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

Leader Election And Local Identifiers For 3D Programmable Matter