Time-Optimal and Energy-Efficient Deterministic Consensus

TL;DR

This paper introduces deterministic consensus algorithms in a sleeping model that are optimal in time and energy efficiency, tolerating crash failures and reducing awake rounds significantly.

Contribution

It presents new deterministic algorithms for crash-tolerant consensus that achieve optimal time complexity and improved energy efficiency in the sleeping model.

Findings

Achieves optimal $f+1$ round time complexity for consensus.

Energy complexity for multi-value consensus is $O(rac{f^2}{n})$ rounds.

Binary consensus can be achieved in $O(rac{f}{ oot{n}})$ rounds.

Abstract

We study fault-tolerant consensus in a variant of the synchronous message passing model, where, in each round, every node can choose to be awake or asleep. This is known as the sleeping model (Chatterjee, Gmyr, Pandurangan PODC 2020) and defines the awake complexity (also called \emph{energy complexity}), which measures the maximum number of rounds that any node is awake throughout the execution. Only awake nodes can send and receive messages in a given round and all messages sent to sleeping nodes are lost. We present new deterministic consensus algorithms that tolerate up to $f<n$ crash failures, where $n$ is the number of nodes. Our algorithms match the optimal time complexity lower bound of $f+1$ rounds. For multi-value consensus, where the input values are chosen from some possibly large set, we achieve an energy complexity of ${O}(\lceil f^2 / n \rceil)$ rounds, whereas for binary consensus, we show that ${O}(\lceil f / \sqrt{n} \rceil)$ rounds are possible.