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+ϵ)-approximation with runtime O(D+ϵlogn) for
unweighted graphs. Here, D is the diameter of G. This improves over both,
the (expected) approximation factor O(logn) and the runtime O(Dlog2n)
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(logn)-approximations as done by the
best previously known algorithm. In addition we derive a deterministic
2-approximation