: # self.test == 'subgraph' |
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512 if not (num1 >= num2): |
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parents:
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513 return False |
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shellac
parents:
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changeset
|
514 |
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parents:
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515 # Otherwise, this node pair is syntactically feasible! |
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parents:
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|
516 return True |
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shellac
parents:
diff
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|
517 |
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shellac
parents:
diff
changeset
|
518 |
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parents:
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|
519 class DiGraphMatcher(GraphMatcher): |
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parents:
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520 """Implementation of VF2 algorithm for matching directed graphs. |
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parents:
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521 |
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parents:
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522 Suitable for DiGraph and MultiDiGraph instances. |
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parents:
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523 """ |
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shellac
parents:
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|
524 |
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parents:
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525 def __init__(self, G1, G2): |
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parents:
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526 """Initialize DiGraphMatcher. |
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shellac
parents:
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527 |
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shellac
parents:
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528 G1 and G2 should be nx.Graph or nx.MultiGraph instances. |
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shellac
parents:
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529 |
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parents:
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530 Examples |
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shellac
parents:
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|
531 -------- |
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parents:
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changeset
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532 To create a GraphMatcher which checks for syntactic feasibility: |
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shellac
parents:
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533 |
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shellac
parents:
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534 >>> from networkx.algorithms import isomorphism |
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parents:
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535 >>> G1 = nx.DiGraph(nx.path_graph(4, create_using=nx.DiGraph())) |
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shellac
parents:
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536 >>> G2 = nx.DiGraph(nx.path_graph(4, create_using=nx.DiGraph())) |
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shellac
parents:
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537 >>> DiGM = isomorphism.DiGraphMatcher(G1, G2) |
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shellac
parents:
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538 """ |
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shellac
parents:
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changeset
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539 super().__init__(G1, G2) |
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shellac
parents:
diff
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540 |
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shellac
parents:
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changeset
|
541 def candidate_pairs_iter(self): |
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shellac
parents:
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542 """Iterator over candidate pairs of nodes in G1 and G2.""" |
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shellac
parents:
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543 |
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shellac
parents:
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544 # All computations are done using the current state! |
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shellac
parents:
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545 |
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shellac
parents:
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changeset
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546 G1_nodes = self.G1_nodes |
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shellac
parents:
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547 G2_nodes = self.G2_nodes |
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shellac
parents:
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548 min_key = self.G2_node_order.__getitem__ |
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shellac
parents:
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changeset
|
549 |
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shellac
parents:
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changeset
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550 # First we compute the out-terminal sets. |
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shellac
parents:
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551 T1_out = [node for node in self.out_1 if node not in self.core_1] |
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shellac
parents:
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552 T2_out = [node for node in self.out_2 if node not in self.core_2] |
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shellac
parents:
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|
553 |
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shellac
parents:
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554 # If T1_out and T2_out are both nonempty. |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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555 # P(s) = T1_out x {min T2_out} |
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shellac
parents:
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changeset
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556 if T1_out and T2_out: |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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557 node_2 = min(T2_out, key=min_key) |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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changeset
|
558 for node_1 in T1_out: |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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559 yield node_1, node_2 |
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shellac
parents:
diff
changeset
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560 |
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561 # If T1_out and T2_out were both empty.... |
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562 # We compute the in-terminal sets. |
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563 |
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564 # elif not (T1_out or T2_out): # as suggested by [2], incorrect |
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565 else: # as suggested by [1], correct |
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566 T1_in = [node for node in self.in_1 if node not in self.core_1] |
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567 T2_in = [node for node in self.in_2 if node not in self.core_2] |
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568 |
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569 # If T1_in and T2_in are both nonempty. |
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570 # P(s) = T1_out x {min T2_out} |
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571 if T1_in and T2_in: |
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572 node_2 = min(T2_in, key=min_key) |
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573 for node_1 in T1_in: |
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574 yield node_1, node_2 |
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575 |
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576 # If all terminal sets are empty... |
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577 # P(s) = (N_1 - M_1) x {min (N_2 - M_2)} |
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578 |
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579 # elif not (T1_in or T2_in): # as suggested by [2], incorrect |
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580 else: # as inferred from [1], correct |
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581 node_2 = min(G2_nodes - set(self.core_2), key=min_key) |
