关于在平面图中插入 $k$ 平面

arXiv - CS - Computational Geometry Pub Date : 2024-02-22 DOI:arxiv-2402.14552

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

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引用次数: 0

摘要

我们引入了 $k$-Plane Insertion into Plane drawing（$k$-PIP）问题：给定一个平面图的平面图 $G$ 和一组边 $F$，将 $F$ 中的边插入到平面图中，这样得到的平面图就是 $k$-平面图。在本文中，我们将重点讨论 $1$-PIP情形。我们针对 $G$ 是三角形的情况提出了一种线性时间算法，同时证明了 $G$ 是双连接且 $F$ 构成路径或匹配的情况下的线性时间完备性。

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On $k$-Plane Insertion into Plane Drawings

We introduce the $k$-Plane Insertion into Plane drawing ($k$-PIP) problem: given a plane drawing of a planar graph $G$ and a set of edges $F$, insert the edges in $F$ into the drawing such that the resulting drawing is $k$-plane. In this paper, we focus on the $1$-PIP scenario. We present a linear-time algorithm for the case that $G$ is a triangulation, while proving NP-completeness for the case that $G$ is biconnected and $F$ forms a path or a matching.

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arXiv - CS - Computational Geometry

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