Stationary and Deterministic Leader Election in Self-organizing Particle Systems

Abstract

We propose the first stationary and deterministic protocol for the leader election problem for non-simply connected particle systems in the geometric Amoebot model in which particles have no unique identifiers but have common chirality. The solution does not require particle movement to break symmetry (stationary) and does not allow particles to make probabilistic choices (deterministic). We show that leader election is possible if and only if the proposed protocol succeeds in electing a unique leader. We show that if the protocol fails to elect a leader, it will always succeed in finding a finite set of (Formula presented) leader candidates and the system must have k-symmetry that prevents the selection of less than k candidates. The protocols runs in (Formula presented) steps, where n is the number of particles in the system. Other solutions to the leader election problem in the Amoebot model are either probabilistic, assume that the system is simply connected, and/or require stronger primitives to break symmetry.