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On Point Set Embeddings for k-Planar Graphs with Few Bends per Edge

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SOFSEM 2019: Theory and Practice of Computer Science (SOFSEM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11376))

Abstract

We consider the point set embedding problem (PSE) for 1-, 2- and k-planar graphs where at most 1, 2, or k crossings resp. are allowed for each edge which greatly extends the well-researched class of planar graphs. For any set of n points and any given embedded graph that belongs to one of the above graph classes, we compute a 1-to-1 mapping of the vertices to the points such that the edges can be routed using only a limited number of bends according to the given embedding and the sequences of crossings. Surprisingly, for the class of 1-planar graphs the same results can be achieved as the best known results for planar graphs. Additionally for k-planar graphs, the bounds are also much better than expected from the first sight.

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Acknowledgement

The author wishes to thanks the participants of the GNV workshop in Heiligkreuztal 2018 for inspiring discussions.

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Authors and Affiliations

  1. Wilhelm-Schickhard-Institut für Informatik, Universität Tübingen, Tübingen, Germany

    Michael Kaufmann

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  1. Michael Kaufmann
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Correspondence to Michael Kaufmann .

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Editors and Affiliations

  1. University of Genoa, Genoa, Italy

    Barbara Catania

  2. Comenius University, Bratislava, Slovakia

    Rastislav Královič

  3. Poznań University of Technology, Poznań, Poland

    Jerzy Nawrocki

  4. Università degli Studi di Milano, Milan, Italy

    Giovanni Pighizzini

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Kaufmann, M. (2019). On Point Set Embeddings for k-Planar Graphs with Few Bends per Edge. In: Catania, B., Královič, R., Nawrocki, J., Pighizzini, G. (eds) SOFSEM 2019: Theory and Practice of Computer Science. SOFSEM 2019. Lecture Notes in Computer Science(), vol 11376. Springer, Cham. https://doi.org/10.1007/978-3-030-10801-4_21

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  • DOI: https://doi.org/10.1007/978-3-030-10801-4_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10800-7

  • Online ISBN: 978-3-030-10801-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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