### Abstract

We are given n stations of which k are active, while the remaining n - k are asleep. The active stations communicate via a multiple-access channel. If a subset Q of active stations transmits in the same round, all active stations can recognize from the signal strength how many stations have transmitted (i.e., they learn the size of set Q), even though they may not be able to decode the contents of transmitted messages. The goal is to let each active station to learn about the set of all active stations. It is well known that Θ(k log_{k+1} n) rounds are enough, even for non-adaptive deterministic algorithms. A natural interesting generalization arises when we are required to identify a subset of m ≤ k active stations. We show that while for randomized or for adaptive deterministic algorithms O(m log_{m+1} n) rounds are sufficient, the non-adaptive deterministic counterpart still requires Θ(k log_{k+1} n) rounds; therefore, finding any subset of active stations is not easier than finding all of them by a nonadaptive deterministic algorithm. We prove our results in the more general framework of combinatorial search theory, where the problem of identifying active stations on a multiple-access channel can be viewed as a variant of the well-known counterfeit coin problem.

Original language | English (US) |
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Title of host publication | ICDCS 2010 - 2010 International Conference on Distributed Computing Systems |

Pages | 728-735 |

Number of pages | 8 |

DOIs | |

State | Published - Aug 27 2010 |

Externally published | Yes |

Event | 30th IEEE International Conference on Distributed Computing Systems, ICDCS 2010 - Genova, Italy Duration: Jun 21 2010 → Jun 25 2010 |

### Publication series

Name | Proceedings - International Conference on Distributed Computing Systems |
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### Conference

Conference | 30th IEEE International Conference on Distributed Computing Systems, ICDCS 2010 |
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Country | Italy |

City | Genova |

Period | 6/21/10 → 6/25/10 |

### Keywords

- Combinatorial search theory
- Distributed learning
- Multiple-access channel
- Randomized algorithms

### ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Networks and Communications

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## Cite this

*ICDCS 2010 - 2010 International Conference on Distributed Computing Systems*(pp. 728-735). [5541631] (Proceedings - International Conference on Distributed Computing Systems). https://doi.org/10.1109/ICDCS.2010.50