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Survivors in leader election algorithms

Author

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  • Kalpathy, Ravi
  • Mahmoud, Hosam M.
  • Rosenkrantz, Walter

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.

Suggested Citation

  • Kalpathy, Ravi & Mahmoud, Hosam M. & Rosenkrantz, Walter, 2013. "Survivors in leader election algorithms," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2743-2749.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:12:p:2743-2749
    DOI: 10.1016/j.spl.2013.09.011
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    Cited by:

    1. Cheng Zhang & Hosam Mahmoud, 2016. "Bivariate Issues in Leader Election Algorithms with Marshall-Olkin Limit Distribution," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 401-418, June.
    2. Kalpathy, Ravi & Ward, Mark Daniel, 2014. "On a leader election algorithm: Truncated geometric case study," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 40-47.

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