Gossiping in cayley graphs by packets

Abstract

Gossiping (also called total exchange or all-to-all communication) is the process of information diffusion in which each node of a network holds a packet that must be communicated to all other nodes in the network. We consider here gossiping in the store- and-forward, full-duplex and Δ-port (or shouting) model. In such a model, the protocol consists of a sequence of rounds and during each round, each node can send (and receive) messages from all its neighbors. The great majority of the previous works on gossiping problems allows the messages to be freely concatenated and so messages of arbitrary length can be transmitted during a round. Here we restrict the problem to the case where at each round communicating nodes can exchange exactly one packet. We give a lower bound of N−1/δ, where δ is the minimum degree, and show that it is attained in Cayley symmetric digraphs with some additional properties. That implies the existence of an optimal gossiping protocol for classical networks like hypercubes, k-dimensional tori, and star-graphs. Furthermore we introduce the notion of complete rotation in Cayley symmetric digraphs which appears to be an interesting property worth of study in itself.

That work was supported by the French GDR/PRC PRS and by the Galileo cooperation project with the University of Salerno