Selecting a Leader in a Network of Finite State Machines

Abstract

This paper studies a variant of the leader election problem under the stone age model (Emek and Wattenhofer, PODC 2013) that considers a network of n randomized finite automata with very weak communication capabilities (a multi-frequency asynchronous generalization of the beeping model's communication scheme). Since solving the classic leader election problem is impossible even in more powerful models, we consider a relaxed variant, referred to as k-leader selection, in which a leader should be selected out of at most k initial candidates. Our main contribution is an algorithm that solves k-leader selection for bounded k in the aforementioned stone age model. On (general topology) graphs of diameter D, this algorithm runs in Õ(D) time and succeeds with high probability. The assumption that k is bounded turns out to be unavoidable: we prove that if k = ω(1), then no algorithm in this model can solve k-leader selection with a (positive) constant probability.