research-article

Fast Nonadaptive Deterministic Algorithm for Conflict Resolution in a Dynamic Multiple-Access Channel

Authors:

Gianluca De Marco,

Dariusz R. KowalskiAuthors Info & Claims

SIAM Journal on Computing, Volume 44, Issue 3

Pages 868 - 888

https://doi.org/10.1137/140982763

Published: 01 January 2015 Publication History

Abstract

A classical problem in addressing a decentralized multiple-access channel is resolving conflicts when a set of stations attempt to transmit at the same time on a shared communication channel. In a static scenario, i.e., when all stations are activated simultaneously, Komlós and Greenberg [IEEE Trans. Inform. Theory, 31 (1985), pp. 302--306] in their seminal work showed that it is possible to resolve the conflict among $k$ stations from an ensemble of $n$, with a nonadaptive deterministic algorithm in time $O(k + k \log(n/k))$ in the worst case. In this paper we show that in a dynamic scenario, when the stations can join the channel at arbitrary rounds, there is a nonadaptive deterministic algorithm guaranteeing a successful transmission for each station in only a slightly bigger time: $O(k\log n\log\log n)$ in the worst case. This almost matches the $\Omega(k\log n/\log k)$ lower bound by Greenberg and Winograd [J. ACM, 32 (1985), pp. 589--596] that holds even in much stronger settings: for adaptive algorithms, in the static scenario, and with additional channel feedback--collision detection. In terms of channel utilization, our result implies throughput, understood as the average number of successful transmissions per time unit, $\Omega(1/(\log n\log\log n))$ on the dynamic deterministic channel.

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Cited By

Chang YDuan RJiang S(2023)Near-Optimal Time–Energy Tradeoffs for Deterministic Leader ElectionACM Transactions on Algorithms10.1145/361442919:4(1-23)Online publication date: 26-Sep-2023
https://dl.acm.org/doi/10.1145/3614429
Bender MGilbert SKuhn FKuszmaul JMédard MAgrawal KLee I(2022)Contention Resolution for Coded Radio NetworksProceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3490148.3538573(119-130)Online publication date: 11-Jul-2022
https://dl.acm.org/doi/10.1145/3490148.3538573
Agrawal KBender MFineman JGilbert SYoung MScheideler CSpear M(2020)Contention Resolution with Message DeadlinesProceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3350755.3400239(23-35)Online publication date: 6-Jul-2020
https://dl.acm.org/doi/10.1145/3350755.3400239
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Index Terms

Fast Nonadaptive Deterministic Algorithm for Conflict Resolution in a Dynamic Multiple-Access Channel
1. Networks
2. Theory of computation
  1. Design and analysis of algorithms
  2. Theory and algorithms for application domains

Index terms have been assigned to the content through auto-classification.

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cover image SIAM Journal on Computing

SIAM Journal on Computing Volume 44, Issue 3

DOI:10.1137/smjcat.44.3

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© 2015, Society for Industrial and Applied Mathematics.

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 January 2015

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Cited By

Chang YDuan RJiang S(2023)Near-Optimal Time–Energy Tradeoffs for Deterministic Leader ElectionACM Transactions on Algorithms10.1145/361442919:4(1-23)Online publication date: 26-Sep-2023
https://dl.acm.org/doi/10.1145/3614429
Bender MGilbert SKuhn FKuszmaul JMédard MAgrawal KLee I(2022)Contention Resolution for Coded Radio NetworksProceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3490148.3538573(119-130)Online publication date: 11-Jul-2022
https://dl.acm.org/doi/10.1145/3490148.3538573
Agrawal KBender MFineman JGilbert SYoung MScheideler CSpear M(2020)Contention Resolution with Message DeadlinesProceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3350755.3400239(23-35)Online publication date: 6-Jul-2020
https://dl.acm.org/doi/10.1145/3350755.3400239
De Marco GJurdziński TKowalski D(2019)Optimal Channel Utilization with Limited FeedbackFundamentals of Computation Theory10.1007/978-3-030-25027-0_10(140-152)Online publication date: 12-Aug-2019
https://dl.acm.org/doi/10.1007/978-3-030-25027-0_10

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