Survivors in leader election algorithms

Ravi Kalpathy, Hosam M. Mahmoud and Walter Rosenkrantz

Statistics & Probability Letters, 2013, vol. 83, issue 12, 2743-2749

Abstract: We consider the number of survivors in a broad class of fair leader election algorithms after a number of election rounds. We give sufficient conditions for the number of survivors to converge to a product of independent identically distributed random variables. The number of terms in the product is determined by the round number considered. Each individual term in the product is a limit of a scaled random variable associated with the splitting protocol. The proof is established via convergence (to 0) of the first-order Wasserstein distance from the product limit. In a broader context, the paper is a case study of a class of stochastic recursive equations. We give two illustrative examples, one with binomial splitting protocol (for which we show that a normalized version is asymptotically Gaussian) and one with uniform splitting protocol.

Keywords: Randomized algorithm; Leader election; Stochastic recurrence; Probability metrics; Weak convergence (search for similar items in EconPapers)
Date: 2013
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spl.2013.09.011

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