Cloture Votes:n /4-resilient Distributed Consensus int + 1 rounds Piotr Berman Juan A. Garay Article

First Online: 22 February 2005 Received: 04 December 1989 Revised: 15 December 1991 DOI :
10.1007/BF01187072

Cite this article as: Berman, P. & Garay, J.A. Math. Systems Theory (1993) 26: 3. doi:10.1007/BF01187072
Abstract TheDistributed Consensus problem involvesn processors each of which holds an initial binary value. At mostt processors may be faulty and ignore any protocol (even behaving maliciously), yet it is required that the nonfaulty processors eventually agree on a value that was initially held by one of them. We measure the quality of a consensus protocol using the following parameters; total number of processorsn , number of rounds of message exchanger , and maximal message sizem . The known lower bounds are respectively 3t + 1,t + 1, and 1.

While no known protocol is optimal in all these three aspects simultaneously,Cloture Votes —the protocol presented in this paper—takes further steps in this direction, by making consensus possible withn = 4t + 1,r = t + 1, and polynomial message size.

Cloture is a parliamentary procedure (also known as “parliamentary guillotine”) which makes it possible to curtail unnecessary long debates. In our protocol the unanimous will of the correct processors (akin to parliamentarian supermajority) may curtail the debate. This is facilitated by having the processors open in each round a new process (debate), which either ends quickly, with the conclusion “continue” or “terminate with the default value,” or lasts through many rounds. Importantly, in the latter case the messages being sent are short.

A preliminary version appeared as a part of “Towards Optimal Distributed Consensus” inProc. 30th IEEE Symp. on Foundations of Computer Science [BGP], and is part of J. A. Garay's Ph.D. dissertation. This work was partially supported by AFOSR Contract 87-0400 and NSF Grant CR 8805978. The work of Juan Garay was also partially supported by the Leo S. Rowe Pan American Fund of the Organization of American States.

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Authors and Affiliations Piotr Berman Juan A. Garay 1. Department of Computer Science The Pennsylvania State University University Park USA 2. IBM T. J. Watson Research Center Yorktown Heights USA