Randomized leader election protocols in radio networks with no collision detection

Abstract

The main contribution of this work is to propose energy-efficient randomized leader election protocols for single-hop, single-chan-nel radio networks (RN) that do not have collision detection (CD) capa-bilities. We first presents a leader election protocol for the case the num-ber n of stations is known beforehand. The protocol runs in O(log f) time slots with no station being awake for more than O(log log f + log f/log n) time slots with probability at least 1 − 1/f for any f ≥ 1. We then pre-sent three leader election protocols for the case where n is not known beforehand. The first protocol terminates, with probability exceeding 1 – 1/f, in O((log n)2 + (log f)2) time slots, with no station being awake for more than O(log n+log f) time slots. Clearly, this first protocol ter-minates in O((log n)2) expected time slots. Our second protocol reduces the expected termination time to O(log n) time slots. This second pro-tocol terminates, with probability exceeding 1 – 1/f in O(f 3/5 log n) time slots. Finally, by combining these two protocols, we obtain a third lea-der election protocol that terminates in O(log n) expected time slots. This latter protocol terminates, with with probability exceeding 1 – 1/f, in O(min((log n)2 + (log f)2; f 35 log n)) time slots, with no station being awake for more than O(log n + log f) time slots.