Families of consensus algorithms
Three main parameters characterize the efficiency of algorithms that solve the Consensus Problem. The ratio between the total number of processors and the maximum number of faulty processors (n and t, respectively), the number of rounds, and the size of any single message. Lower bounds exist for each one of the three. In this paper we present two families of algorithms, each achieving the lower bound for one parameter and a trade-off between the other two. The first family includes algorithms where, given an integer k, the algorithm always requires the minimal possible number of rounds (t+1), with n=k(3t+1) processors and messages of size at most t O(t/k). To the second family belong algorithms in which all messages are of one bit size, the number of processors is t O((k+1)/k) and the number of rounds is t+t O ((k−1)/k). These two families are based on a very simple algorithm with (2t+1)(t+1) processors using the minimal number of rounds and the minimal message size (one bit).
KeywordsMessage Size Consensus Problem Consensus Algorithm Initial Round Single Message
Unable to display preview. Download preview PDF.
- [BDDS]A. Bar-Noy, D. Dolev, C. Dwork, and H. R. Strong, “Shifting Gears: Changing Algorithms on the Fly to Expedite Byzantine Agreement,” proceedings, the 6th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, Aug. 87, pp. 42–51.Google Scholar
- [Co]B. A. Coan, “A Communication-Efficient Canonical Form for Fault-Tolerant Distributed Protocols,” Proceedings, the 5th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, Aug. 1986.Google Scholar
- [DLM]R. DeMillo, N. A. Lynch, and M. Merritt, “Cryptographic Protocols,” Proceedings, the 14th Annual ACM Symposium on Theory of Computing, pp. 383–400, 1982.Google Scholar
- [DRS]D. Dolev, R. Reischuk, and H. R. Strong, “Early Stopping in Byzantine Agreement,” IBM Research Report RJ5406 (55357), 1986.Google Scholar
- [PSL]M. Pease, R. Shostak, and L. Lamport, “Reaching Agreement in the Presence of Faults,” JACM, Vol. 27, 1980.Google Scholar