Affiliations: [a] Department of Computer Science and Engineering, University of Colorado Denver, Denver, Colorado 80217, USA. [email protected] | [b] Dipartimento di Informatica, Università degli Studi di Salerno, Fisciano, 84084 Salerno, Italy. [email protected] | [c] Bilgisayar Mühendisliği, Munzur Üniversitesi, 62000 Tunceli, Turkey. [email protected]
Correspondence:
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Address for correspondence: Department of Computer Science and Engineering, University of Colorado Denver, Denver, Colorado 80217, USA. The work of this author was supported by the National Science Foundation under Grant 1016847.
Note: [†] This work was conducted while the author was with the University of Colorado Denver and was supported by the National Science Foundation under Grant 1016847.
Abstract: 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.
Keywords: beeping channel, anonymous network, randomized algorithm, Las Vegas algorithm, Monte Carlo algorithm, lower bound
