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Parameterized Algorithms for Beyond-Planar Crossing Numbers

Authors Miriam Münch , Ignaz Rutter

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LIPIcs.GD.2024.25.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
Keywords
  • FPT
  • Beyond-planarity
  • Crossing-number
  • Crossing Patterns

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Abstract

Beyond-planar graph classes are usually defined via forbidden configurations or patterns in a drawing. In this paper, we formalize these concepts on a combinatorial level and show that, for any fixed family ℱ of crossing patterns, deciding whether a given graph G admits a drawing that avoids all patterns in F and that has at most c crossings is FPT w.r.t. c. In particular, we show that for any fixed k, deciding whether a graph is k-planar, k-quasi-planar, fan-crossing, fan-crossing-free or min-k-planar, respectively, is FPT with respect to the corresponding beyond-planar crossing number.

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Miriam Münch and Ignaz Rutter. Parameterized Algorithms for Beyond-Planar Crossing Numbers. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 25:1-25:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.GD.2024.25

Author Details

Miriam Münch
  • Faculty of Computer Science and Mathematics, University of Passau, Germany
Ignaz Rutter
  • Faculty of Computer Science and Mathematics, University of Passau, Germany

Funding

Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 541433306.

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