### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 199-219 |

Number of pages | 21 |

Journal | Fundamenta Informaticae |

Volume | 153 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2017 |

Externally published | Yes |

### Fingerprint

### Keywords

- anonymous network
- beeping channel
- Las Vegas algorithm
- lower bound
- Monte Carlo algorithm
- randomized algorithm

### ASJC Scopus subject areas

- Theoretical Computer Science
- Algebra and Number Theory
- Information Systems
- Computational Theory and Mathematics

### Cite this

*Fundamenta Informaticae*,

*153*(3), 199-219. https://doi.org/10.3233/FI-2017-1537

**Naming a channel with beeps.** / Chlebus, Bogdan S.; De Marco, Gianluca; Taloy, Muhammed.

Research output: Contribution to journal › Article

*Fundamenta Informaticae*, vol. 153, no. 3, pp. 199-219. https://doi.org/10.3233/FI-2017-1537

}

TY - JOUR

T1 - Naming a channel with beeps

AU - Chlebus, Bogdan S.

AU - De Marco, Gianluca

AU - Taloy, Muhammed

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

KW - anonymous network

KW - beeping channel

KW - Las Vegas algorithm

KW - lower bound

KW - Monte Carlo algorithm

KW - randomized algorithm

UR - http://www.scopus.com/inward/record.url?scp=85020875968&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85020875968&partnerID=8YFLogxK

U2 - 10.3233/FI-2017-1537

DO - 10.3233/FI-2017-1537

M3 - Article

AN - SCOPUS:85020875968

VL - 153

SP - 199

EP - 219

JO - Fundamenta Informaticae

JF - Fundamenta Informaticae

SN - 0169-2968

IS - 3

ER -