Leader Election And Local Identifiers For 3D Programmable Matter

TL;DR

This paper introduces two deterministic algorithms for leader election in 3D programmable matter on a face-centered cubic grid, along with a method for assigning local identifiers efficiently.

Contribution

The paper presents novel leader election algorithms with different initial assumptions and a new local identifier assignment method for 3D programmable matter.

Findings

First algorithm requires strong initial configuration assumptions.

Second algorithm requires fewer initial assumptions but has limited applicability.

Local identifiers can be assigned with memory independent of the total number of particles.

Abstract

In this paper, we present two deterministic leader election algorithms for programmable matter on the face-centered cubic grid. The face-centered cubic grid is a 3-dimensional 12-regular infinite grid that represents an optimal way to pack spheres (i.e., spherical particles or modules in the context of the programmable matter) in the 3-dimensional space. While the first leader election algorithm requires a strong hypothesis about the initial configuration of the particles and no hypothesis on the system configurations that the particles are forming, the second one requires fewer hypothesis about the initial configuration of the particles but does not work for all possible particles' arrangement. We also describe a way to compute and assign-local identifiers to the particles in this grid with a memory space not dependent on the number of particles. A-local identifier is a variable assigned to each particle in such a way that particles at distance at most each have a different identifier.