1. On $k$-Plane Insertion into Plane Drawings
- Author
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Katheder, Julia, Kindermann, Philipp, Klute, Fabian, Parada, Irene, and Rutter, Ignaz
- Subjects
Computer Science - Computational Geometry - 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.
- Published
- 2024