Journal of Parallel and Distributed Computing
OPODIS'05 Proceedings of the 9th international conference on Principles of Distributed Systems
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Distributed algorithms in dynamic networks often employcommunication patterns whose purpose is to disseminateinformation among the participants. Gossiping is oneform of such communication pattern. In dynamic settingsthe set of participants can change substantially as new participantsjoin, and as failures and voluntary departures removethose who have joined previously. A natural questionfor such settings is: how soon can newly joined nodes discovereach other by means of gossiping? This paper abstractsand studies the Join Problem for dynamic systemsthat use all-to-all gossip. The problem is studied in terms ofjoin-connectivity graphs where vertices represent the participantsand where each edge represents one participant'sknowledge about another. Ideally, such a graph has diameterone, i.e., all participants know each other. The diametercan grow as new participants join, and as failures removeedges from the graph. Gossip helps participants discoverone another, decreasing the diameter. The results describethe lower and upper bounds on the number of communicationrounds such that the participants who have previouslyjoined discover one another, under a variety of assumptionsabout the joining and failures. For example, inthe case when new participants join at multiple participantsand participants may crash, the number of rounds cannot bebounded. In the more benign cases when the failures can becontrolled or when new participants join at only one participant,the bound on rounds is shown to be logarithmic inthe diameter of the initial configuration.