TY - GEN

T1 - Towards power-sensitive communication on a multiple-access channel

AU - De Marco, Gianluca

AU - Kowalski, Dariusz R.

PY - 2010/8/27

Y1 - 2010/8/27

N2 - 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 logk+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 logm+1 n) rounds are sufficient, the non-adaptive deterministic counterpart still requires Θ(k logk+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.

AB - 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 logk+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 logm+1 n) rounds are sufficient, the non-adaptive deterministic counterpart still requires Θ(k logk+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.

KW - Combinatorial search theory

KW - Distributed learning

KW - Multiple-access channel

KW - Randomized algorithms

UR - http://www.scopus.com/inward/record.url?scp=77955910353&partnerID=8YFLogxK

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U2 - 10.1109/ICDCS.2010.50

DO - 10.1109/ICDCS.2010.50

M3 - Conference contribution

AN - SCOPUS:77955910353

SN - 9780769540597

T3 - Proceedings - International Conference on Distributed Computing Systems

SP - 728

EP - 735

BT - ICDCS 2010 - 2010 International Conference on Distributed Computing Systems

T2 - 30th IEEE International Conference on Distributed Computing Systems, ICDCS 2010

Y2 - 21 June 2010 through 25 June 2010

ER -