Author ORCID Identifier
Haitao Wang https://orcid.org/0000-0001-8134-7409
37th International Symposium on Computational Geometry
Leibniz International Proceedings in Informatics
NSF, Division of Computing and Communication Foundations (CCF) 2005323
NSF, Division of Computing and Communication Foundations (CCF)
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
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.
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.