Consensus with an Abstract MAC Layer

TL;DR

This paper explores the fundamental limits and possibilities of achieving distributed consensus in wireless networks using an abstract MAC layer model, providing new bounds and algorithms that inform both theory and practice.

Contribution

It generalizes known impossibility results to wireless settings, establishes network knowledge requirements, and offers new algorithms matching lower bounds for consensus.

Findings

Consensus is impossible without unique IDs or network size knowledge.

New deterministic algorithms are provided for single-hop and multihop topologies.

Lower bounds on time complexity are established.

Abstract

In this paper, we study distributed consensus in the radio network setting. We produce new upper and lower bounds for this problem in an abstract MAC layer model that captures the key guarantees provided by most wireless MAC layers. In more detail, we first generalize the well-known impossibility of deterministic consensus with a single crash failure [FLP 1895] from the asynchronous message passing model to our wireless setting. Proceeding under the assumption of no faults, we then investigate the amount of network knowledge required to solve consensus in our model---an important question given that these networks are often deployed in an ad hoc manner. We prove consensus is impossible without unique ids or without knowledge of network size (in multihop topologies). We also prove a lower bound on optimal time complexity. We then match these lower bounds with a pair of new deterministic consensus algorithms---one for single hop topologies and one for multihop topologies---providing a comprehensive characterization of the consensus problem in the wireless setting. From a theoretical perspective, our results shed new insight into the role of network information and the power of MAC layer abstractions in solving distributed consensus. From a practical perspective, given the level of abstraction used by our model, our upper bounds can be easily implemented in real wireless devices on existing MAC layers while preserving their correctness guarantees---facilitating the development of wireless distributed systems.