Covering Convex Polygons by Two Congruent Disks

TL;DR

This paper introduces an efficient $O(n ext{log}n)$ algorithm for covering convex polygons with two congruent disks, improving the computational complexity over previous methods.

Contribution

The paper presents the first $O(n ext{log}n)$ algorithm for the convex polygon two-center problem, enhancing efficiency in computational geometry.

Findings

Achieved $O(n ext{log}n)$ time complexity for the problem

Improved upon previous algorithms' efficiency

Provides a practical solution for covering convex polygons with two disks

Abstract

We consider the planar two-center problem for a convex polygon: given a convex polygon in the plane, find two congruent disks of minimum radius whose union contains the polygon. We present an $O(n\log n)$-time algorithm for the two-center problem for a convex polygon, where $n$ is the number of vertices of the polygon. This improves upon the previous best algorithm for the problem.