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DOI: 10.4230/LIPIcs.ICDT.2020.10

On Equivalence and Cores for Incomplete Databases in Open and Closed Worlds

Authors: Henrik Forssell, Evgeny Kharlamov, and Evgenij Thorstensen

Published in: LIPIcs, Volume 155, 23rd International Conference on Database Theory (ICDT 2020)

Abstract

Data exchange heavily relies on the notion of incomplete database instances. Several semantics for such instances have been proposed and include open (OWA), closed (CWA), and open-closed (OCWA) world. For all these semantics important questions are: whether one incomplete instance semantically implies another; when two are semantically equivalent; and whether a smaller or smallest semantically equivalent instance exists. For OWA and CWA these questions are fully answered. For several variants of OCWA, however, they remain open. In this work we adress these questions for Closed Powerset semantics and the OCWA semantics of [Leonid Libkin and Cristina Sirangelo, 2011]. We define a new OCWA semantics, called OCWA*, in terms of homomorphic covers that subsumes both semantics, and characterize semantic implication and equivalence in terms of such covers. This characterization yields a guess-and-check algorithm to decide equivalence, and shows that the problem is NP-complete. For the minimization problem we show that for several common notions of minimality there is in general no unique minimal equivalent instance for Closed Powerset semantics, and consequently not for the more expressive OCWA* either. However, for Closed Powerset semantics we show that one can find, for any incomplete database, a unique finite set of its subinstances which are subinstances (up to renaming of nulls) of all instances semantically equivalent to the original incomplete one. We study properties of this set, and extend the analysis to OCWA*.

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Henrik Forssell, Evgeny Kharlamov, and Evgenij Thorstensen. On Equivalence and Cores for Incomplete Databases in Open and Closed Worlds. In 23rd International Conference on Database Theory (ICDT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 155, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{forssell_et_al:LIPIcs.ICDT.2020.10,
  author =	{Forssell, Henrik and Kharlamov, Evgeny and Thorstensen, Evgenij},
  title =	{{On Equivalence and Cores for Incomplete Databases in Open and Closed Worlds}},
  booktitle =	{23rd International Conference on Database Theory (ICDT 2020)},
  pages =	{10:1--10:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-139-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{155},
  editor =	{Lutz, Carsten and Jung, Jean Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2020.10},
  URN =		{urn:nbn:de:0030-drops-119343},
  doi =		{10.4230/LIPIcs.ICDT.2020.10},
  annote =	{Keywords: Incomplete Databases, Cores, Semantics, Open and Closed Worlds}
}

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DOI: 10.4230/LIPIcs.STACS.2011.12

Structural Decomposition Methods and What They are Good For

Authors: Markus Aschinger, Conrad Drescher, Georg Gottlob, Peter Jeavons, and Evgenij Thorstensen

Published in: LIPIcs, Volume 9, 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)

Abstract

This paper reviews structural problem decomposition methods, such as tree and path decompositions. It is argued that these notions can be applied in two distinct ways: Either to show that a problem is efficiently solvable when a width parameter is fixed, or to prove that the unrestricted (or some width-parameter free) version of a problem is tractable by using a width-notion as a mathematical tool for directly solving the problem at hand. Examples are given for both cases. As a new showcase for the latter usage, we report some recent results on the Partner Units Problem, a form of configuration problem arising in an industrial context. We use the notion of a path decomposition to identify and solve a tractable class of instances of this problem with practical relevance.

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Markus Aschinger, Conrad Drescher, Georg Gottlob, Peter Jeavons, and Evgenij Thorstensen. Structural Decomposition Methods and What They are Good For. In 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 9, pp. 12-28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{aschinger_et_al:LIPIcs.STACS.2011.12,
  author =	{Aschinger, Markus and Drescher, Conrad and Gottlob, Georg and Jeavons, Peter and Thorstensen, Evgenij},
  title =	{{Structural Decomposition Methods and What They are Good For}},
  booktitle =	{28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)},
  pages =	{12--28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-25-5},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{9},
  editor =	{Schwentick, Thomas and D\"{u}rr, Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2011.12},
  URN =		{urn:nbn:de:0030-drops-29960},
  doi =		{10.4230/LIPIcs.STACS.2011.12},
  annote =	{Keywords: decompositions}
}

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Documents authored by Thorstensen, Evgenij

On Equivalence and Cores for Incomplete Databases in Open and Closed Worlds

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Structural Decomposition Methods and What They are Good For

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