Shortest Path Separators in Unit Disk Graphs
Computational Geometry
2024-07-24 v1 Data Structures and Algorithms
Abstract
We introduce a new balanced separator theorem for unit-disk graphs involving two shortest paths combined with the 1-hop neighbours of those paths and two other vertices. This answers an open problem of Yan, Xiang and Dragan [CGTA '12] and improves their result that requires removing the 3-hop neighborhood of two shortest paths. Our proof uses very different ideas, including Delaunay triangulations and a generalization of the celebrated balanced separator theorem of Lipton and Tarjan [J. Appl. Math. '79] to systems of non-intersecting paths.
Keywords
Cite
@article{arxiv.2407.15980,
title = {Shortest Path Separators in Unit Disk Graphs},
author = {Elfarouk Harb and Zhengcheng Huang and Da Wei Zheng},
journal= {arXiv preprint arXiv:2407.15980},
year = {2024}
}
Comments
To appear in ESA 2024. 15 pages, 7 figures