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Graph Edit Distance (GED) is a general and domain-agnostic metric to measuregraph similarity, widely used in graph search or retrieving tasks. However, theexact GED computation is known to be NP-complete. For instance, the widely usedA* algorithms explore the entire search space to find the optimal solutionwhich inevitably suffers scalability issues. Learning-based methods apply graphrepresentation techniques to learn the GED by formulating a regression task,which can not recover the edit path and lead to inaccurate GED approximation(i.e., the predicted GED is smaller than the exact). To this end, in this work,we present a data-driven hybrid approach MATA* for approximate GED computationbased on Graph Neural Networks (GNNs) and A* algorithms, which models from theperspective of learning to match nodes instead of directly regressing GED.Specifically, aware of the structure-dominant operations (i.e.,node and edgeinsertion/deletion) property in GED computation, a structure-enhanced GNN isfirstly designed to jointly learn local and high-order structural informationfor node embeddings for node matchings. Second, top-k candidate nodes areproduced via a differentiable top-k operation to enable the training for nodematchings, which is adhering to another property of GED, i.e., multiple optimalnode matchings. Third, benefiting from the candidate nodes, MATA* only performson the promising search directions, reaching the solution efficiently. Finally,extensive experiments show the superiority of MATA* as it significantlyoutperforms the combinatorial search-based, learning-based and hybrid methodsand scales well to large-size graphs.

MATA*: Combining Learnable Node Matching with A* Algorithm for Approximate Graph Edit Distance Computation

MATA: Combining Learnable Node Matching with A Algorithm for Approximate Graph Edit Distance Computation