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582 for node_1 in G1_nodes: |
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583 if node_1 not in self.core_1: |
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584 yield node_1, node_2 |
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585 |
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586 # For all other cases, we don't have any candidate pairs. |
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587 |
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588 def initialize(self): |
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589 """Reinitializes the state of the algorithm. |
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590 |
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591 This method should be redefined if using something other than DiGMState. |
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592 If only subclassing GraphMatcher, a redefinition is not necessary. |
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593 """ |
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594 |
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595 # core_1[n] contains the index of the node paired with n, which is m, |
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596 # provided n is in the mapping. |
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597 # core_2[m] contains the index of the node paired with m, which is n, |
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598 # provided m is in the mapping. |
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599 self.core_1 = {} |
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600 self.core_2 = {} |
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601 |
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602 # See the paper for definitions of M_x and T_x^{y} |
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603 |
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604 # in_1[n] is non-zero if n is in M_1 or in T_1^{in} |
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605 # out_1[n] is non-zero if n is in M_1 or in T_1^{out} |
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606 # |
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607 # in_2[m] is non-zero if m is in M_2 or in T_2^{in} |
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608 # out_2[m] is non-zero if m is in M_2 or in T_2^{out} |
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609 # |
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610 # The value stored is the depth of the search tree when the node became |
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611 # part of the corresponding set. |
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612 self.in_1 = {} |
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613 self.in_2 = {} |
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614 self.out_1 = {} |
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615 self.out_2 = {} |
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616 |
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617 self.state = DiGMState(self) |
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618 |
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619 # Provide a convenient way to access the isomorphism mapping. |
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620 self.mapping = self.core_1.copy() |
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621 |
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622 def syntactic_feasibility(self, G1_node, G2_node): |
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623 """Returns True if adding (G1_node, G2_node) is syntactically feasible. |
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624 |
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625 This function returns True if it is adding the candidate pair |
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626 to the current partial isomorphism/monomorphism mapping is allowable. |
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627 The addition is allowable if the inclusion of the candidate pair does |
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628 not make it impossible for an isomorphism/monomorphism to be found. |
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629 """ |
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630 |
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631 # The VF2 algorithm was designed to work with graphs having, at most, |
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632 # one edge connecting any two nodes. This is not the case when |
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633 # dealing with an MultiGraphs. |
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634 # |
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635 # Basically, when we test the look-ahead rules R_pred and R_succ, we |
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636 # will make sure that the number of edges are checked. We also add |
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637 # a R_self check to verify that the number of selfloops is acceptable. |
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638 |
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639 # Users might be comparing DiGraph instances with MultiDiGraph |
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640 # instances. So the generic DiGraphMatcher class must work with |
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641 # MultiDiGraphs. Care must be taken since the value in the innermost |
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642 # dictionary is a singlet for DiGraph instances. For MultiDiGraphs, |
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643 # the value in the innermost dictionary is a list. |
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644 |
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645 ### |
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646 # Test at each step to get a return value as soon as possible. |
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647 ### |
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648 |
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649 # Look ahead 0 |
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650 |
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651 # R_self |
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652 |
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653 # The number of selfloops for G1_node must equal the number of |
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654 # self-loops for G2_node. Without this check, we would fail on R_pred |
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655 # at the next recursion level. This should prune the tree even further. |
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656 if self.test == "mono": |
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657 if self.G1.number_of_edges(G1_node, G1_node) < self.G2.number_of_edges( |
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658 G2_node, G2_node |
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659 ): |
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660 return False |
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661 else: |
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662 if self.G1.number_of_edges(G1_node, G1_node) != self.G2.number_of_edges( |
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663 G2_node, G2_node |
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664 ): |
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665 return False |
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666 |
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667 # R_pred |
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668 |
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669 # For each predecessor n' of n in the partial mapping, the |
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670 # corresponding node m' is a predecessor of m, and vice versa. Also, |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
671 # the number of edges must be equal |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
672 if self.test != "mono": |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
673 for predecessor in self.G1.pred[G1_node]: |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
674 if predecessor in self.core_1: |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
675 if not (self.core_1[predecessor] in self.G2.pred[G2_node]): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
676 return False |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
677 elif self.G1.number_of_edges( |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
678 predecessor, G1_node |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
679 ) != self.G2.number_of_edges(self.core_1[predecessor], G2_node): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
680 return False |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
681 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
682 for predecessor in self.G2.pred[G2_node]: |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
683 if predecessor in self.core_2: |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
684 if not (self.core_2[predecessor] in self.G1.pred[G1_node]): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
685 return False |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
686 elif self.test == "mono": |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
687 if self.G1.number_of_edges( |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
