Asymptotic Analysis of a Leader Election Algorithm
Christian Lavault (LIPN), Guy Louchard (ULB)

TL;DR
This paper provides a precise asymptotic analysis of the average number of rounds in a leader election algorithm, including moments, distribution, and generalizations, confirming theoretical results with numerical data.
Contribution
It offers exact asymptotic expressions for the moments and distribution of the rounds in the leader election algorithm, extending analysis to generalized probability parameters.
Findings
Asymptotic limit of average rounds is approximately 2.4417.
Derived asymptotic expressions for second moments and distributions.
Identified a unique minimum of the expected rounds function for certain parameters.
Abstract
Itai and Rodeh showed that, on the average, the communication of a leader election algorithm takes no more than bits, where and denotes the size of the ring. We give a precise asymptotic analysis of the average number of rounds M(n) required by the algorithm, proving for example that , where is the number of starting candidates in the election. Accurate asymptotic expressions of the second moment of the discrete random variable at hand, its probability distribution, and the generalization to all moments are given. Corresponding asymptotic expansions are provided for sufficiently large , where counts the number of rounds. Our numerical results show that all computations perfectly fit the observed values. Finally, we investigate the generalization to…
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Taxonomy
TopicsDNA and Biological Computing · Opinion Dynamics and Social Influence · Cellular Automata and Applications
