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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Bibliographic Details
Published in:Statistics & probability letters Vol. 101; pp. 40 - 48
Main Authors: Louchard, Guy, Ward, Mark Daniel
Format: Journal Article
Language:English
Published: Elsevier B.V 01.06.2015
Subjects:
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
Online Access:Get full text
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Summary: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