688 self.core_2[predecessor], G1_node |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
689 ) < self.G2.number_of_edges(predecessor, G2_node): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
690 return False |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
691 else: |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
692 if self.G1.number_of_edges( |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
693 self.core_2[predecessor], G1_node |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
694 ) != self.G2.number_of_edges(predecessor, G2_node): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
695 return False |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
696 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
697 # R_succ |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
698 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
699 # For each successor n' of n in the partial mapping, the corresponding |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
700 # node m' is a successor of m, and vice versa. Also, the number of |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
701 # edges must be equal. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
702 if self.test != "mono": |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
703 for successor in self.G1[G1_node]: |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
704 if successor in self.core_1: |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
705 if not (self.core_1[successor] in self.G2[G2_node]): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
706 return False |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
707 elif self.G1.number_of_edges( |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
708 G1_node, successor |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
709 ) != self.G2.number_of_edges(G2_node, self.core_1[successor]): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
710 return False |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
711 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
712 for successor in self.G2[G2_node]: |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
713 if successor in self.core_2: |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
714 if not (self.core_2[successor] in self.G1[G1_node]): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
715 return False |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
716 elif self.test == "mono": |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
717 if self.G1.number_of_edges( |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
718 G1_node, self.core_2[successor] |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
719 ) < self.G2.number_of_edges(G2_node, successor): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
720 return False |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
721 else: |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
722 if self.G1.number_of_edges( |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
723 G1_node, self.core_2[successor] |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
724 ) != self.G2.number_of_edges(G2_node, successor): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
725 return False |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
726 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
727 if self.test != "mono": |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
728 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
729 # Look ahead 1 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
730 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
731 # R_termin |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
732 # The number of predecessors of n that are in T_1^{in} is equal to the |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
733 # number of predecessors of m that are in T_2^{in}. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
734 num1 = 0 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
735 for predecessor in self.G1.pred[G1_node]: |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
736 if (predecessor in self.in_1) and (predecessor not in self.core_1): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
737 num1 += 1 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
738 num2 = 0 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
739 for predecessor in self.G2.pred[G2_node]: |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
740 if (predecessor in self.in_2) and (predecessor not in self.core_2): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
741 num2 += 1 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
742 if self.test == "graph": |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
743 if not (num1 == num2): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
744 return False |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
745 else: # self.test == 'subgraph' |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
746 if not (num1 >= num2): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
747 return False |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
748 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
749 # The number of successors of n that are in T_1^{in} is equal to the |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
750 # number of successors of m that are in T_2^{in}. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
751 num1 = 0 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
752 for successor in self.G1[G1_node]: |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
753 if (successor in self.in_1) and (successor not in self.core_1): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
754 num1 += 1 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
755 num2 = 0 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
756 for successor in self.G2[G2_node]: |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
757 if (successor in self.in_2) and (successor not in self.core_2): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
758 num2 += 1 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
759 if self.test == "graph": |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
760 if not (num1 == num2): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
761 return False |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
762 else: # self.test == 'subgraph' |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
763 if not (num1 >= num2): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
764 return False |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
765 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
766 # R_termout |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
767 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
768 # The number of predecessors of n that are in T_1^{out} is equal to the |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
769 # number of predecessors of m that are in T_2^{out}. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
770 num1 = 0 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
771 for predecessor in self.G1.pred[G1_node]: |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
772 if (predecessor in self.out_1) and (predecessor not in self.core_1): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
773 num1 += 1 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
774 num2 = 0 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
775 for predecessor in self.G2.pred[G2_node]: |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
776 if (predecessor in self.out_2) and (predecessor not in self.core_2): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
777 num2 += 1 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
778 if self.test == "graph": |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
779 if not (num1 == num2): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
780 return False |
4f3585e2f14b
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parents:
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|
781 else: # self.test == 'subgraph' |
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parents:
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|
782 if not (num1 >= num2): |
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shellac
parents:
diff
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|
783 return False |
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shellac
parents:
diff
changeset
|
784 |
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parents:
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changeset
|
785 # The number of successors of n that are in T_1^{out} is equal to the |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
786 # number of successors of m that are in T_2^{out}. |
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shellac
parents:
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|
787 num1 = 0 |
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shellac
parents:
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|
788 for successor in self.G1[G1_node]: |
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shellac
parents:
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changeset
|
789 if (successor in self.out_1) and (successor not in self.core_1): |
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parents:
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|
790 num1 += 1 |
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shellac
parents:
diff
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|
791 num2 = 0 |
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shellac
parents:
