On Gossip and Populations

Gossip protocols are simple, robust and scalable and have been consistently applied to many (mostly wired) distributed systems. Nevertheless, most validation in this area has been empirical so far and there is a lack of a theoretical counterpart to characterize what can and cannot be computed with gossip protocols. Population protocols, on the other hand, benefit from a sound theoretical framework but little empirical evaluation. In this paper, we establish a correlation between population and gossip-based protocols. We propose a classification of gossip-based protocols, based on the nature of the underlying peer sampling service. First, we show that the class of gossip protocols, where each node relies on an arbitrary sample, is equivalent to population protocols. Second, we show that gossip-based protocols, relying on a more powerful peer sampling service providing peers using a clearly identified set of other peers, are equivalent to community protocols, a modern variant of population protocols. Leveraging the resemblances between population and gossip protocols enables to provide a theoretical framework for distributed systems where global behaviors emerge from a set of local interactions, both in wired and wireless settings. The practical validations of gossip-protocols provide empirical evidence of quick convergence times of such algorithms and demonstrate their practical relevance. While existing results in each area can be immediately applied, this also leaves the space to transfer any new results, practical or theoretical, from one domain to the other.