D2Match: Leveraging Deep Learning and Degeneracy for Subgraph Matching

Xuanzhou Liu, Lin Zhang, Jiaqi Sun, Yujiu Yang, Haiqin Yang

Abstract: Subgraph matching is a fundamental building block for many graph-based applications and is challenging due to its high-order combinatorial nature. However, previous methods usually tackle it by combinatorial optimization or representation learning and suffer from exponential computational cost or matching without theoretical guarantees. In this paper, we develop D2Match by leveraging the efficiency of Deep learning and Degeneracy for subgraph matching. More specifically, we prove that subgraph matching can degenerate to subtree matching, and subsequently is equivalent to finding a perfect matching on a bipartite graph. This matching procedure can be implemented by the built-in tree-structured aggregation mechanism on graph neural networks, which yields linear time complexity. Moreover, circle structures, abstracted as {\em supernodes}, and node attributes can be easily incorporated in D2Match to boost the matching. Finally, we conduct extensive experiments to show the superior performance of our D2Match and confirm that our D2Match indeed tries to exploit the subtrees and differs from existing learning-based subgraph matching methods that depend on memorizing the data distribution divergence.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics

Submission Guidelines: Yes

Please Choose The Closest Area That Your Submission Falls Into: Deep Learning and representational learning

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/d2match-leveraging-deep-learning-and/code)