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.
@InProceedings{casel_et_al:LIPIcs.ICDT.2021.19, author = {Casel, Katrin and Schmid, Markus L.}, title = {{Fine-Grained Complexity of Regular Path Queries}}, booktitle = {24th International Conference on Database Theory (ICDT 2021)}, pages = {19:1--19:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-179-5}, ISSN = {1868-8969}, year = {2021}, volume = {186}, editor = {Yi, Ke and Wei, Zhewei}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2021.19}, URN = {urn:nbn:de:0030-drops-137277}, doi = {10.4230/LIPIcs.ICDT.2021.19}, annote = {Keywords: Graph Databases, Regular Path Queries, Enumeration, Fine-Grained Complexity} }
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