License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICDT.2017.15
URN: urn:nbn:de:0030-drops-70479
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7047/
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Gogacz, Tomasz ; Torunczyk, Szymon

Entropy Bounds for Conjunctive Queries with Functional Dependencies

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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.

BibTeX - Entry

@InProceedings{gogacz_et_al:LIPIcs:2017:7047,
  author =	{Tomasz Gogacz and Szymon Torunczyk},
  title =	{{Entropy Bounds for Conjunctive Queries with Functional Dependencies}},
  booktitle =	{20th International Conference on Database Theory (ICDT 2017)},
  pages =	{15:1--15:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-024-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{68},
  editor =	{Michael Benedikt and Giorgio Orsi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7047},
  URN =		{urn:nbn:de:0030-drops-70479},
  doi =		{10.4230/LIPIcs.ICDT.2017.15},
  annote =	{Keywords: database theory, conjunctive queries, size bounds, entropy, finite groups, entropy cone}
}

Keywords: database theory, conjunctive queries, size bounds, entropy, finite groups, entropy cone
Collection: 20th International Conference on Database Theory (ICDT 2017)
Issue Date: 2017
Date of publication: 17.03.2017

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