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Dualization on Partially Ordered Sets: Preliminary Results

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Information Search, Integration and Personalization (ISIP 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 497))

Abstract

The dualization problem on arbitrary posets is a crucial step in many applications in logics, databases, artificial intelligence and pattern mining.

The objective of this paper is to study reductions of the dualization problem on arbitrary posets to the dualization problem on boolean lattices, for which output quasi-polynomial time algorithms exist. We introduce convex embedding and poset reflection as key notions to characterize such reductions. As a consequence, we identify posets, which are not boolean lattices, for which the dualization problem remains quasi-polynomial and propose a classification of posets with respect to dualization.

As far as we know, this is the first contribution to explicit non-trivial reductions for studying the hardness of dualization problems on arbitrary posets.

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Notes

  1. 1.

    It also works for infinite partially ordered sets that are well ordered, i.e. all antichains are finite.

  2. 2.

    Dual sets are also known as blocker and anti-blocker or positive and negative borders.

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Author information

Authors and Affiliations

  1. Clermont-Université, Université Blaise Pascal, LIMOS, CNRS, Aubière, France

    Lhouari Nourine

  2. Université de Lyon, CNRS, LIRIS, INSA, Lyon, France

    Jean Marc Petit

Authors
  1. Lhouari Nourine
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  2. Jean Marc Petit
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Corresponding author

Correspondence to Jean Marc Petit .

Editor information

Editors and Affiliations

  1. Lab. ETIS, Sciences Informatiques, Université de Cergy-Pontoise, Pontoise, France

    Dimitrios Kotzinos

  2. HELP University, Kuala Lumpur, Malaysia

    Yeow Wei Choong

  3. LRI, University of Paris South, Orsay, France

    Nicolas Spyratos

  4. Information Science, Knowledge Media Lab, Hokkaido University, Sapporo, Hokkaido, Japan

    Yuzuru Tanaka

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© 2016 Springer International Publishing Switzerland

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Nourine, L., Petit, J.M. (2016). Dualization on Partially Ordered Sets: Preliminary Results. In: Kotzinos, D., Choong, Y., Spyratos, N., Tanaka, Y. (eds) Information Search, Integration and Personalization. ISIP 2014. Communications in Computer and Information Science, vol 497. Springer, Cham. https://doi.org/10.1007/978-3-319-38901-1_2

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  • DOI: https://doi.org/10.1007/978-3-319-38901-1_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-38900-4

  • Online ISBN: 978-3-319-38901-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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