A Bicriteria Approximation Scheme for the Minimum Well-Separated Pair Decomposition

A well-separated pair decomposition (WSPD) of a set $P$ of $n$ points covers all $\binom{n}{2}$ pairs of points by a family of dumbbells $\{X,Y\}$, each covering the pairs of $X\times Y$, such that the diameters of $X$ and $Y$ are at most an $\varepsilon$-fraction of their distance. In $\mathbb{R}^d