Distributed leader election and computation of local identifiers for programmable matter

TL;DR

This paper introduces a leader election algorithm for programmable matter particles on infinite grids, assigning local identifiers to particles so that nearby particles have distinct IDs, using minimal memory.

Contribution

It presents a novel leader election algorithm that assigns local identifiers with proximity differentiation, requiring only constant memory per particle.

Findings

Particles can elect a leader in infinite grid environments.

The algorithm assigns local identifiers ensuring nearby particles have different IDs.

Memory usage per particle is constant (O(1)).

Abstract

The context of this paper is programmable matter, which consists of a set of computational elements, called particles, in an infinite graph. The considered infinite graphs are the square, triangular and king grids. Each particle occupies one vertex, can communicate with the adjacent particles, has the same clockwise direction and knows the local positions of neighborhood particles. Under these assumptions, we describe a new leader election algorithm affecting a variable to the particles, called the k-local identifier, in such a way that particles at close distance have each a different k-local identifier. For all the presented algorithms, the particles only need a O(1)-memory space.