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|
792 for successor in self.G2[G2_node]: |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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changeset
|
793 if (successor in self.out_2) and (successor not in self.core_2): |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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|
794 num2 += 1 |
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parents:
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|
795 if self.test == "graph": |
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parents:
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|
796 if not (num1 == num2): |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
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parents:
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|
797 return False |
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shellac
parents:
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|
798 else: # self.test == 'subgraph' |
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parents:
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|
799 if not (num1 >= num2): |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
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parents:
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|
800 return False |
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parents:
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changeset
|
801 |
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parents:
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|
802 # Look ahead 2 |
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parents:
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|
803 |
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parents:
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|
804 # R_new |
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parents:
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|
805 |
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parents:
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changeset
|
806 # The number of predecessors of n that are neither in the core_1 nor |
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shellac
parents:
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|
807 # T_1^{in} nor T_1^{out} is equal to the number of predecessors of m |
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parents:
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|
808 # that are neither in core_2 nor T_2^{in} nor T_2^{out}. |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
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parents:
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|
809 num1 = 0 |
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shellac
parents:
diff
changeset
|
810 for predecessor in self.G1.pred[G1_node]: |
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shellac
parents:
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changeset
|
811 if (predecessor not in self.in_1) and (predecessor not in self.out_1): |
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shellac
parents:
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changeset
|
812 num1 += 1 |
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shellac
parents:
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|
813 num2 = 0 |
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parents:
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changeset
|
814 for predecessor in self.G2.pred[G2_node]: |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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changeset
|
815 if (predecessor not in self.in_2) and (predecessor not in self.out_2): |
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shellac
parents:
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|
816 num2 += 1 |
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parents:
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changeset
|
817 if self.test == "graph": |
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shellac
parents:
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|
818 if not (num1 == num2): |
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parents:
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|
819 return False |
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parents:
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|
820 else: # self.test == 'subgraph' |
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parents:
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|
821 if not (num1 >= num2): |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
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parents:
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|
822 return False |
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parents:
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|
823 |
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parents:
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changeset
|
824 # The number of successors of n that are neither in the core_1 nor |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
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parents:
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|
825 # T_1^{in} nor T_1^{out} is equal to the number of successors of m |
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parents:
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changeset
|
826 # that are neither in core_2 nor T_2^{in} nor T_2^{out}. |
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parents:
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|
827 num1 = 0 |
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shellac
parents:
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|
828 for successor in self.G1[G1_node]: |
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shellac
parents:
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changeset
|
829 if (successor not in self.in_1) and (successor not in self.out_1): |
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parents:
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|
830 num1 += 1 |
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parents:
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|
831 num2 = 0 |
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shellac
parents:
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changeset
|
832 for successor in self.G2[G2_node]: |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
833 if (successor not in self.in_2) and (successor not in self.out_2): |
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parents:
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|
834 num2 += 1 |
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shellac
parents:
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|
835 if self.test == "graph": |
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parents:
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|
836 if not (num1 == num2): |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
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parents:
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|
837 return False |
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shellac
parents:
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|
838 else: # self.test == 'subgraph' |
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shellac
parents:
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|
839 if not (num1 >= num2): |
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shellac
parents:
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|
840 return False |
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shellac
parents:
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changeset
|
841 |
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parents:
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changeset
|
842 # Otherwise, this node pair is syntactically feasible! |
4f3585e2f14b
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shellac
parents:
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|
843 return True |
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shellac
parents:
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|
844 |
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parents:
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|
845 |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
846 class GMState: |
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shellac
parents:
diff
changeset
|
847 """Internal representation of state for the GraphMatcher class. |
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shellac
parents:
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|
848 |
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shellac
parents:
diff
changeset
|
849 This class is used internally by the GraphMatcher class. It is used |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
850 only to store state specific data. There will be at most G2.order() of |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
851 these objects in memory at a time, due to the depth-first search |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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changeset
|
852 strategy employed by the VF2 algorithm. |
4f3585e2f14b
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shellac
parents:
diff
changeset
|
853 """ |
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shellac
parents:
diff
changeset
|
854 |
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shellac
