The Power of Abstract MAC Layer: A Fault-tolerance Perspective
Qinzi Zhang, Lewis Tseng
TL;DR
This work analyzes the power of the abstract MAC layer for fault-tolerant primitives in a single-hop asynchronous setting. It first provides computability results, showing how a wait-free store-collect object can implement a linearizable register and how ($n-1$)-set consensus is impossible, while enabling anonymous, storage-efficient primitives. It then introduces four anonymous randomized/binary consensus algorithms—notably MAC-AdoptCommit, MAC-RBC, and MAC-RBC2—achieving $O(n \log n)$ expected broadcasts, with RBC2 further improving time via doubling-based size estimation and a first-mover conciliator. Collectively, the results demonstrate that the abstract MAC layer can realize strong, storage-efficient primitives without node identities, offering practical pathways for implementing fault-tolerant primitives atop real wireless MAC protocols.
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 four wait-free consensus algorithms that only need constant storage complexity. (Two approximate consensus and two randomized binary consensus algorithms.) One randomized algorithm terminates with O(n log n) expected broadcasts. All our consensus algorithms are anonymous, meaning that at the algorithm level, nodes do not need to have a unique identifier.