Asynchronous Latency and Fast Atomic Snapshot

TL;DR

The paper tackles the challenge of measuring latency for asynchronous, long‑lived distributed abstractions (LA and ASO) by exposing deficiencies in existing time metrics and proposing a unifying, operation‑level latency framework. It develops a fast, fault‑tolerant LA protocol built on buffering, helping, and full data relaying, and shows how to implement a SW MR ASO atop LA with a principled join‑semilattice construction. The resulting LA/ASO scheme achieves optimal two‑round latency in fault‑free, no‑contention runs, eight rounds under contention, and amortized constant latency in long executions despite $O(n^2)$ total message complexity; the worst‑case latency scales as $O(k)$ where $k$ is the number of active faulty processes. By introducing Iterative Round Assignment and a generalized CR/NTR framework, the paper enables fair, rigorous comparisons with prior work and clarifies how holes in executions affect latency assessments, providing a solid foundation for evaluating long‑lived asynchronous protocols.

Abstract

This paper introduces a novel, fast atomic-snapshot protocol for asynchronous message-passing systems. In the process of defining what ``fast'' means exactly, we spot a few interesting issues that arise when conventional time metrics are applied to long-lived asynchronous algorithms. We reveal some gaps in latency claims made in earlier work on snapshot algorithms, which hamper their comparative time-complexity analysis. We then come up with a new unifying time-complexity metric that captures the latency of an operation in an asynchronous, long-lived implementation. This allows us to formally grasp latency improvements of our atomic-snapshot algorithm with respect to the state-of-the-art protocols: optimal latency in fault-free runs without contention, short constant latency in fault-free runs with contention, the worst-case latency proportional to the number of active concurrent failures, and constant, amortized latency.

Figures (10)

• Figure 1: Example of round assignment using $\textbf{IRA}$. Arrows represent message transmissions and the number below an event corresponds to its round. A "hole" in communication appears betwen events $e_3$ and $e_5$.
• Figure 2: Example of an execution with 2 rounds in the Round, CR and NTR metrics.
• Figure 3: Example of a reliable broadcast protocol execution.
• Figure 4: Examples of non-covered and covered executions.
• Figure 5: An execution in which there are $2$$\textbf{CR}$ rounds between $e_2$ and $e_4$. However, the difference of the rounds assigned to $e_2$ and $e_4$ using $\textbf{NTR}$ is $1$.

Theorems & Definitions (49)

• Definition 1: Lattice Agreement (LA)
• Theorem 2
• Lemma 3
• Lemma 4
• Lemma 5
• Theorem 6
• Corollary 7
• Definition 8: Iterative Round Assignment - Informal
• Definition 9: $\textbf{IRA}$ - Arbitrary Events
• Theorem 10