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A Peep through the Looking Glass: Articulation Points in Lattices

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Formal Concept Analysis (ICFCA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7278))

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Abstract

We define as an ’articulation point’ in a lattice an element which is comparable to all the other elements, but is not extremum.

We investigate a property which holds for both the lattice of a binary relation and for the lattice of the complement relation (which we call the mirror relation): one has an articulation point if and only if the other has one also.

We give efficient algorithms to generate all the articulation points. We discuss artificially creating such an articulation point by adding or removing crosses of the relation, and also creating a chain lattice.

We establish the strong relationships with bipartite and co-bipartite graphs; in particular, we derive efficient algorithms to compute a minimal triangulation and a maximal sub-triangulation of a co-bipartite graph, as well as to find the clique minimal separators and the corresponding decomposition.

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Author information

Authors and Affiliations

  1. LIMOS UMR CNRS 6158 Ensemble Scientifique des Cézeaux, Université Blaise Pascal, 63 173, Aubière, France

    Anne Berry & Alain Sigayret

Authors
  1. Anne Berry
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  2. Alain Sigayret
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Editor information

Editors and Affiliations

  1. Computer Science Department, University of Nicosia, 46 Makedonitissas Ave., 1700, Nicosia, Cyprus

    Florent Domenach

  2. Higher School of Economics, National Research University, Pokrovsky Boulevard, 109028, Moscow, Russia

    Dmitry I. Ignatov

  3. Faculty of Business and Economics, Katholieke Universiteit Leuven, Naamsestraat 69, 3000, Leuven, Belgium

    Jonas Poelmans

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© 2012 Springer-Verlag Berlin Heidelberg

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Berry, A., Sigayret, A. (2012). A Peep through the Looking Glass: Articulation Points in Lattices. In: Domenach, F., Ignatov, D.I., Poelmans, J. (eds) Formal Concept Analysis. ICFCA 2012. Lecture Notes in Computer Science(), vol 7278. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29892-9_10

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  • DOI: https://doi.org/10.1007/978-3-642-29892-9_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29891-2

  • Online ISBN: 978-3-642-29892-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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