Time-Optimal Self-Stabilizing Leader Election on Rings in Population Protocols

TL;DR

This paper introduces a self-stabilizing leader election protocol for directed rings in population protocols, achieving optimal convergence time with bounded states when the population size is known approximately.

Contribution

It presents a new protocol that elects a leader efficiently with optimal time complexity given an upper bound on population size.

Findings

Elects a unique leader within O(nN) expected steps

Uses O(N) states, optimal when N=O(n)

Works from any initial configuration

Abstract

We propose a self-stabilizing leader election protocol on directed rings in the model of population protocols. Given an upper bound $N$ on the population size $n$, the proposed protocol elects a unique leader within $O(nN)$ expected steps starting from any configuration and uses $O(N)$ states. This convergence time is optimal if a given upper bound $N$ is asymptotically tight, i.e., $N=O(n)$.