Fine-Grained Complexity of Regular Path Queries

TL;DR

This paper investigates the computational complexity of evaluating regular path queries (RPQs) in graph databases, analyzing the efficiency of the product graph approach and proposing methods for faster enumeration with sub-linear delay.

Contribution

It provides a detailed complexity analysis of the PG-approach for RPQ evaluation, including conditional lower bounds and new algorithms for faster enumeration.

Findings

PG-approach can achieve optimal or near-optimal complexity bounds.

Enumeration delay is linear in the database size for the PG-approach.

Three methods for sub-linear delay enumeration are proposed.

Abstract

A regular path query (RPQ) is a regular expression q that returns all node pairs (u, v) from a graph database that are connected by an arbitrary path labelled with a word from L(q). The obvious algorithmic approach to RPQ-evaluation (called PG-approach), i.e., constructing the product graph between an NFA for q and the graph database, is appealing due to its simplicity and also leads to efficient algorithms. However, it is unclear whether the PG-approach is optimal. We address this question by thoroughly investigating which upper complexity bounds can be achieved by the PG-approach, and we complement these with conditional lower bounds (in the sense of the fine-grained complexity framework). A special focus is put on enumeration and delay bounds, as well as the data complexity perspective. A main insight is that we can achieve optimal (or near optimal) algorithms with the PG-approach, but the delay for enumeration is rather high (linear in the database). We explore three successful approaches towards enumeration with sub-linear delay: super-linear preprocessing, approximations of the solution sets, and restricted classes of RPQs.