A regular path query (RPQ) is a regular expression q that returns all node pairs (u, v) from a graph database that are connected by an arbitrary path labelled with a word from L(q). The obvious algorithmic approach to RPQ-evaluation (called PG-approach), i.e., constructing the product graph between an NFA for q and the graph database, is appealing due to its simplicity and also leads to efficient algorithms. However, it is unclear whether the PG-approach is optimal. We address this question by thoroughly investigating which upper complexity bounds can be achieved by the PG-approach, and we complement these with conditional lower bounds (in the sense of the fine-grained complexity framework). A special focus is put on enumeration and delay bounds, as well as the data complexity perspective. A main insight is that we can achieve optimal (or near optimal) algorithms with the PG-approach, but the delay for enumeration is rather high (linear in the database). We explore three successful approaches towards enumeration with sub-linear delay: super-linear preprocessing, approximations of the solution sets, and restricted classes of RPQs.

中文翻译：

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规则路径查询的细粒度复杂度

正则路径查询（RPQ）是一个正则表达式q，它返回图形数据库中的所有节点对（u，v），这些节点对通过用L（q）中的单词标记的任意路径连接。RPQ评估的一种明显的算法方法（称为PG方法），即在q的NFA和图数据库之间构造乘积图，由于其简单性而吸引人，并且还导致了高效的算法。但是，尚不清楚PG方法是否最佳。我们通过彻底研究PG方法可以实现哪些较高的复杂度界限来解决这个问题，并通过有条件的较低界限（在细粒度的复杂度框架的意义上）对它们进行补充。特别关注枚举和延迟范围以及数据复杂性的观点。一个主要的见解是，我们可以使用PG方法实现最佳（或接近最佳）算法，但是枚举的延迟相当高（数据库中是线性的）。我们探索了使用亚线性延迟进行枚举的三种成功方法：超线性预处理，解集的逼近和RPQ的受限类。