eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-03-17
14:1
14:17
10.4230/LIPIcs.ICDT.2023.14
article
Uniform Reliability for Unbounded Homomorphism-Closed Graph Queries
Amarilli, Antoine
1
https://orcid.org/0000-0002-7977-4441
LTCI, Télécom Paris, Institut Polytechnique de Paris, France
We study the uniform query reliability problem, which asks, for a fixed Boolean query Q, given an instance I, how many subinstances of I satisfy Q. Equivalently, this is a restricted case of Boolean query evaluation on tuple-independent probabilistic databases where all facts must have probability 1/2. We focus on graph signatures, and on queries closed under homomorphisms. We show that for any such query that is unbounded, i.e., not equivalent to a union of conjunctive queries, the uniform reliability problem is #P-hard. This recaptures the hardness, e.g., of s-t connectedness, which counts how many subgraphs of an input graph have a path between a source and a sink.
This new hardness result on uniform reliability strengthens our earlier hardness result on probabilistic query evaluation for unbounded homomorphism-closed queries [Amarilli and Ceylan, 2021]. Indeed, our earlier proof crucially used facts with probability 1, so it did not apply to the unweighted case. The new proof presented in this paper avoids this; it uses our recent hardness result on uniform reliability for non-hierarchical conjunctive queries without self-joins [Antoine Amarilli and Benny Kimelfeld, 2022], along with new techniques.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol255-icdt2023/LIPIcs.ICDT.2023.14/LIPIcs.ICDT.2023.14.pdf
Uniform reliability
#P-hardness
probabilistic databases