Document Type
Conference Paper
Author ORCID Identifier
Haitao Wang https://orcid.org/0000-0001-8134-7409
Journal/Book Title/Conference
37th International Symposium on Computational Geometry
Publisher
Leibniz International Proceedings in Informatics
Publication Date
2-6-2021
Award Number
NSF, Division of Computing and Communication Foundations (CCF) 2005323
Funder
NSF, Division of Computing and Communication Foundations (CCF)
First Page
1
Last Page
15
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Abstract
Given a set S of m point sites in a simple polygon P of n vertices, we consider the problem of computing the geodesic farthest-point Voronoi diagram for S in P. It is known that the problem has an Ω(n + m log m) time lower bound. Previously, a randomized algorithm was proposed [Barba, SoCG 2019] that can solve the problem in O(n + m log m) expected time. The previous best deterministic algorithms solve the problem in O(n log log n + m log m) time [Oh, Barba, and Ahn, SoCG 2016] or in O(n + m log m + m log2 n) time [Oh and Ahn, SoCG 2017]. In this paper, we present a deterministic algorithm of O(n + m log m) time, which is optimal. This answers an open question posed by Mitchell in the Handbook of Computational Geometry two decades ago.
Recommended Citation
Wang, Haitao. “An Optimal Deterministic Algorithm for Geodesic Farthest-Point Voronoi Diagrams in Simple Polygons.” ArXiv:2103.00076 [Cs], May 2021. arXiv.org, http://arxiv.org/abs/2103.00076.
