Naming a Channel with Beeps

We consider a communication channel in which the only available mode of communication is transmitting beeps. A beep transmitted by a station attached to the channel reaches all the other stations instantaneously. Stations are anonymous, in that they do not have any individual identifiers. The algorithmic goal is to assign names to the stations in such a manner that the names make a contiguous segment of positive integers starting from 1. We develop a Las Vegas naming algorithm, for the case when the number of stations n is known, and a Monte Carlo algorithm, for the case when the number of stations n is not known. The given randomized algorithms are provably optimal with respect to the expected time O (n log n), the expected number of used random bits O (n log n), and the probability of error.