Document Type

Conference Paper

Author ORCID Identifier

Haitao Wang

Journal/Book Title/Conference

37th International Symposium on Computational Geometry


Leibniz International Proceedings in Informatics

Publication Date


Award Number

NSF, Division of Computing and Communication Foundations (CCF) 2005323


NSF, Division of Computing and Communication Foundations (CCF)

First Page


Last Page


Creative Commons License

Creative Commons Attribution 4.0 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.