A near-optimal algorithm for gossiping in a d-dimensional mesh bus interconnection network

We present a near-optimal algorithm for gossiping in a d-dimensional mesh interconnection network (for arbitrary d⩾2) of busses, under the assumptions that a processor may send/receive simultaneously on all its ports, and message transmission takes unit time regardless of length. For d>2, this significantly improves the known upper bound for gossiping on the d-dimensional mesh bus. The algorithm has an interesting geometric characterization for d=3. We speculate on a possible improvement which, if realizable, would make the algorithm optimal for d=3