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An Algebraic Approach to the Complexity of Generalized Conjunctive Queries

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Theory and Applications of Satisfiability Testing (SAT 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3542))

Abstract

Conjunctive-query containment is considered as a fundamental problem in database query evaluation and optimization. Kolaitis and Vardi pointed out that constraint satisfaction and conjunctive query containment are essentially the same problem. We study the Boolean conjunctive queries under a more detailed scope, where we investigate their counting problem by means of the algebraic approach through Galois theory, taking advantage of Post’s lattice. We prove a trichotomy theorem for the generalized conjunctive query counting problem, showing this way that, contrary to the corresponding decision problems, constraint satisfaction and conjunctive-query containment differ for other computational goals. We also study the audit problem for conjunctive queries asking whether there exists a frozen variable in a given query. This problem is important in databases supporting statistical queries. We derive a dichotomy theorem for this audit problem that sheds more light on audit applicability within database systems.

Supported by ÉGIDE 05835SH, DAAD D/0205776 and DFG VO 630/5-1.

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Author information

Authors and Affiliations

  1. Theoretische Informatik, Universität Hannover, Germany

    Michael Bauland & Heribert Vollmer

  2. GREYC (UMR 6072), Université de Caen, France

    Philippe Chapdelaine

  3. LIF (UMR 6166), Univ. de la Méditerranée, France

    Nadia Creignou

  4. LIX (UMR 7161), École Polytechnique, France

    Miki Hermann

Authors
  1. Michael Bauland
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  2. Philippe Chapdelaine
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  3. Nadia Creignou
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  4. Miki Hermann
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  5. Heribert Vollmer
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of British Columbia Vancouver, V6T 1Z4, B.C., Canada

    Holger H. Hoos

  2. Computational Logic Laboratory, Simon Fraser University, Burnaby, BC, Canada

    David G. Mitchell

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© 2005 Springer-Verlag Berlin Heidelberg

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Bauland, M., Chapdelaine, P., Creignou, N., Hermann, M., Vollmer, H. (2005). An Algebraic Approach to the Complexity of Generalized Conjunctive Queries. In: Hoos, H.H., Mitchell, D.G. (eds) Theory and Applications of Satisfiability Testing. SAT 2004. Lecture Notes in Computer Science, vol 3542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11527695_3

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  • DOI: https://doi.org/10.1007/11527695_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-27829-0

  • Online ISBN: 978-3-540-31580-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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