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International Conference on Formal Concept Analysis

ICFCA 2021: Formal Concept Analysis pp 224–240Cite as

Force-Directed Layout of Order Diagrams Using Dimensional Reduction

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 12733)

Abstract

Order diagrams allow human analysts to understand and analyze structural properties of ordered data. While an expert can create easily readable order diagrams, the automatic generation of those remains a hard task. In this work, we adapt force-directed approaches, which are known to generate aesthetically-pleasing drawings of graphs, to the realm of order diagrams. Our algorithm ReDraw thereby embeds the order in a high dimension and then iteratively reduces the dimension until a two-dimensional drawing is achieved. To improve aesthetics, this reduction is equipped with two force-directed steps where one step optimizes the distances of nodes and the other one the distances of lines in order to satisfy a set of a priori fixed conditions. By respecting an invariant about the vertical position of the elements in each step of our algorithm we ensure that the resulting drawings satisfy all necessary properties of order diagrams. Finally, we present the results of a user study to demonstrate that our algorithm outperforms comparable approaches on drawings of lattices with a high degree of distributivity.

Keywords

  • Ordered sets
  • Order diagram drawing
  • Lattice drawing
  • Force-directed algorithms
  • Dimensional reduction
  • Graph drawing

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Notes

  1. 1.

    https://github.com/domduerr/redraw.

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Author information

Authors and Affiliations

  1. Knowledge and Data Engineering Group, University of Kassel, Kassel, Germany

    Dominik Dürrschnabel & Gerd Stumme

  2. Interdisciplinary Research Center for Information System Design, University of Kassel, Kassel, Germany

    Dominik Dürrschnabel & Gerd Stumme

Authors
  1. Dominik Dürrschnabel
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  2. Gerd Stumme
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Corresponding author

Correspondence to Dominik Dürrschnabel .

Editor information

Editors and Affiliations

  1. ICube, University of Strasbourg, Illkirch, France

    Agnès Braud

  2. NRU Higher School of Economics, Perm, Russia

    Aleksey Buzmakov

  3. University of Kassel, Kassel, Germany

    Tom Hanika

  4. ICube, University of Strasbourg, Illkirch, France

    Florence Le Ber

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Dürrschnabel, D., Stumme, G. (2021). Force-Directed Layout of Order Diagrams Using Dimensional Reduction. In: Braud, A., Buzmakov, A., Hanika, T., Le Ber, F. (eds) Formal Concept Analysis. ICFCA 2021. Lecture Notes in Computer Science(), vol 12733. Springer, Cham. https://doi.org/10.1007/978-3-030-77867-5_14

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  • DOI: https://doi.org/10.1007/978-3-030-77867-5_14

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