  We present a new algorithm, which solves the problem of distributively
finding a minimum diameter spanning tree of any (non-negatively) real-weighted
graph $G = (V,E,\omega)$. As an intermediate step, we use a new, fast,
linear-time all-pairs shortest paths distributed algorithm to find an absolute
center of $G$. The resulting distributed algorithm is asynchronous, it works
for named asynchronous arbitrary networks and achieves $\mathcal{O}(|V|)$ time
complexity and $\mathcal{O}\left(|V|\,|E|\right)$
