Amortized Constant Round Atomic Snapshot in Message-Passing Systems

TL;DR

This paper presents a crash-tolerant atomic snapshot algorithm with amortized constant round complexity in asynchronous message-passing systems, improving efficiency especially when failures are limited.

Contribution

It introduces the first early-stopping lattice agreement algorithm in asynchronous systems and achieves amortized constant round complexity for atomic snapshots.

Findings

Achieves amortized constant round complexity when failures are limited.

First early-stopping lattice agreement algorithm in asynchronous systems.

Unconditional O(1) rounds in failure-free executions.

Abstract

We study the lattice agreement (LA) and atomic snapshot problems in asynchronous message-passing systems where up to $f$ nodes may crash. Our main result is a crash-tolerant atomic snapshot algorithm with \textit{amortized constant round complexity}. To the best of our knowledge, the best prior result is given by Delporte et al. [TPDS, 18] with amortized $O(n)$ complexity if there are more scans than updates. Our algorithm achieves amortized constant round if there are $\Omega(\sqrt{k})$ operations, where $k$ is the number of actual failures in an execution and is bounded by $f$. Moreover, when there is no failure, our algorithm has $O(1)$ round complexity unconditionally. To achieve amortized constant round complexity, we devise a simple \textit{early-stopping} lattice agreement algorithm and use it to "order" the update and scan operations for our snapshot object. Our LA algorithm has $O(\sqrt{k})$ round complexity. It is the first early-stopping LA algorithm in asynchronous systems.