  We study the NP-hard problem of approximating a Minimum Routing Cost Spanning
Tree in the message passing model with limited bandwidth (CONGEST model). In
this problem one tries to find a spanning tree of a graph $G$ over $n$ nodes
that minimizes the sum of distances between all pairs of nodes. In the
considered model every node can transmit a different (but short) message to
each of its neighbors in each synchronous round. We provide a randomized
$(2+\epsilon)$-approximation with runtime $O(D+\frac{\log n}{\epsilon})$ for
unweighted graphs. Here, $D$ is the diameter of $G$. This improves over both,
the (expected) approximation factor $O(\log n)$ and the runtime $O(D\log^2 n)$
of the best previously known algorithm.
  Due to stating our results in a very general way, we also derive an (optimal)
runtime of $O(D)$ when considering $O(\log n)$-approximations as done by the
best previously known algorithm. In addition we derive a deterministic
$2$-approximation.
