An Optimal Deterministic Algorithm for Geodesic Farthest-Point Voronoi Diagrams in Simple Polygons

Given in the plane a set S of m point sites simple polygon P n vertices, we consider problem computing geodesic farthest-point Voronoi diagram for P. It is known that has an $$\Omega (n+m\log m)$$ time lower bound. Previously, randomized algorithm was proposed [Barba, SoCG 2019] solves $$O(n+m\log expected time. The previous best deterministic algorithms solve $$O(n\log \log n+ m\log [Oh, Barba, and Ahn, 2016] or m+m\log ^2\!n)$$ [Oh 2017]. In this paper, present takes time, which optimal. This answers affirmatively open question posed by Mitchell Handbook Computational Geometry two decades ago.