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Parameterized Approaches to Orthogonal Compaction

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SOFSEM 2023: Theory and Practice of Computer Science (SOFSEM 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13878))

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Abstract

Orthogonal graph drawings are used in applications such as UML diagrams, VLSI layout, cable plans, and metro maps. We focus on drawing planar graphs and assume that we are given an that describes the desired shape, but not the exact coordinates of a drawing. Our aim is to compute an orthogonal drawing on the grid that has minimum area among all grid drawings that adhere to the given orthogonal representation.

This problem is called orthogonal compaction (OC) and is known to be NP-hard, even for orthogonal representations of cycles [Evans et al. 2022]. We investigate the complexity of OC with respect to several parameters. Among others, we show that OC is fixed-parameter tractable with respect to the most natural of these parameters, namely, the number of of the orthogonal representation: the presence of pairs of kitty corners in an orthogonal representation makes the OC problem hard. Informally speaking, a pair of kitty corners is a pair of reflex corners of a face that point at each other. Accordingly, the number of kitty corners is the number of corners that are involved in some pair of kitty corners.

This research was initiated at Dagstuhl Seminar 21293: Parameterized Complexity in Graph Drawing. Work partially supported by: (i) Dep. of Engineering, Perugia University, grant RICBA21LG: Algoritmi, modelli e sistemi per la rappresentazione visuale di reti, (ii) Engineering and Physical Sciences Research Council (EPSRC) grant EP/V007793/1, (vi) European Research Council (ERC) grant termed PARAPATH.

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Authors and Affiliations

  1. Universitá degli Studi di Perugia, Perugia, Italy

    Walter Didimo & Giuseppe Liotta

  2. University of Warwick, Coventry, UK

    Siddharth Gupta

  3. Universität Trier, Trier, Germany

    Philipp Kindermann

  4. Universität Würzburg, Würzburg, Germany

    Alexander Wolff

  5. Ben-Gurion University of the Negev, Beersheba, Israel

    Meirav Zehavi

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  1. Walter Didimo
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  2. Siddharth Gupta
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  4. Giuseppe Liotta
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  5. Alexander Wolff
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  6. Meirav Zehavi
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Correspondence to Siddharth Gupta .

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  1. University of Liverpool, Liverpool, UK

    Leszek Gąsieniec

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Didimo, W., Gupta, S., Kindermann, P., Liotta, G., Wolff, A., Zehavi, M. (2023). Parameterized Approaches to Orthogonal Compaction. In: Gąsieniec, L. (eds) SOFSEM 2023: Theory and Practice of Computer Science. SOFSEM 2023. Lecture Notes in Computer Science, vol 13878. Springer, Cham. https://doi.org/10.1007/978-3-031-23101-8_8

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