SIAM Journal on Applied Mathematics
Epidemic algorithms for replicated database maintenance
PODC '87 Proceedings of the sixth annual ACM Symposium on Principles of distributed computing
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Proceedings of the international workshop on Broadcasting and gossiping 1990
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Communications of the ACM
Introduction to Coding Theory
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Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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DISC'06 Proceedings of the 20th international conference on Distributed Computing
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DISC'11 Proceedings of the 25th international conference on Distributed computing
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Robust network supercomputing without centralized control
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STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
The worst case behavior of randomized gossip
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
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We study the communication complexity of rumor spreading in the random phone-call model. Suppose nplayers communicate in parallel rounds, where in each round every player calls a randomly selected communication partner. A player u is allowed to exchange messages during a round only with the player that u called, and with all the players that $u$ received calls from, in that round. In every round, a (possibly empty) set of rumors to be distributed among all players is generated, and each of the rumors is initially placed in a subset of the players. Karp et. al \cite{Karp2000} showed that no rumor-spreading algorithm that spreads a rumor to all players with constant probability can be both time-optimal, taking O(lg n) rounds, and message-optimal, using O(n) messages per rumor. For address-oblivious algorithms, in particular, they showed that Ω(n lg lg n) messages per rumor are required, and they described an algorithm that matches this bound and takes O(lg n) rounds. We investigate the number of communication bits required for rumor spreading. On the lower-bound side, we establish that any address-oblivious algorithm taking O(lg n) rounds requires Ω(n (b+ lg lg n)) communication bits to distribute a rumor of size b bits. On the upper-bound side, we propose an address-oblivious algorithm that takes O(lg n) rounds and uses O(n(b+ lg lg n lg b)) bits. These results show that, unlike the case for the message complexity, optimality in terms of both the running time and the bit communication complexity is attainable, except for very small rumor sizes b n lg lg lg n.