Bridging the Gap between Population and Gossip-based Protocols

Gossip-based protocols are simple, robust and scalable and have been consistently applied in many distributed, mostly wired, settings. Most validation in this area has been so far empirical and there is a clear lack of a theoretical counterpart clearly defining what can and cannot be computed with gossip-based protocols. Population protocols, on the other hand, provide a clear and formal model for mobile sensor networks, capturing their power and limitations. In this paper, we establish a correlation between population and gossip-based protocols. Studying the equivalence between them, 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 providing peers using a clearly identified set of other peers, are equivalent to community protocols, a variant of population protocols. Leveraging the resemblances between these areas enables to provide a theoretical framework for distributed systems where global behaviours emerge from a set of local interactions, both in wired and wireless settings. Likewise, 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. As an application of this possibility, we also propose a new result in the area of population protocols and show that a uniform distribution of interactions is optimal for population and community protocols with respect to convergence time. Consequently, we can conclude that the gossip-based random peer sampling service provides such an optimal sampling for gossip-based protocols, corroborating practical evidences. Key-words: Population protocols, Gossip-based protocols, Community protocols, Theoretical analysis, Equivalence, Complexity. ∗ IRISA / Université de Rennes 1 † IRISA / INSA Rennes ‡ IRISA / INRIA Rennes – Bretagne Atlantique in ria -0 03 38 09 8, v er si on 1 11 N ov 2 00 8 Combler le fossé entre les protocoles épidémiques et de populations Résumé : Les contributions de ce rapport de recherche proviennent de multiples observations. Principalement, nous avons constaté que les protocoles de population en général et les protocoles épidémiques, présentés ci-après, possèdent de nombreuses ressemblances, bien que les uns soient issus d’une approche théorique et les autres aient une origine plus pratique. Ceci nous mène à proposer une première classification de ces protocoles épidémiques. Inspirés de cette remarque, nous présentons ensuite les motivations qui nous ont menés aux résultats de ce chapitre. Puis, après avoir étendu notre classification en une seconde à granularité plus fine, nous montrons les relations d’équivalence existantes entre tous ces modèles. Nous concluons ce rapport de recherche par divers exemples de transfert de contributions issues d’un domaine vers l’autre. Mots-clés : Protocoles de population, Protocoles épidémiques, Protocoles de communauté, Analyse théorique, Équivalence, Complexité. in ria -0 03 38 09 8, v er si on 1 11 N ov 2 00 8 Bridging the Gap between Population and Gossip-based Protocols 3