FineGrained Complexity of Regular Path Queries
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 RPQevaluation (called PGapproach), 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 PGapproach is optimal. We address this question by thoroughly investigating which upper complexity bounds can be achieved by the PGapproach, and we complement these with conditional lower bounds (in the sense of the finegrained 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 PGapproach, but the delay for enumeration is rather high (linear in the database). We explore three successful approaches towards enumeration with sublinear delay: superlinear preprocessing, approximations of the solution sets, and restricted classes of RPQs.
 Publication:

arXiv eprints
 Pub Date:
 January 2021
 arXiv:
 arXiv:2101.01945
 Bibcode:
 2021arXiv210101945C
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Computational Complexity;
 Computer Science  Databases;
 Computer Science  Formal Languages and Automata Theory