The subgraph isomorphism problem (SIP) is a challenging problem with wide practical applications. In the last decade, despite being a theoretical hard problem, researchers designed various algorithms for solving SIP. In this work, we propose five main strategies and develop an improved exact algorithm for SIP. First, we design a probing search procedure to try whether the search procedure can successfully obtain a solution at first sight. Second, we design a novel matching ordering strategy as a value-ordering heuristic, which uses some useful information obtained from the probing search procedure to preferentially select some promising target vertices. Third, we discuss the characteristics of different propagation methods in the context of SIP and present an adaptive propagation method to make a good balance between these methods. Moreover, to further improve the performance of solving large graphs, we propose an enhanced implementation of the edge constraint method and a domain limitation strategy, which aims to accelerate the search process. Experimental results on a broad range of classic and graph-database benchmarks show that our proposed algorithm performs better than several state-of-the-art algorithms for the SIP.

中文翻译：

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PathLAD+： 面向子图同构问题的有效精确方法


子图同构问题 （SIP） 是一个具有挑战性的问题，具有广泛的实际应用。在过去的十年中，尽管这是一个理论上的难题，但研究人员设计了各种算法来解决 SIP。在这项工作中，我们提出了五种主要策略，并为 SIP 开发了一种改进的精确算法。首先，我们设计了一个探测搜索过程，以尝试搜索过程是否能一见钟情地成功获得解。其次，我们设计了一种新的匹配排序策略作为值排序启发式方法，它使用从探测搜索过程中获得的一些有用信息来优先选择一些有前途的目标顶点。第三，我们讨论了 SIP 上下文中不同传播方法的特点，并提出了一种自适应传播方法，以便在这些方法之间取得良好的平衡。此外，为了进一步提高求解大型图的性能，我们提出了边缘约束方法的增强实现和域限制策略，旨在加速搜索过程。在广泛的经典和图数据库基准上的实验结果表明，我们提出的算法比几种最先进的 SIP 算法性能更好。