# Quasi-Optimal Leader Election Algorithms in Radio Networks with Loglogarithmic Awake Time Slots

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A radio network RN is a distributed system consisting of $n$ radio stations. We design and analyze two distributed leader election protocols in RN where the number $n$ of radio stations is unknown. The first algorithm runs under the assumption of {\it limited collision detection}, while the second assumes that {\it no collision detection} is available. By limited collision detection, we mean that if exactly one station sends broadcasts a message, then all stations including the transmitter that are listening at this moment receive the sent message. By contrast, the second no-collision-detection algorithm assumes that a station cannot simultaneously send and listen signals. Moreover, both protocols allow the stations to keep asleep as long as possible, thus minimizing their awake time slots such algorithms are called {\it energy-efficient}. Both randomized protocols in RN areshown to elect a leader in $O\log{n}$ expected time, with no station being awake for more than $O\log{\log{n}}$ time slots. Therefore, a new class of efficient algorithms is set up that match the $\Omega\log{n}$ time lower-bound established by Kushilevitz and Mansour.

Autor: Christian Lavault; Jean-François Marckert; Vlady Ravelomanana

Fuente: https://archive.org/