Abstract
Consider an asynchronous system where each process begins with an arbitrary real value. Given some fixed ε> 0, an approximate agreement algorithm must have all non-faulty processes decide on values that are at most ε from each other and are in the range of the initial values of the non-faulty processes.
Previous constructions solved asynchronous approximate agreement only when there were at least 5t+1 processes, t of which may be Byzantine. In this paper we close an open problem raised by Dolev et al. in 1983. We present a deterministic optimal resilience approximate agreement algorithm that can tolerate any t Byzantine faults while requiring only 3t+1 processes.
The algorithm’s rate of convergence and total message complexity are efficiently bounded as a function of the range of the initial values of the non-faulty processes. All previous asynchronous algorithms that are resilient to Byzantine failures may require arbitrarily many messages to be sent.
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References
Bracha, G.: An asynchronous \(\lfloor (n-1)/3\rfloor\)-resilient consensus protocol. In: Proceedings of the third annual ACM symposium on Principles of distributed computing, pp. 154–162. ACM Press, New York (1984)
Dolev, D.: The byzantine generals strike again. J. Algorithms 3(1) (1982)
Dolev, D., Lynch, N.A., Pinter, S.S., Stark, E.W., Weihl, W.E.: Reaching approximate agreement in the presence of faults. In: Proceedings of the 3rd Symposium on Reliability in Distributed Systems (1983)
Dolev, D., Lynch, N.A., Pinter, S.S., Stark, E.W., Weihl, W.E.: Reaching approximate agreement in the presence of faults. J. ACM 33(3), 499–516 (1986)
Fekete, A.D.: Asymptotically optimal algorithms for approximate agreement. In: Proceedings of the fifth annual ACM symposium on Principles of distributed computing, pp. 73–87. ACM Press, New York (1986)
Fekete, A.D.: Asynchronous approximate agreement. In: Proceedings of the sixth annual ACM Symposium on Principles of distributed computing, pp. 64–76. ACM Press, New York (1987)
Fischer, M.J., Lynch, N.A., Merritt, M.: Easy impossibility proofs for distributed consensus problems. In: Proceedings of the fourth annual ACM symposium on Principles of distributed computing, pp. 59–70. ACM Press, New York (1985)
Fischer, M.J., Lynch, N.A., Paterson, M.S.: Impossibility of distributed consensus with one faulty process. Journal of the ACM 32(2), 374–382 (1985)
Kieckhafer, R.M., Azadmanesh, M.H.: Reaching approximate agreement with mixed-mode faults. IEEE Trans. Parallel Distrib. Syst. 5(1), 53–63 (1994)
Mahaney, S.R., Schneider, F.B.: Inexact agreement: accuracy, precision, and graceful degradation. In: Proceedings of the fourth annual ACM symposium on Principles of distributed computing, pp. 237–249. ACM Press, New York (1985)
Srikanth, T.K., Toueg, S.: Simulating authenticated broadcasts to derive simple fault-tolerant algorithms. Distributed Computing 2(2), 80–94 (1987)
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Abraham, I., Amit, Y., Dolev, D. (2005). Optimal Resilience Asynchronous Approximate Agreement. In: Higashino, T. (eds) Principles of Distributed Systems. OPODIS 2004. Lecture Notes in Computer Science, vol 3544. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11516798_17
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DOI: https://doi.org/10.1007/11516798_17
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