D2Match: Leveraging Deep Learning and Degeneracy for Subgraph Matching

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.