Conjunctive Regular Path Queries with Capture Groups

Abstract

In practice, regular expressions are usually extended by so-called capture groups or capture variables, which allow to capture a subexpression by a variable that can be referenced in the regular expression in order to describe repetitions of subwords. We investigate how this concept could be used for pattern-based graph querying; i.e., we investigate conjunctive regular path queries (CRPQs) that are extended by capture variables. If capture variables are added to CRPQs in a completely unrestricted way, then Boolean evaluation becomes PSPACE-hard in data complexity, even for single-edge graph patterns. On the other hand, if capture variables do not occur under a Kleene star, then the data complexity drops to NL-completeness. Combined complexity is in EXPSPACE but drops to PSPACE-completeness if the depth (i.e., the nesting depth of capture variables) is bounded, and it drops to NP-completeness if the size of the images of capture variables is bounded by a constant (regardless of the depth or of whether capture variables occur under a Kleene star). In the application of regular expressions as string searching tools, references to capture variables only describe exact repetitions of subwords (i.e., they implement the equality relation on strings). Following recent developments in graph database research, we also study CRPQs with capture variables that describe arbitrary regular relations. We show that if the expressions have depth 0, or if the size of the images of capture variables is bounded by a constant, then we can allow arbitrary regular relations while staying in the same complexity bounds. We also investigate the problems of checking whether a given tuple is in the solution set and computing the whole solution set. On the conceptual side, we add capture variables to CRPQs in such a way that they can be defined in an expression on one arc of the graph pattern but also referenced in expressions on other arcs. Hence, they add to CRPQs the possibility to define inter-dependencies between different paths, which is a relevant feature of pattern-based graph querying.