Experiments with Unit Disk Cover Algorithms for Covering Massive Pointsets

Abstract: Given a set of $n$ points in the plane, the Unit Disk Cover (UDC) problem asks to compute the minimum number of unit disks required to cover the points, along with a placement of the disks. The problem is NP-hard and several approximation algorithms have been designed over the last three decades. In this paper, we have engineered and experimentally compared practical performances of some of these algorithms on massive pointsets. The goal is to investigate which algorithms run fast and give good approximation in practice. We present a simple $7$-approximation algorithm for UDC that runs in $O(n)$ expected time and uses $O(s)$ extra space, where $s$ denotes the size of the generated cover. In our experiments, it turned out to be the speediest of all. We also present two heuristics to reduce the sizes of covers generated by it without slowing it down by much. To our knowledge, this is the first work that experimentally compares geometric covering algorithms. Experiments with them using massive pointsets (in the order of millions) throw light on their practical uses. We share the engineered algorithms via GitHub - https://github.com/ghoshanirban/UnitDiskCoverAlgorithms for broader uses and future research in the domain of geometric optimization.