Dispersion in Unit Disks

Adrian Dumitrescu & Minghui Jiang
We present two new approximation algorithms with (improved) constant ratios for selecting $n$ points in $n$ unit disks such that the minimum pairwise distance among the points is maximized. (I) A very simple $O(n \log{n})$-time algorithm with ratio $0.5110$ for disjoint unit disks. In combination with an algorithm of Cabello~\cite{Ca07}, it yields a $O(n^2)$-time algorithm with ratio of $0.4487$ for dispersion in $n$ not necessarily disjoint unit disks. (II) A more sophisticated LP-based algorithm with...