Enumeration Problems for Regular Path Queries

TL;DR

This paper studies the enumeration of paths matching regular path queries in graphs, analyzing different semantics and their computational complexities, and provides practical insights into feasible cases for common RPQs.

Contribution

It introduces a parameterized complexity analysis for RPQ enumeration, establishing dichotomies for simple and trail path semantics, and highlights practical tractability for most common RPQs.

Findings

Polynomial delay enumeration for arbitrary and shortest paths.

Intractability of simple and trail paths in general, with exceptions in practical cases.

W[1]-hardness of the disjoint paths problem when parameterized by path length.

Abstract

Evaluation of regular path queries (RPQs) is a central problem in graph databases. We investigate the corresponding enumeration problem, that is, given a graph and an RPQ, enumerate all paths in the graph that match the RPQ. We consider several versions of this problem, corresponding to different semantics of RPQs that have recently been considered: arbitrary paths, shortest paths, simple paths, and trails. Whereas arbitrary and shortest paths can be enumerated in polynomial delay, the situation is much more intricate for simple paths and trails. For instance, already the question if a given graph contains a simple path or trail of a certain length has cases with highly non-trivial solutions and cases that are long-standing open problems. In this setting, we study RPQ evaluation from a parameterized complexity perspective. We define a class of simple transitive expressions that is prominent in practice and for which we can prove two dichotomy-like results: one for simple paths and one for trails paths. We observe that, even though simple path semantics and trail semantics are intractable for RPQs in general, they are feasible for the vast majority of the kinds of RPQs that users use in practice. At the heart of this study is a result of independent interest on the parameterized complexity of finding disjoint paths in graphs: the two disjoint paths problem is W[1]-hard if parameterized by the length of one of the two paths.