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Entropy Bounds for Conjunctive Queries with Functional Dependencies

Authors Tomasz Gogacz, Szymon Torunczyk



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Tomasz Gogacz
Szymon Torunczyk

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Tomasz Gogacz and Szymon Torunczyk. Entropy Bounds for Conjunctive Queries with Functional Dependencies. In 20th International Conference on Database Theory (ICDT 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 68, pp. 15:1-15:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.ICDT.2017.15

Abstract

We study the problem of finding the worst-case size of the result Q(D) of a fixed conjunctive query Q applied to a database D satisfying given functional dependencies. We provide a characterization of this bound in terms of entropy vectors, and in terms of finite groups. In particular, we show that an upper bound provided by [Gottlob, Lee, Valiant and Valiant, J.ACM, 2012] is tight, and that a correspondence of [Chan and Yeung, ACM TOIT, 2002] is preserved in the presence of functional dependencies. However, tightness of a weaker upper bound provided by Gottlob et al., which would have immediate applications to evaluation of join queries ([Khamis, Ngo, and Suciu, PODS, 2016]) remains open. Our result shows that the problem of computing the worst-case size bound, in the general case, is closely related to difficult problems from information theory.
Keywords
  • database theory
  • conjunctive queries
  • size bounds
  • entropy
  • finite groups
  • entropy cone

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References

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