Circuit-Switched Gossiping in the 3-Dimensional Torus Networks

In this paper we describe, in the case of short messages, an efficient gossiping algorithm for 3-dimensional torus networks (wrap-around or toroidal meshes) that uses synchronous circuit-switched routing. The algorithm is based on a recursive decomposition of a torus. The algorithm requires an optimal number of rounds and a quasi-optimal number of intermediate switch settings to gossip in an $7^i \times 7^i \times 7^i$ torus.