Abstract
In a Distributed Consensus protocol n processors, of which at most t may be faulty, are given initial binary values; after exchanging messages all the processors that are correct must agree on one of the initial values. We measure the quality of a consensus protocol by the following parameters: the total number of processors n, the number of rounds of message exchange r, and the communication complexity, given by the maximal message size.
This paper presents a protocol that achieves Distributed Consensus with n=(3 + ɛ)t, r=t + 1, and polynomial message size for ɛ ≥ 1/log t, Thus, this is the first consensus protocol to use simultaneously nearly optimal number of processors (n= 3t + 1 is the known lower bound). optimal number of rounds, and short messages. Previous round-optimal protocols with polynomial communication required n=Ω(t2), n > 6t and n > 4t, respectively.
In order to obtain this result, we introduce new techniques for the abbreviation of messages in the classical full information consensus protocol. In particular, we introduce the Dynamic Fault Masking technique, called that way because the values that the correct processors use to mask the faults is computed on the fly during the execution of the protocol.
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References
H. Attiya, C. Dwork, N. Lynch and L. Stockmeyer, “Bounds on the time to reach agreement in the presence of timing uncertainty,” Proc. 23rd STOC, May 1991.
A. Bar-Noy and D. Dolev, “Families of Consensus Algorithms,” Proc. 3rd Aegean Workshop on Computing, pp. 380–390, June/July 1988.
A. Bar-Noy, D. Dolev, C. Dwork and H.R. Strong, “Shifting gears: changing algorithms on the fly to expedite Byzantine Agreement,” Proc. 6th PODC, pp. 42–51, August 1987.
P. Berman and J.A. Garay, “Optimal Early Stopping in Distributed Consensus,” IBM Research Report RC 16746, December 1990.
P. Berman, J.A. Garay and K.J. Perry, “Towards Optimal Distributed Consensus,” Proc. 30th FOCS, pp. 410–415, October/November 1989.
B. Coan, “A communication-efficient canonical form for fault-tolerant distributed protocols,” Proc. 5th PODC, pp. 63–72, August 1986.
D. Dolev, R. Reischuk and H.R. Strong, “Eventual is Earlier than Immediate,” Proc. 23rd STOC, 1982. Revised version appears in “Early Stopping in Byzantine Agreement,” JACM, Vol. 37, No. 4 (1990), pp. 720–741.
D. Dolev and H.R. Strong, “Polynomial Algorithms for Multiple Processor Agreement,” Proc. 14th STOC, pp. 401–407, May 1982.
M. Fisher, N. Lynch and M. Paterson, “Impossibility of Distributed Consensus with one faulty process,” JACM, Vol. 32, No. 2 (1985), pp. 374–382.
P. Feldman and S. Micali, “Optimal Algorithms for Byzantine Agreement,” Proc. 20th STOC, pp. 148–161, May 1988.
J. Halpern and Y. Moses, “Knowledge and common knowledge in a distributed environment,” JACM, Vol. 37, No. 3 (1990), pp. 549–587.
L. Lamport, R.E. Shostak and M. Pease, “The Byzantine Generals Problem,” ACM ToPLaS, Vol. 4, No. 3, pp. 382–401, July 1982.
Y. Moses and O. Waarts, “Coordinated Traversal: (t+l)-Round Byzantine Agreement in Polynomial Time,” Proc. 29th FOCS, pp. 246–255, October 1988.
O. Waarts, “Coordinated Traversal: Byzantine Agreement in polynomial time,” M.Sc. Thesis, Weizmann Institute of Science, Rehovot, Israel, August 1988.
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© 1992 Springer-Verlag Berlin Heidelberg
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Berman, P., Garay, J.A. (1992). Efficient distributed consensus with n=(3 + ɛ)t processors. In: Toueg, S., Spirakis, P.G., Kirousis, L. (eds) Distributed Algorithms. WDAG 1991. Lecture Notes in Computer Science, vol 579. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022442
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DOI: https://doi.org/10.1007/BFb0022442
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