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Improving the Performance of Lindig-Style Algorithms with Empty Intersections

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Graph-Based Representation and Reasoning (ICCS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12879))

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Abstract

The building of a concept lattice and its line diagram from a set of formal concepts is an important task in formal concept analysis (FCA), since it allows one to express relationships among formal concepts in a concise and comprehensible form. One may enumerate direct neighbors of each formal concept and build a concept lattice or its line diagram in a straightforward way. This is the main idea behind the algorithm proposed by Lindig. This algorithm, as well as other algorithms in FCA, must contend with the fact that some formal concepts are enumerated multiple times. In practice a substantial amount of redundant computations is related to the top (or bottom) formal concept. The In-Close4 algorithm came up with an optimization technique that allows one to eliminate such redundant computations and significantly improves the performance of algorithms from the Close-by-One family. We show that this technique can be used in the Lindig-type algorithms to improve their performance as well.

The research was supported by the grant JG 2019 of Palacký University Olomouc, No. JG_2019_008.

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Authors and Affiliations

  1. Department of Computer Science, Palacký University Olomouc, 17. listopadu 12, 77146, Olomouc, Czech Republic

    Petr Krajča

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  1. Petr Krajča
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Correspondence to Petr Krajča .

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Editors and Affiliations

  1. University of Lübeck, Lübeck, Germany

    Tanya Braun

  2. University of Lübeck, Lübeck, Germany

    Marcel Gehrke

  3. University of Kassel, Kassel, Germany

    Tom Hanika

  4. University of Toulouse, Toulouse, France

    Nathalie Hernandez

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Krajča, P. (2021). Improving the Performance of Lindig-Style Algorithms with Empty Intersections. In: Braun, T., Gehrke, M., Hanika, T., Hernandez, N. (eds) Graph-Based Representation and Reasoning. ICCS 2021. Lecture Notes in Computer Science(), vol 12879. Springer, Cham. https://doi.org/10.1007/978-3-030-86982-3_7

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  • DOI: https://doi.org/10.1007/978-3-030-86982-3_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-86981-6

  • Online ISBN: 978-3-030-86982-3

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