Randomized O(log log n)-round leader election protocols in packet radio networks

The main contribution of this work is to propose efficient randomized leader election protocols in Packet Radio Networks (PRN). We show that in a one-channel PRN a leader can be elected among n identical stations in O(log log n) broadcast rounds with probability at least 1 - O(1/log n) or in O(log n) broadcast rounds with probability at least 1-O(1/n). We begin by designing such a protocol for the case where the number n of stations is known beforehand. Next, we show that the leader election can be completed within the same number of broadcast rounds even if n is not known. We show that our protocols are optimal in the sense that no randomized protocol that terminates in O(log n) rounds can elect a leader with probability higher than 1 - O(1/n) and no randomized protocol that terminates in o(log log n) rounds can elect a leader with probability higher than 1 - O(1/log n).