Randomized Leader Election Protocols in Noisy Radio Networks with a Single Transceiver

In this work, we present leader election protocols for single-hop, single-channel noisy radio networks that do not have collision detection (CD) capabilities. In most leader election protocols presented so far, it is assumed that every station has the ability to transmit and monitor the channel at the same time, it requires every station to be equipped with two transceivers. This assumption, however, is unrealistic for most mobile stations due to constraints in cost, size, and energy dissipation. Our main contribution is to show that it is possible to elect a leader in an anonymous radio network where each station is equipped with a single transceiver. We first present a leader election protocol for the case the number n of stations is known beforehand. The protocol runs in O(logf) time slots with probability at least $1-{1\over f}$ for any f> 1. We then present a leader election protocol for the case where n is not known beforehand but an upper bound u of n is known. This protocol runs in O(logflogu) time slots with probability at least $1-{1\over f}$ for any f> 1. We also prove that these protocols are optimal. More precisely, we show that any leader election protocol elect a leader with probability at least $1-{1\over f}$ must run in Ω(logf) time slots if n is known. Also, we proved that any leader election protocol elect a leader with probability at least $1-{1\over f}$ must run in Ω(logflogu) time slots if an upper bound u of n is known.

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