Keywords and Synonyms
Agreement; Byzantine agreement
Problem Definition
This problem is concerned with using the multi-writer multi-reader register primitive in the shared memory model to design a fast, wait-free implementation of consensus. Below are detailed descriptions of each of these terms.
Consensus Problems
There are n processors and the goal is to design distributed algorithms to solve the following two consensus problems for these processors.
Problem 1 (Binary consensus)
Input: Processor i has input bit b i .
Output: Each processor i has output bit \( { b^{\prime}_i } \) such that: 1) all the output bits \( { b^{\prime}_i } \) equal the same value v; and 2) \( { v = b_i } \) for some processor i.
Problem 2 (Id consensus)
Input: Processor i has a unique id u i .
Output: Each processor i has output value \( { u^{\prime}_i } \) such that: 1) all the output values \( { u^{\prime}_i } \) equal the same value u; and 2) \( { u = u_i } \) for some processor i.
Wait-Free
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Aspnes, J.: Randomized protocols for asynchronous consensus. Distrib. Comput. 16(2–3), 165–175 (2003)
Aspnes, J., Waarts, O.: Randomized consensus in expected \( { o(n \log^2 n) } \) operations per processor. In: Proceedings of the 33rd Symposium on Foundations of Computer Science. 24–26 October 1992, pp. 137–146. IEEE Computer Society, Pittsburgh (1992)
Attiya, H., Censor, K.: Tight bounds for asynchronous randomized consensus. In: Proceedings of the Symposium on the Theory of Computation. San Diego, 11–13 June 2007 ACM Special Interest Group on Algorithms and Computation Theory (SIGACT) (2007)
Aumann, Y.: Efficient asynchronous consensus with the weak adversary scheduler. In: Symposium on Principles of Distrib. Comput.(PODC) Santa Barbara, 21–24 August 1997, pp. 209–218. ACM Special Interest Group on Algorithms and Computation Theory (SIGACT) (1997)
Aumann, Y., Kapach-Levy, A.: Cooperative sharing and asynchronous consensus using single-reader/single-writer registers. In: Proceedings of 10th Annual ACM-SIAM Symposium of Discrete Algorithms (SODA) Baltimore, 17–19 January 1999, pp. 61–70. Society for Industrial and Applied Mathematics (SIAM) (1999)
Dolev, D., Dwork, C., Stockmeyer, L.: On the minimal synchronism needed for distributed consensus. J. ACM (JACM) 34(1), 77–97 (1987)
Fischer, M.J., Lynch, N.A., Paterson, M.: Impossibility of distributed consensus with one faulty process. In: Proceedings of the 2nd ACM SIGACT-SIGMOD Symposium on Principles of Database System (PODS) Atlante, 21–23 March, pp. 1–7. Association for Computational Machinery (ACM) (1983)
Herlihy, M.: Wait-free synchronization. ACM Trans. Programm. Lang. Syst. 13(1), 124–149 (1991)
Lynch, N.: Distributed Algorithms. Morgan Kaufmann, San Mateo (1996)
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Chandra, T.D. (2008). Randomization in Distributed Computing. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_321
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