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 $\Omega(n+m\log m)$ 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 $O(n+m\log m+m\log^2 n)$ 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.

翻译：考虑到在简单多边形的1美元顶点中设定的1美元美元点点位置,我们考虑用1美元计算远点地缘Voronoi图表的问题。众所周知,问题有1美元=Omega(n+m\log m)美元,时间约束较低。以前,提出了[Barba, SoCG 20199]的随机算法,该算法可以用预期时间(n+m=m美元)解决问题。以前的最佳确定算法用美元(n\log n+m)解决了问题。这是在20年前的《罗马测量手册》中米切尔提出的一个未决问题。