Tps: A new way to find good vertex-search order for exact subgraph matching

Exact subgraph matching is fundamental to numerous graph data applications. The inherent NP-completeness of subgraph isomorphism poses significant challenges in developing efficient matching algorithms. Current methods show limited success, particularly in their filtering and verification stages. Selecting an optimal vertex-searching order can greatly improve a subgraph searching algorithm's effectiveness, yet a comprehensive theory for this selection is lacking. In this paper, we introduce the Multistage Graph Search Model (MGSM), a novel approach addressing this gap. MGSM provides insights for identifying the most efficient vertex-searching order and offers a systematic framework for evaluating existing algorithms. Using MGSM, we identify two main challenges in optimizing the search order and present a new matching algorithm “Tps” noted for its strategic vertex-searching order. Extensive experiments demonstrate the superior performance of Tps and its effectiveness and soundness in optimizing search orders.