Uniform leader election protocols for radio networks

A radio network is a distributed system with no central arbiter, consisting of n radio transceivers, henceforth referred to as stations. We assume that the stations are identical and cannot be distinguished by serial or manufacturing number. The leader election problem asks to designate one of the stations as leader. In this work, we focus on single-channel, single-hop radio networks. We assume that time is slotted and all transmissions occur at slot boundaries. In each time slot, the stations transmit on the channel with some probability until, eventually, one of the stations is declared leader. A leader election protocol is said to be uniform if, in each time slot, every station transmits with the same probability. In a seminal paper, Willard (1986) presented a uniform leader election protocol for single-channel single-hop radio stations terminating in log log n+o(log log n) expected time slots. It was open for more than 15 years whether Willard's protocol featured the same time performance with "high probability." One of our main contributions is to show that, unfortunately, this is not the case. Specifically, we prove that for every parameter f∈e^O(n), in order to ensure termination with probability exceeding 1-1/f, Willard's protocol must take log log n+Ω(√f) time slots. The highlight of this work is a novel uniform leader election protocol that terminates, with probability exceeding 1-1/f, in log log n+o(log log n)+O(log f) time slots. Finally, we provide simulation results that show that our leader election protocol outperforms Willard's protocol in practice