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The Asymmetric Leader Election Algorithm: Another Approach
Guy Louchard1 and Helmut Prodinger2
1Universit\'e Libre de Bruxelles, D\'epartement d'Informatique, CP 212, Boulevard du Triomphe, B-1050 Bruxelles, Belgium
2Helmut Prodinger, Mathematics Department, Stellenbosch University, 7602 Stellenbosch, South Africa
Annals of Combinatorics 12 (4) pp.445-474 December, 2008
AMS Subject Classification: 68R05, 60C05
The asymmetric leader election algorithm has obtained quite a bit of attention lately. In this paper we want to analyze the following asymptotic properties of the number of rounds: Limiting distribution function, all moments in a simple automatic way, asymptotics for $p\ra 0$, $p\ra 1 $ (where $p$ denotes the ``killing'' probability). This also leads to a few interesting new identities. We use two paradigms: First, in some urn model, we have asymptotic independence of urns behaviour as far as random variables related to urns with a fixed number of balls are concerned. Next, we use a technique easily leading to the asymptotics of the moments of extreme-value related distribution functions.
Keywords: leader election, Gumbel distribution, urn model, Mellin transform


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