  This paper presents a near-optimal distributed approximation algorithm for
the minimum-weight connected dominating set (MCDS) problem. The presented
algorithm finds an $O(\log n)$ approximation in $\tilde{O}(D+\sqrt{n})$ rounds,
where $D$ is the network diameter and $n$ is the number of nodes.
  MCDS is a classical NP-hard problem and the achieved approximation factor
$O(\log n)$ is known to be optimal up to a constant factor, unless P=NP.
Furthermore, the $\tilde{O}(D+\sqrt{n})$ round complexity is known to be
optimal modulo logarithmic factors (for any approximation), following [Das
Sarma et al.---STOC'11].
