  We study a clustering problem where the goal is to maximize the coverage of
the input points by $k$ chosen centers. Specifically, given a set of $n$ points
$P \subseteq \mathbb{R}^d$, the goal is to pick $k$ centers $C \subseteq
\mathbb{R}^d$ that maximize the service $ \sum_{p \in P}\mathsf{\varphi}\bigl(
\mathsf{d}(p,C) \bigr) $ to the points $P$, where $\mathsf{d}(p,C)$ is the
distance of $p$ to its nearest center in $C$, and $\mathsf{\varphi}$ is a
non-increasing service function $\mathsf{\varphi} : \mathbb{R}^+ \to
\mathbb{R}^+$. This includes problems of placing $k$ base stations as to
maximize the total bandwidth to the clients -- indeed, the closer the client is
to its nearest base station, the more data it can send/receive, and the target
is to place $k$ base stations so that the total bandwidth is maximized. We
provide an $n^{\varepsilon^{-O(d)}}$ time algorithm for this problem that
achieves a $(1-\varepsilon)$-approximation. Notably, the runtime does not
depend on the parameter $k$ and it works for an arbitrary non-increasing
service function $\mathsf{\varphi} : \mathbb{R}^+ \to \mathbb{R}^+$.
