The Asymmetric Leader Election Algorithm: Another Approach

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 → 0, p → 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 extremevalue related distribution functions.