Covering the Boundary of a Simple Polygon with Geodesic Unit Disks

TL;DR

This paper introduces an efficient approximation algorithm for covering the boundary of a simple polygon with the fewest geodesic unit disks, achieving a 2-approximation in near-linear time.

Contribution

It presents the first O(n log^2 n + k) time 2-approximation algorithm for this boundary covering problem.

Findings

Algorithm runs in O(n log^2 n + k) time.

Achieves a 2-approximation ratio.

Effective for polygons with complex boundaries.

Abstract

We consider the problem of covering the boundary of a simple polygon on n vertices using the minimum number of geodesic unit disks. We present an O(n \log^2 n+k) time 2-approximation algorithm for finding the centers of the disks, with k denoting the number centers found by the algorithm.