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On the Complexity of Computing Generators of Closed Sets

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Formal Concept Analysis (ICFCA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4933))

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Abstract

We investigate the computational complexity of some decision and counting problems related to generators of closed sets fundamental in Formal Concept Analysis. We recall results from the literature about the problem of checking the existence of a generator with a specified cardinality, and about the problem of determining the number of minimal generators. Moreover, we show that the problem of counting minimum cardinality generators is -complete. We also present an incremental-polynomial time algorithm from relational database theory that can be used for computing all minimal generators of an implication-closed set.

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Author information

Authors and Affiliations

  1. LIX (CNRS, UMR 7161), École Polytechnique, 91128 Palaiseau, France

    Miki Hermann

  2. Institut für Theoretische Informatik, TU Dresden, Germany

    Barış Sertkaya

Authors
  1. Miki Hermann
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  2. Barış Sertkaya
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Raoul Medina Sergei Obiedkov

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Hermann, M., Sertkaya, B. (2008). On the Complexity of Computing Generators of Closed Sets. In: Medina, R., Obiedkov, S. (eds) Formal Concept Analysis. ICFCA 2008. Lecture Notes in Computer Science(), vol 4933. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78137-0_12

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  • DOI: https://doi.org/10.1007/978-3-540-78137-0_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78136-3

  • Online ISBN: 978-3-540-78137-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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