Worm-Hole Gossiping on Meshes

Several algorithms for performing gossiping on one-and higher dimensional meshes are presented. As a routing model, we assume the practically important worm-hole routing. For one-dimensional arrays, we give a novel lower bound and an asymptotically optimal gossiping algorithm. For two-dimensional meshes, we present a simple algorithm composed of one-dimensional phases. For an important range of packet and mesh sizes, it gives clear improvements. The algorithm is analyzed theoretically, but, the achieved improvements are also convincingly demonstrated by simulations and by an implementation on the Paragon. For higher dimensional meshes, we give algorithms which are based on a generalized notion of a diagonal.