Computing a Geodesic Two-Center of Points in a Simple Polygon

TL;DR

This paper introduces the first exact algorithm for efficiently computing an optimal two-center in a simple polygon based on geodesic distances, addressing a specific case of the geodesic k-center problem.

Contribution

It presents the first efficient exact algorithm for the geodesic 2-center problem in a simple polygon, advancing computational geometry methods.

Findings

Developed an exact algorithm for the geodesic 2-center problem.

Algorithm efficiently computes optimal centers within a simple polygon.

Addresses a previously unresolved case in geodesic k-center problems.

Abstract

Given a simple polygon $P$ and a set $Q$ of points contained in $P$, we consider the geodesic $k$-center problem where we want to find $k$ points, called \emph{centers}, in $P$ to minimize the maximum geodesic distance of any point of $Q$ to its closest center. In this paper, we focus on the case for $k=2$ and present the first exact algorithm that efficiently computes an optimal $2$-center of $Q$ with respect to the geodesic distance in $P$.