Extremal Fitting Problems for Conjunctive Queries
Abstract
The fitting problem for conjunctive queries (CQs) is the problem to construct a CQ that fits a given set of labeled data examples. When a fitting CQ exists, it is in general not unique. This leads us to proposing natural refinements of the notion of a fitting CQ, such as most-general fitting CQ, most-specific fitting CQ, and unique fitting CQ. We give structural characterizations of these notions in terms of (suitable refinements of) homomorphism dualities, frontiers, and direct products, which enable the construction of the refined fitting CQs when they exist. We also pinpoint the complexity of the associated existence and verification problems, and determine the size of fitting CQs. We study the same problems for UCQs and for the more restricted class of tree CQs.
Keywords
Cite
@article{arxiv.2206.05080,
title = {Extremal Fitting Problems for Conjunctive Queries},
author = {Balder ten Cate and Victor Dalmau and Maurice Funk and Carsten Lutz},
journal= {arXiv preprint arXiv:2206.05080},
year = {2025}
}
Comments
This is a expanded version of a paper published in Proceedings of PODS 2023, which is currently under review for a journal