Consider $n$ points and a distance function $d$ that satisfies the triangle inequality. We are also given a number $r$.
Each point $p$ defines a set $B_p$ (or a ball) that covers all other points that lie within a distance $r$ from $p$. Find $k$ sets (or balls) that covers the most number of points.
Obviously, we could find a $1-1/e$ approximation (via greedy) as this is a special case of the maximum $k$-set coverage problem.
But is there a hardness result for this problem? I would also like to consider the Euclidean distance case.