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arXiv · 2402.14552

On $k$-Plane Insertion into Plane Drawings

Julia Katheder·Philipp Kindermann·Fabian Klute·Irene Parada·Ignaz Rutter
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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 $k\ge 1$, 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, Ignaz Rutter. 2024-02-22. On $k$-Plane Insertion into Plane Drawings. https://arxiv.org/abs/2402.14552

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