  We consider the following natural problem that generalizes min-sum-radii
clustering: Given is $k\in\mathbb{N}$ as well as some metric space $(V,d)$
where $V=F\cup C$ for facilities $F$ and clients $C$. The goal is to find a
clustering given by $k$ facility-radius pairs $(f_1,r_1),\dots,(f_k,r_k)\in
F\times\mathbb{R}_{\geq 0}$ such that $C\subseteq B(f_1,r_1)\cup\dots\cup
B(f_k,r_k)$ and $\sum_{i=1,\dots,k} g(r_i)$ is minimized for some increasing
function $g:\mathbb{R}_{\geq 0}\rightarrow\mathbb{R}_{\geq 0}$. Here, $B(x,r)$
is the radius-$r$ ball centered at $x$. For the case that $(V,d)$ is the
shortest-path metric of some edge-weighted graph of bounded treewidth, we
present a dynamic program that is tailored to this class of problems and
achieves a polynomial running time, establishing that the problem is in
$\mathsf{XP}$ with parameter treewidth.
