Shortest Path Separators in Unit Disk Graphs

Autor:	Harb, Elfarouk, Huang, Zhengcheng, Zheng, Da Wei
Rok vydání:	2024
Předmět:	Computer Science - Computational Geometry Computer Science - Data Structures and Algorithms
Druh dokumentu:	Working Paper
Popis:	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. Comment: To appear in ESA 2024. 15 pages, 7 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2407.15980 Zobrazit plný text záznamu View this record from Arxiv