Number of survivors in the presence of a demon
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This paper complements the analysis of Louchard and Prodinger [LP08] on the number of rounds in a coin-flipping selection algorithm that occurs in the presence of a demon. We precisely analyze a very different aspect of the selection algorithm, using different methods of analysis. Specifically, we obtain precise descriptions of the distribution and all moments of the number of participants ultimately selected during the execution of the algorithm. The selection algorithm is robust in at least two significant ways. The presence of a demon allows for the precise analysis even when errors may occur between the rounds of the selection process. (The analysis also handles the more traditional case, in which no demon is involved.) The selection algorithm can also use either biased or unbiased coins.
Key words and phrasesanalysis of algorithms leader election coin flip survivor demon asymptotic approximation trie q-Pochhammer symbol factorial moment distribution generating function recurrence poissonization
Mathematics subject classification numbers05A16 05A30 60C05 68W20 68W40
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- [FS09]P. Flajolet and R. Sedgewick, Analytic Combinatorics, Cambridge, 2009.Google Scholar