  Subgraph matching is a fundamental building block for graph-based
applications and is challenging due to its high-order combinatorial nature.
Existing studies usually tackle it by combinatorial optimization or
learning-based methods. However, they suffer from exponential computational
costs or searching the 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 first prove that subgraph matching
can degenerate to subtree matching, and subsequently is equivalent to finding a
perfect matching on a bipartite graph. We can then yield an implementation of
linear time complexity by the built-in tree-structured aggregation mechanism on
graph neural networks. Moreover, circle structures and node attributes can be
easily incorporated in D2Match to boost the matching performance. Finally, we
conduct extensive experiments to show the superior performance of our D2Match
and confirm that our D2Match indeed exploits the subtrees and differs from
existing GNNs-based subgraph matching methods that depend on memorizing the
data distribution divergence

Machine Learning;Artificial Intelligence