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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)


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.


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

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  • DOI: 10.1007/978-3-030-77867-5_14
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Correspondence to Dominik Dürrschnabel .

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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.

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