  We present a time-optimal deterministic distributed algorithm for
approximating a minimum weight vertex cover in hypergraphs of rank $f$. This
problem is equivalent to the Minimum Weight Set Cover Problem in which the
frequency of every element is bounded by $f$. The approximation factor of our
algorithm is $(f+\epsilon)$. Let $\Delta$ denote the maximum degree in the
hypergraph. Our algorithm runs in the CONGEST model and requires
$O(\log{\Delta} / \log \log \Delta)$ rounds, for constants $\epsilon \in (0,1]$
and $f\in\mathbb N^+$. This is the first distributed algorithm for this problem
whose running time does not depend on the vertex weights or the number of
vertices. Thus adding another member to the exclusive family of \emph{provably
optimal} distributed algorithms.
  For constant values of $f$ and $\epsilon$, our algorithm improves over the
$(f+\epsilon)$-approximation algorithm of \cite{KuhnMW06} whose running time is
$O(\log \Delta + \log W)$, where $W$ is the ratio between the largest and
smallest vertex weights in the graph.
