Alexandru-Mihai Hurjui

arXiv2026

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

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.

cs.DB↗

arXiv2025

Output-Sensitive Evaluation of Acyclic Conjunctive Regular Path Queries

Conjunctive Regular Path Queries, or CRPQs for short, are an essential construct in graph query languages. In this paper, we propose the first output-sensitive algorithm for evaluating acyclic CRPQs. It is output-sensitive in the sense that its complexity is a function of the sizes of the input graph and of the query output. In particular, it does not depend on the output sizes of the regular expressions that appear in the query, as these sizes can be much larger than the query output size. Our algorithm proceeds in two stages. In the first stage, it contracts the given query into a free-connex acyclic one such that the output of the original query can be obtained from the output of the contracted one. This contraction removes bound variables by composing regular expressions or by promoting bound variables to free ones. The minimum necessary number of promoted bound variables gives the contraction width, which is a novel parameter specific to CRPQs. In the second stage, our algorithm evaluates the free-connex acyclic CRPQ and projects away the columns of the promoted bound variables. It ensures output-sensitivity by computing the calibrated outputs of the regular expressions appearing in the free-connex acyclic CRPQ in time proportional to their sizes. Our algorithm has lower complexity than the state-of-the-art approaches for problem instances where (i) the query output is asymptotically smaller than the worst-case output size or (ii) the largest output size of any of the regular expression in the query.

cs.DB↗