A trichotomy for regular simple path queries on graphs

Abstract

Regular path queries (RPQs) select nodes connected by some path in a graph. The edge labels of such a path have to form a word that matches a given regular expression. We investigate the evaluation of RPQs with an additional constraint that prevents multiple traversals of the same nodes. Those regular simple path queries (RSPQs) find several applications in practice, yet they quickly become intractable, even for basic languages such as (aa) * or a * ba * .In this paper, we establish a comprehensive classification of regular languages with respect to the complexity of the corresponding regular simple path query problem. More precisely, we identify the fragment that is maximal in the following sense: regular simple path queries can be evaluated in polynomial time for every regular language L that belongs to this fragment and evaluation is NP-complete for languages outside this fragment. We thus fully characterize the frontier between tractability and intractability for RSPQs, and we refine our results to show the following trichotomy: Evaluations of RSPQs is either AC 0 , NL-complete or NP-complete in data complexity, depending on the regular language L. The fragment identified also admits a simple characterization in terms of regular expressions.Finally, we also discuss the complexity of the following decision problem: decide, given a language L, whether finding a regular simple path for L is tractable. We consider several alternative representations of L: DFAs, NFAs or regular expressions, and prove that this problem is NL-complete for the first representation and PSPACE-complete for the other two. As a conclusion we extend our results from edgelabeled graphs to vertex-labeled graphs and vertex-edge labeled graphs.

Navigating the Maze of Wikidata Query Logs

“…There were even expression types which occurred more often in the TO (timeout) logs than in the OK logs, such as ∼(ab) * . This is interesting, because such expressions are known to be complex (NP-complete) to evaluate under simple path semantics [3]. Additional Insights on Wikidata Property Paths.…”

“…Furthermore, all property paths except 198 (98) are in C tract , which is a broader class introduced by Bagan et al [3] and which precisely characterizes the set of regular expressions for which the data complexity under simple path semantics is tractable if P NP.…”

“…Several empirical studies of SPARQL query logs have been conducted in the literature investigating statistical features, such as such as occurrences of triple patterns and types of queries [3,15,23,29] along with recent studies on more complex features of the queries, such as structural features and complexity of the queries [10,27]. However, the analysis of Wikidata queries has been limited in the past due to their unavailability.…”

“…They made several observations on which we build in this paper, namely that robotic query traffic dominates organic query traffic in terms of volume and query load, and that robotic queries are issued by a single source whereas organic queries are typically multi-source. They also identified a massive presence of recursive queries in these logs, whose prominent fragment consists of queries only containing joins and property paths, 3 also known as conjunctive 2-way regular path queries (C2RPQs) in the literature. These massive logs of recursive queries are the first encountered so far, as opposed to negligible percentages of these queries in previous large-scale logs, including DBpedia queries [9].…”

Graph Queries

“…This wide array of possibilities, in terms of query input and output, along with the complexity of query evaluation, drives and motivates our current research in the area [23,16,22,18,8,15,7,13,12,9], part of which we revisit in this paper.…”