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June 2011 Asymptotic properties of a leader election algorithm
Ravi Kalpathy, Hosam M. Mahmoud, Mark Daniel Ward
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J. Appl. Probab. 48(2): 569-575 (June 2011). DOI: 10.1239/jap/1308662645

Abstract

We consider a serialized coin-tossing leader election algorithm that proceeds in rounds until a winner is chosen, or all contestants are eliminated. The analysis allows for either biased or fair coins. We find the exact distribution for the duration of any fixed contestant; asymptotically, it turns out to be a geometric distribution. Rice's method (an analytic technique) shows that the moments of the duration contain oscillations, which we give explicitly for the mean and variance. We also use convergence in the Wasserstein metric space to show that the distribution of the total number of coin flips (among all participants), suitably normalized, approaches a normal limiting random variable.

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Ravi Kalpathy. Hosam M. Mahmoud. Mark Daniel Ward. "Asymptotic properties of a leader election algorithm." J. Appl. Probab. 48 (2) 569 - 575, June 2011. https://doi.org/10.1239/jap/1308662645

Information

Published: June 2011
First available in Project Euclid: 21 June 2011

zbMATH: 1219.60008
MathSciNet: MR2840317
Digital Object Identifier: 10.1239/jap/1308662645

Subjects:
Primary: 60C05
Secondary: 05C05, 60F05, 68W40

Rights: Copyright © 2011 Applied Probability Trust

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Vol.48 • No. 2 • June 2011
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