Self-stabilizing Snapshot Objects for Asynchronous Failure-Prone Networked Systems

Abstract

A snapshot object simulates the behavior of an array of single-writer/multi-reader shared registers that can be read atomically. Delporte-Gallet et al. proposed two fault-tolerant algorithms for snapshot objects in asynchronous crash-prone message-passing systems. Their first algorithm is non-blocking; it allows snapshot operations to terminate once all write operations had ceased. It uses $\mathcal {O}(n)$ messages of $\mathcal {O}(n \cdot \nu )$ bits, where n is the number of nodes and $\nu$ is the number of bits it takes to represent the object. Their second algorithm allows snapshot operations to always terminate independently of write operations. It incurs $\mathcal {O}(n^2)$ messages. The fault model of Delporte-Gallet et al. considers node failures (crashes). We aim at the design of even more robust snapshot objects. We do so through the lenses of self-stabilization—a very strong notion of fault-tolerance. In addition to Delporte-Gallet et al. ’s fault model, a self-stabilizing algorithm can recover after the occurrence of transient faults; these faults represent arbitrary violations of the assumptions according to which the system was designed to operate (as long as the code stays intact). In particular, in this work, we propose self-stabilizing variations of Delporte-Gallet et al. ’s non-blocking algorithm and always-terminating algorithm. Our algorithms have similar communication costs to the ones by Delporte-Gallet et al. and $\mathcal {O}(1)$ recovery time (in terms of asynchronous cycles) from transient faults. The main differences are that our proposal considers repeated gossiping of $\mathcal {O}(\nu )$ bits messages and deals with bounded space, which is a prerequisite for self-stabilization.