Approximation algorithms for the unit disk cover problem in 2D and 3D

Given a set P of n points in the plane, we consider the problem of covering P with a minimum number of unit disks. This problem is known to be NP-hard. We present a simple 4-approximation algorithm for this problem which runs in O(nlog⁡n)-time. We also show how to extend this algorithm to other metrics, and to three dimensions.