Graph database is designed to store bidirectional relationships between objects and facilitate the traversal process to extract a subgraph. However, the subgraph matching process is an NP-Complete problem. Existing solutions to this problem usually employ a filter-and-verification framework and a divide-and-conquer method. The filter-and-verification framework minimizes the number of inputs to the verification stage by filtering and pruning invalid candidates as much as possible. Meanwhile, subgraph matching is performed on the substructure decomposed from the larger graph to yield partial embedding. Subsequently, the recursive traversal or set intersection technique combines the partial embedding into a complete subgraph. In this paper, we first present a comprehensive literature review of the state-of-the-art solutions. l2Match, a subgraph isomorphism algorithm for small queries utilizing a Label-Pair Index and filtering method, is then proposed and presented as a proof of concept. Empirical experimentation shows that l2Match outperforms related state-of-the-art solutions, and the proposed methods optimize the existing algorithms.

翻译：图数据库旨在存储对象之间的双向关系，并简化提取子图的遍历过程。然而，子图匹配问题属于NP完全问题。现有解决方案通常采用过滤-验证框架与分治方法：过滤-验证框架通过尽可能过滤和剪枝无效候选集来最小化验证阶段的输入数量；同时，子图匹配在大图分解的子结构上执行以生成部分嵌入，随后通过递归遍历或集合交集技术将部分嵌入组合成完整子图。本文首先对现有前沿解决方案进行了全面文献综述，随后提出并展示了l2Match——一种针对小规模查询、利用标签对索引与过滤方法的子图同构算法作为概念验证。实验结果表明，l2Match优于相关前沿解决方案，且所提方法对现有算法具有优化作用。