parents:
diff
changeset
|
855 def __init__(self, GM, G1_node=None, G2_node=None): |
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shellac
parents:
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|
856 """Initializes GMState object. |
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shellac
parents:
diff
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|
857 |
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shellac
parents:
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changeset
|
858 Pass in the GraphMatcher to which this GMState belongs and the |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
859 new node pair that will be added to the GraphMatcher's current |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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changeset
|
860 isomorphism mapping. |
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shellac
parents:
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|
861 """ |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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changeset
|
862 self.GM = GM |
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shellac
parents:
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|
863 |
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shellac
parents:
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changeset
|
864 # Initialize the last stored node pair. |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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|
865 self.G1_node = None |
4f3585e2f14b
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parents:
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|
866 self.G2_node = None |
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shellac
parents:
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|
867 self.depth = len(GM.core_1) |
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shellac
parents:
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|
868 |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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changeset
|
869 if G1_node is None or G2_node is None: |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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changeset
|
870 # Then we reset the class variables |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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changeset
|
871 GM.core_1 = {} |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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|
872 GM.core_2 = {} |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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|
873 GM.inout_1 = {} |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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|
874 GM.inout_2 = {} |
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shellac
parents:
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|
875 |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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changeset
|
876 # Watch out! G1_node == 0 should evaluate to True. |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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|
877 if G1_node is not None and G2_node is not None: |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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changeset
|
878 # Add the node pair to the isomorphism mapping. |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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changeset
|
879 GM.core_1[G1_node] = G2_node |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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changeset
|
880 GM.core_2[G2_node] = G1_node |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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|
881 |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
882 # Store the node that was added last. |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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|
883 self.G1_node = G1_node |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
884 self.G2_node = G2_node |
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shellac
parents:
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changeset
|
885 |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
886 # Now we must update the other two vectors. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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changeset
|
887 # We will add only if it is not in there already! |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
888 self.depth = len(GM.core_1) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
889 |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
890 # First we add the new nodes... |
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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
891 if G1_node not in GM.inout_1: |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
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892 GM.inout_1[G1_node] = self.depth |
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893 if G2_node not in GM.inout_2: |
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894 GM.inout_2[G2_node] = self.depth |
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895 |
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896 # Now we add every other node... |
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897 |
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898 # Updates for T_1^{inout} |
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899 new_nodes = set() |
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900 for node in GM.core_1: |
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901 new_nodes.update( |
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902 [neighbor for neighbor in GM.G1[node] if neighbor not in GM.core_1] |
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903 ) |
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904 for node in new_nodes: |
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905 if node not in GM.inout_1: |
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906 GM.inout_1[node] = self.depth |
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907 |
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908 # Updates for T_2^{inout} |
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909 new_nodes = set() |
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910 for node in GM.core_2: |
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911 new_nodes.update( |
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912 [neighbor for neighbor in GM.G2[node] if neighbor not in GM.core_2] |
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913 ) |
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914 for node in new_nodes: |
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915 if node not in GM.inout_2: |
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916 GM.inout_2[node] = self.depth |
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917 |
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918 def restore(self): |
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919 """Deletes the GMState object and restores the class variables.""" |
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920 # First we remove the node that was added from the core vectors. |
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921 # Watch out! G1_node == 0 should evaluate to True. |
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922 if self.G1_node is not None and self.G2_node is not None: |
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923 del self.GM.core_1[self.G1_node] |
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924 del self.GM.core_2[self.G2_node] |
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925 |
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926 # Now we revert the other two vectors. |
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927 # Thus, we delete all entries which have this depth level. |
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928 for vector in (self.GM.inout_1, self.GM.inout_2): |
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929 for node in list(vector.keys()): |
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930 if vector[node] == self.depth: |
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931 del vector[node] |
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932 |
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933 |
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934 class DiGMState: |
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935 """Internal representation of state for the DiGraphMatcher class. |
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936 |
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937 This class is used internally by the DiGraphMatcher class. It is used |
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938 only to store state specific data. There will be at most G2.order() of |
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939 these objects in memory at a time, due to the depth-first search |
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940 strategy employed by the VF2 algorithm. |
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941 |
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942 """ |
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943 |
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944 def __init__(self, GM, G1_node=None, G2_node=None): |
