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

TL;DR

This paper explores the capabilities and limitations of the abstract MAC layer model in fault-tolerant distributed systems, presenting new algorithms for consensus with minimal storage and analyzing computability constraints.

Contribution

It introduces wait-free algorithms for atomic register implementation and constant storage consensus, and analyzes the computability limits of the model.

Findings

Atomic register can be implemented wait-free in the model.

Constant storage consensus algorithms are feasible.

Some consensus problems are impossible in this model.

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 {\Omega}(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.