Gossiping in meshes in all-port mode and with short packets

Abstract

Gossiping is the communication problem in which each node has a unique message to be transmitted to every other node. The nodes exchange their message by packets. A solution to the problem is judged by how many rounds of packet sending it requires. In this thesis, we consider the version of the problem in which small-size packets each carrying exactly one message are used. The nodes of the target meshes are assumed to be all-port (a node's incident edges can all be active at the same time); and their edges are either half-duplex or full-duplex, also known as the H* model and the F* model respectively. We study the class of 2D meshes. Soch and Tvrdik (SIROCCO'97, pp. 253–265; Tech. rep. DC-97-04, Dept. of CS&E, Czech Technical University) have obtained optimal algorithms for the F* model (for square or nonsquare meshes). Lau and Zhang (IEEE Trans. on Parallel and Distributed Systems Vol. 13, No. 4, pp. 349–358, 2002) have obtained fast algorithms for the H* model. We present optimal algorithms for square meshes under both models, and a fast algorithm for general 2D meshes under the H* model. All of these algorithms route messages along the shortest paths. Note that for the F* model, although Soch and Tvrdik have optimally solved the problem, we present yet another optimal F* algorithm because in square meshes there is an interesting property that the F* algorithm and the H* one route their messages along the same paths and in the same order—i.e., for any edge {u, v}, the i-th message from u to v under either model is the same message.