Fast Deterministic Consensus in a Noisy Environment

TL;DR

This paper introduces a noisy scheduling model where environmental randomness enables deterministic algorithms to solve consensus efficiently, achieving logarithmic or constant time solutions.

Contribution

It demonstrates that environmental noise can replace algorithmic randomness, allowing a deterministic consensus algorithm to operate efficiently in asynchronous and noisy environments.

Findings

Deterministic consensus is solvable in logarithmic time under noisy scheduling.

Quantum and priority scheduling can achieve constant-time consensus.

The approach shows robustness across different scheduling models.

Abstract

It is well known that the consensus problem cannot be solved deterministically in an asynchronous environment, but that randomized solutions are possible. We propose a new model, called noisy scheduling, in which an adversarial schedule is perturbed randomly, and show that in this model randomness in the environment can substitute for randomness in the algorithm. In particular, we show that a simplified, deterministic version of Chandra's wait-free shared-memory consensus algorithm (PODC, 1996, pp. 166-175) solves consensus in time at most logarithmic in the number of active processes. The proof of termination is based on showing that a race between independent delayed renewal processes produces a winner quickly. In addition, we show that the protocol finishes in constant time using quantum and priority-based scheduling on a uniprocessor, suggesting that it is robust against the choice of model over a wide range.