A fast 25/6-approximation for the minimum unit disk cover problem

TL;DR

This paper introduces a fast approximation algorithm for the minimum unit disk cover problem in 2D, achieving a 25/6-approximation in Euclidean norm with efficient runtime, extending to Lp norms.

Contribution

The paper presents a simple, efficient algorithm with a provable approximation factor for covering points with unit disks, improving speed over existing methods.

Findings

Approximation factor of 25/6 in Euclidean norm

Runtime of O(n log n), space O(n)

Extends to any Lp norm and outperforms existing algorithms

Abstract

Given a point set P in 2D, the problem of finding the smallest set of unit disks that cover all of P is NP-hard. We present a simple algorithm for this problem with an approximation factor of 25/6 in the Euclidean norm and 2 in the max norm, by restricting the disk centers to lie on parallel lines. The run time and space of this algorithm is O(n log n) and O(n) respectively. This algorithm extends to any Lp norm and is asymptotically faster than known alternative approximation algorithms for the same approximation factor.