Existence of an optimal perpetual gossiping scheme for arbitrary networks

Abstract

Gossiping is a problem in which a peer-to-peer network must disperse the information held by each machine to all other machines in the minimum number of communication steps. In perpetual gossiping, new information may be introduced to any machine at any time, and the objective is to find a perpetual communication scheme which guarantees that new information will be completely dispersed in optimal time. The basic gossiping problem has a well-known solution, but the perpetual gossiping extension has defied a general solution. Additionally, prior to this paper, it has not been shown that there is even a means to arrive at an optimal solution on a case-by-case basis. Attempts at optimization have thus far taken place in a series of progressive refinements, broadening the scope of network topologies for which optimal or near-optimal solutions are known. This paper proceeds from the opposite direction, by demonstrating an algorithm which is guaranteed to find an optimal perpetual gossiping scheme for an arbitrary graph. The network model is then generalized so as to apply to a broader class of communication schemes.