On $k$-Plane Insertion into Plane Drawings
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913492537180160 |
|---|---|
| author | Katheder, Julia Kindermann, Philipp Klute, Fabian Parada, Irene Rutter, Ignaz |
| author_facet | Katheder, Julia Kindermann, Philipp Klute, Fabian Parada, Irene Rutter, Ignaz |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14552 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $k$-Plane Insertion into Plane Drawings Katheder, Julia Kindermann, Philipp Klute, Fabian Parada, Irene Rutter, Ignaz Computational Geometry 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. |
| title | On $k$-Plane Insertion into Plane Drawings |
| topic | Computational Geometry |
| url | https://arxiv.org/abs/2402.14552 |