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A Quasi-Optimal Leader Election Algorithm in Radio Networks with Log-Logarithmic Awake Time Slots

Christian Lavault·Jean-François Marckert·Vlady Ravelomanana
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Abstract

Radio networks (RN) are distributed systems (\textit{ad hoc networks}) consisting in $n \ge 2$ radio stations. Assuming the number $n$ unknown, two distinct models of RN without collision detection (\textit{no-CD}) are addressed: the model with \textit{weak no-CD} RN and the one with \textit{strong no-CD} RN. We design and analyze two distributed leader election protocols, each one running in each of the above two (no-CD RN) models, respectively. Both randomized protocols are shown to elect a leader within $\BO(\log{(n)})$ expected time, with no station being awake for more than $\BO(\log{\log{(n)}})$ time slots (such algorithms are said to be \textit{energy-efficient}). Therefore, a new class of efficient algorithms is set up that matchthe $Ω(\log{(n)})$ time lower-bound established by Kushilevitz and Mansour.

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Christian Lavault, Jean-François Marckert, Vlady Ravelomanana. 2006-07-07. A Quasi-Optimal Leader Election Algorithm in Radio Networks with Log-Logarithmic Awake Time Slots. https://arxiv.org/abs/cs/0607028

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