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International Conference on Formal Concept Analysis

ICFCA 2005: Formal Concept Analysis pp 391–402Cite as

Planarity of Lattices

An Approach Based on Attribute Additivity

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 3403)

Abstract

Popular lattice drawing algorithms do not take planarity into account and find plane diagrams mainly heuristically. We present a characterization of planar lattices based on a theorem of Dushnik and Miller [4] and the “left”-relation introduced by Kelly and Rival [6]. In particular, our work is helpful for drawing plane attribute additive diagrams.

Keywords

  • Linear Order
  • Planar Lattice
  • Concept Lattice
  • Maximal Chain
  • Lattice Element

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Baker, K.A., Fishburn, P., Roberts, F.S.: Partial Orders of Dimension 2. Networks 2, 11–28 (1971)

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  2. Birkhoff, G.: Lattice Theory, 3rd edn. Amer. Math. Soc., Providence (1967)

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  4. Dushnik, B., Miller, E.W.: Partially Ordered Sets. Amer. J. Math. 63, 600–610 (1941)

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  5. Eades, P.: A Heuristic for Graph Drawing. Congressus Numerantium 42, 149–160 (1984)

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  6. Kelly, D., Rival, I.: Planar Lattices. Can. J. Math. 27(3), 636–665 (1975)

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  7. Ganter, B., Wille, R.: Formal Concept Analysis. Springer, Heidelberg (1999)

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  8. Skorsky, M.: Endliche Verbände - Diagramme und Eigenschaften. PhD thesis, TH Darmstadt (1992)

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  9. Zschalig, C.: Ein Force Directed Placement Algorithmus zum Zeichnen von Liniendiagrammen von Verbänden. Diploma Thesis, TU Dresden (2002)

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Author information

Authors and Affiliations

  1. Institut für Algebra, TU Dresden, Germany

    Christian Zschalig

Authors
  1. Christian Zschalig
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Editor information

Editors and Affiliations

  1. Institute of Algebra, University of Technology, Dresden, Germany

    Bernhard Ganter

  2. Département d’informatique, UQAM, P.O. Box, Montréal, (Qc), Canada

    Robert Godin

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© 2005 Springer-Verlag Berlin Heidelberg

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Zschalig, C. (2005). Planarity of Lattices. In: Ganter, B., Godin, R. (eds) Formal Concept Analysis. ICFCA 2005. Lecture Notes in Computer Science(), vol 3403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32262-7_27

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  • DOI: https://doi.org/10.1007/978-3-540-32262-7_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24525-4

  • Online ISBN: 978-3-540-32262-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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