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The Power of Abstract MAC Layer: A Fault-Tolerance Perspective

Authors Qinzi Zhang , Lewis Tseng

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Author Details

Qinzi Zhang
  • Boston University, MA, USA
Lewis Tseng
  • UMass-Lowell, MA, USA

Funding

  • Tseng, Lewis: This material is based upon work partially supported by the National Science Foundation under Grant CNS-2334021.

Acknowledgements

The authors want to thank the anonymous reviewers for insightful comments. The work was partially done when Lewis Tseng was affiliated with Boston College and Clark University.

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Qinzi Zhang and Lewis Tseng. The Power of Abstract MAC Layer: A Fault-Tolerance Perspective. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 39:1-39:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.DISC.2024.39

Abstract

This paper studies the power of the "abstract MAC layer" model in a single-hop asynchronous network. The model captures primitive properties of modern wireless MAC protocols. In this model, Newport [PODC '14] proves that it is impossible to achieve deterministic consensus when nodes may crash. Subsequently, Newport and Robinson [DISC '18] present randomized consensus algorithms that terminate with O(n³ log n) expected broadcasts in a system of n nodes. We are not aware of any results on other fault-tolerant distributed tasks in this model. We first study the computability aspect of the abstract MAC layer. We present a wait-free algorithm that implements an atomic register. Furthermore, we show that in general, k-set consensus is impossible. Second, we aim to minimize storage complexity. Existing algorithms require Ω(n log n) bits. We propose two wait-free approximate consensus and two wait-free randomized binary consensus algorithms that only need constant storage complexity (except for the phase index). One randomized algorithm terminates with O(n log n) expected broadcasts. All our algorithms are anonymous, meaning that at the algorithm level, nodes do not need to have a unique identifier.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Abstract MAC Layer
  • Computation Power
  • Consensus

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