Regular path queries (RPQs) are a central component of graph databases. We investigate decision and enumeration problems concerning the evaluation of RPQs under several semantics that have recently been considered: arbitrary paths, shortest paths, paths without node repetitions (simple paths), and paths without edge repetitions (trails). Whereas arbitrary and shortest paths can be dealt with efficiently, simple paths and trails become computationally difficult already for very small RPQs. We study RPQ evaluation for simple paths and trails from a parameterized complexity perspective and define a class of simple transitive expressions that is prominent in practice and for which we can prove dichotomies for the evaluation problem. We observe that, even though simple path and trail semantics are intractable for RPQs in general, they are feasible for the vast majority of RPQs that are used in practice. At the heart of this study is a result of independent interest: the two disjoint paths problem in directed graphs is W[1]-hard if parameterized by the length of one of the two paths.

中文翻译：

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评估简单正则路径查询的二分法

常规路径查询 (RPQ) 是图形数据库的核心组件。我们研究了在最近考虑的几种语义下评估 RPQ 的决策和枚举问题：任意路径、最短路径、没有节点重复的路径（简单路径）和没有边缘重复的路径（轨迹）。尽管可以有效地处理任意和最短的路径，但对于非常小的 RPQ，简单的路径和路径在计算上已经变得困难。我们从参数化复杂性的角度研究简单路径和轨迹的 RPQ 评估，并定义了一类简单及物表达这在实践中很突出，我们可以为此证明评估问题的二分法。我们观察到，即使简单的路径和轨迹语义对于 RPQ 通常来说是难以处理的，但它们对于实践中使用的绝大多数 RPQ 都是可行的。这项研究的核心是一个独立利益的结果：如果通过两条路径之一的长度参数化，有向图中的两条不相交路径问题是 W[1] 困难的。