Stabilizing consensus with the power of two choices

B. Doerr, L.A. Goldberg, L. Minder, T. Sauerwald, C. Scheideler, in:, Proceedings of the 23rd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 2011, pp. 149–158.

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In the standard consensus problem there are n processes with possibly di®erent input values and the goal is to eventually reach a point at which all processes commit to exactly one of these values. We are studying a slight variant of the consensus problem called the stabilizing consensus problem [2]. In this problem, we do not require that each process commits to a ¯nal value at some point, but that eventually they arrive at a common, stable value without necessarily being aware of that. This should work irrespective of the states in which the processes are starting. Our main result is a simple randomized algorithm called median rule that, with high probability, just needs O(logmlog log n + log n) time and work per process to arrive at an almost stable consensus for any set of m legal values as long as an adversary can corrupt the states of at most p n processes at any time. Without adversarial involvement, just O(log n) time and work is needed for a stable consensus, with high probability. As a by-product, we obtain a simple distributed algorithm for approximating the median of n numbers in time O(logmlog log n + log n) under adversarial presence.
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Proceedings of the 23rd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA)
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149-158
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Doerr B, Goldberg LA, Minder L, Sauerwald T, Scheideler C. Stabilizing consensus with the power of two choices. In: Proceedings of the 23rd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA).; 2011:149-158. doi:10.1145/1989493.1989516.
Doerr, B., Goldberg, L. A., Minder, L., Sauerwald, T., & Scheideler, C. (2011). Stabilizing consensus with the power of two choices. In Proceedings of the 23rd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA) (pp. 149–158). http://doi.org/10.1145/1989493.1989516
@inbook{Doerr_Goldberg_Minder_Sauerwald_Scheideler_2011, title={Stabilizing consensus with the power of two choices}, DOI={10.1145/1989493.1989516}, booktitle={Proceedings of the 23rd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA)}, author={Doerr, Benjamin and Goldberg, Leslie Ann and Minder, Lorenz and Sauerwald, Thomas and Scheideler, Christian}, year={2011}, pages={149–158}}
Doerr, Benjamin, Leslie Ann Goldberg, Lorenz Minder, Thomas Sauerwald, and Christian Scheideler. “Stabilizing Consensus with the Power of Two Choices.” In Proceedings of the 23rd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 149–58, 2011. doi:10.1145/1989493.1989516.
B. Doerr, L. A. Goldberg, L. Minder, T. Sauerwald, and C. Scheideler, “Stabilizing consensus with the power of two choices,” in Proceedings of the 23rd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 2011, pp. 149–158.
Doerr, Benjamin et al. “Stabilizing Consensus with the Power of Two Choices.” Proceedings of the 23rd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA). N.p., 2011. 149–158. Web.
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