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On k-Plane Insertion into Plane Drawings

Authors Julia Katheder , Philipp Kindermann , Fabian Klute , Irene Parada , Ignaz Rutter

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LIPIcs.GD.2024.35.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatoric problems
Keywords
  • Graph drawing
  • edge insertion
  • k-planarity

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Abstract

We introduce the k-Plane Insertion into Plane drawing (k-PIP) problem: given a plane drawing of a planar graph G and a set F of edges, insert the edges in F into the drawing such that the resulting drawing is k-plane. In this paper, we show that the problem is NP-complete for every k ≥ 1, even when G is biconnected and the set F of edges forms a matching or a path. On the positive side, we present a linear-time algorithm for the case that k = 1 and G is a triangulation.

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Julia Katheder, Philipp Kindermann, Fabian Klute, Irene Parada, and Ignaz Rutter. On k-Plane Insertion into Plane Drawings. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 35:1-35:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.GD.2024.35

Author Details

Julia Katheder
  • Universität Tübingen, Germany
Philipp Kindermann
  • Universität Trier, Germany
Fabian Klute
  • Universitat Politècnica de Catalunya, Barcelona, Spain
Irene Parada
  • Department of Mathematics, Universitat Politècnica de Catalunya, Barcelona, Spain
Ignaz Rutter
  • Universität Passau, Germany

Funding

  • Katheder, Julia: Funded by the Deutsche Forschungsgemeinschaft (DFG) - 364468267.
  • Klute, Fabian: F. K. is supported by a “María Zambrano grant for attracting international talent” and by grant PID2019-104129GB-I00 funded by MICIU/AEI/10.13039/501100011033.
  • Parada, Irene: I. P. is a Serra Húnter Fellow. Partially supported by grant 2021UPC-MS-67392 funded by the Spanish Ministry of Universities and the European Union (NextGenerationEU) and by grant PID2019-104129GB-I00 funded by MICIU/AEI/10.13039/501100011033.
  • Rutter, Ignaz: Funded by the Deutsche Forschungsgemeinschaft (DFG) - 541433306.

References

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