Acyclic Conjunctive Regular Path Queries are no Harder than Corresponding Conjunctive Queries

TL;DR

This paper introduces an output-sensitive algorithm for evaluating acyclic Conjunctive Regular Path Queries (CRPQs) that matches the complexity of their non-recursive counterparts, showing recursion does not increase evaluation complexity.

Contribution

It presents a novel algorithm that achieves optimal output-sensitive complexity for acyclic CRPQs, aligning with the complexity of corresponding conjunctive queries, thus bridging a gap in understanding recursion's impact.

Findings

Algorithm matches best known complexity for corresponding CQs

Recursion in acyclic CRPQs does not add extra complexity

Improves understanding of CRPQ evaluation complexity

Abstract

We present an output-sensitive algorithm for evaluating an acyclic Conjunctive Regular Path Query (CRPQ). Its complexity is written in terms of the input size, the output size, and a well-known parameter of the query that is called the "free-connex fractional hypertree width". Our algorithm improves upon the complexity of the recently introduced output-sensitive algorithm for acyclic CRPQs. More notably, the complexity of our algorithm for a given acyclic CRPQ Q matches the best known output-sensitive complexity for the "corresponding" conjunctive query (CQ), that is the CQ that has the same structure as the CRPQ Q except that each RPQ is replaced with a binary atom (or a join of two binary atoms). This implies that it is not possible to improve upon our complexity for acyclic CRPQs without improving the state-of-the-art on output-sensitive evaluation for acyclic CQs. Our result is surprising because RPQs, and by extension CRPQs, are equivalent to recursive Datalog programs, which are generally poorly understood from a complexity standpoint. Yet, our result implies that the recursion aspect of acyclic CRPQs does not add any extra complexity on top of the corresponding (non-recursive) CQs, at least as far as output-sensitive analysis is concerned.