Tina Trautner | Searcharxiv

arXiv2020

Containment of Simple Regular Path Queries

Testing containment of queries is a fundamental reasoning task in knowledge representation. We study here the containment problem for Conjunctive Regular Path Queries (CRPQs), a navigational query language extensively used in ontology and graph database querying. While it is known that containment of CRPQs is expspace-complete in general, we focus here on severely restricted fragments, which are known to be highly relevant in practice according to several recent studies. We obtain a detailed overview of the complexity of the containment problem, depending on the features used in the regular expressions of the queries, with completeness results for np, pitwo, pspace or expspace.

cs.AI↗

arXiv2017

Enumeration Problems for Regular Path Queries

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.

cs.DB↗