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945 """Initializes DiGMState object. |
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946 |
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947 Pass in the DiGraphMatcher to which this DiGMState belongs and the |
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948 new node pair that will be added to the GraphMatcher's current |
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949 isomorphism mapping. |
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950 """ |
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951 self.GM = GM |
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952 |
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953 # Initialize the last stored node pair. |
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954 self.G1_node = None |
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955 self.G2_node = None |
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956 self.depth = len(GM.core_1) |
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957 |
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958 if G1_node is None or G2_node is None: |
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959 # Then we reset the class variables |
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960 GM.core_1 = {} |
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961 GM.core_2 = {} |
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962 GM.in_1 = {} |
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963 GM.in_2 = {} |
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964 GM.out_1 = {} |
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965 GM.out_2 = {} |
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966 |
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967 # Watch out! G1_node == 0 should evaluate to True. |
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968 if G1_node is not None and G2_node is not None: |
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969 # Add the node pair to the isomorphism mapping. |
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970 GM.core_1[G1_node] = G2_node |
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971 GM.core_2[G2_node] = G1_node |
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972 |
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973 # Store the node that was added last. |
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974 self.G1_node = G1_node |
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975 self.G2_node = G2_node |
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976 |
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977 # Now we must update the other four vectors. |
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978 # We will add only if it is not in there already! |
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979 self.depth = len(GM.core_1) |
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980 |
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981 # First we add the new nodes... |
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982 for vector in (GM.in_1, GM.out_1): |
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983 if G1_node not in vector: |
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984 vector[G1_node] = self.depth |
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985 for vector in (GM.in_2, GM.out_2): |
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986 if G2_node not in vector: |
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987 vector[G2_node] = self.depth |
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988 |
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989 # Now we add every other node... |
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990 |
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991 # Updates for T_1^{in} |
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992 new_nodes = set() |
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993 for node in GM.core_1: |
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994 new_nodes.update( |
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995 [ |
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996 predecessor |
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997 for predecessor in GM.G1.predecessors(node) |
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998 if predecessor not in GM.core_1 |
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999 ] |
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1000 ) |
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1001 for node in new_nodes: |
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1002 if node not in GM.in_1: |
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1003 GM.in_1[node] = self.depth |
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1004 |
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1005 # Updates for T_2^{in} |
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1006 new_nodes = set() |
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1007 for node in GM.core_2: |
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1008 new_nodes.update( |
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1009 [ |
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1010 predecessor |
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1011 for predecessor in GM.G2.predecessors(node) |
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1012 if predecessor not in GM.core_2 |
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1013 ] |
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1014 ) |
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1015 for node in new_nodes: |
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1016 if node not in GM.in_2: |
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1017 GM.in_2[node] = self.depth |
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1018 |
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1019 # Updates for T_1^{out} |
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1020 new_nodes = set() |
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1021 for node in GM.core_1: |
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1022 new_nodes.update( |
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1023 [ |
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1024 successor |
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1025 for successor in GM.G1.successors(node) |
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1026 if successor not in GM.core_1 |
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1027 ] |
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1028 ) |
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1029 for node in new_nodes: |
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1030 if node not in GM.out_1: |
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1031 GM.out_1[node] = self.depth |
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1032 |
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1033 # Updates for T_2^{out} |
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1034 new_nodes = set() |
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1035 for node in GM.core_2: |
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1036 new_nodes.update( |
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1037 [ |
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1038 successor |
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1039 for successor in GM.G2.successors(node) |
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1040 if successor not in GM.core_2 |
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1041 ] |
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1042 ) |
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1043 for node in new_nodes: |
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1044 if node not in GM.out_2: |
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1045 GM.out_2[node] = self.depth |
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1046 |
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1047 def restore(self): |
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1048 """Deletes the DiGMState object and restores the class variables.""" |
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1049 |
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1050 # First we remove the node that was added from the core vectors. |
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1051 # Watch out! G1_node == 0 should evaluate to True. |
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1052 if self.G1_node is not None and self.G2_node is not None: |
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1053 del self.GM.core_1[self.G1_node] |
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1054 del self.GM.core_2[self.G2_node] |
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1055 |
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1056 # Now we revert the other four vectors. |
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1057 # Thus, we delete all entries which have this depth level. |
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1058 for vector in (self.GM.in_1, self.GM.in_2, self.GM.out_1, self.GM.out_2): |
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1059 for node in list(vector.keys()): |
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1060 if vector[node] == self.depth: |
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1061 del vector[node] |