An Optimal Self-Stabilizing Firing Squad

TL;DR

This paper introduces FireAlg, the first self-stabilizing algorithm for the firing squad problem in fully connected networks, ensuring rapid convergence and response despite crashes and arbitrary initial states.

Contribution

It presents FireAlg, an optimal self-stabilizing firing squad algorithm that guarantees quick convergence and response times in crash-prone networks.

Findings

FireAlg guarantees simultaneous firing after a GO input.

It converges to a safe state as fast as existing algorithms.

It responds to external inputs with minimal delay.

Abstract

Consider a fully connected network where up to $t$ processes may crash, and all processes start in an arbitrary memory state. The self-stabilizing firing squad problem consists of eventually guaranteeing simultaneous response to an external input. This is modeled by requiring that the non-crashed processes "fire" simultaneously if some correct process received an external "GO" input, and that they only fire as a response to some process receiving such an input. This paper presents FireAlg, the first self-stabilizing firing squad algorithm. The FireAlg algorithm is optimal in two respects: (a) Once the algorithm is in a safe state, it fires in response to a GO input as fast as any other algorithm does, and (b) Starting from an arbitrary state, it converges to a safe state as fast as any other algorithm does.