The truncated geometric election algorithm: Duration of the election

The present paper makes three distinct improvements over an earlier investigation of Kalpathy and Ward. We analyze the length of the entire election process (not just one participant’s duration), for a randomized election algorithm, with a truncated geometric number of survivors in each round. We no...

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Vydané v:	Statistics & probability letters Ročník 101; s. 40 - 48
Hlavní autori:	Louchard, Guy, Ward, Mark Daniel
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier B.V 01.06.2015
Predmet:	Analysis of algorithms Asymptotic analysis Generating function Leader election Recurrence 60C05 Recurrence 68W40 Generating function Leader election Analysis of algorithms Asymptotic analysis
ISSN:	0167-7152, 1879-2103
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Shrnutí:	The present paper makes three distinct improvements over an earlier investigation of Kalpathy and Ward. We analyze the length of the entire election process (not just one participant’s duration), for a randomized election algorithm, with a truncated geometric number of survivors in each round. We not only analyze the mean and variance; we analyze the asymptotic distribution of the entire election process. We also introduce a new variant of the election that guarantees a unique winner will be chosen; this methodology should be more useful in practice than the previous methodology. The method of analysis includes a precise analytic (complex-valued) approach, relying on singularity analysis of probability generating functions.
ISSN:	0167-7152 1879-2103
DOI:	10.1016/j.spl.2015.02.018