Brief Announcement: Fault-Tolerant 3D Leader Election in the Amoebot Model

Abstract

We study leader election for programmable matter in the amoebot model when particles operate on a lattice graph and may experience crash-recovery failures. We propose a lattice-group view that captures both the classical 2D triangular grid and the 3D face-centered cubic (FCC) grid, including configurations with holes and the full lattice symmetry group. To the best of our knowledge, this is the first leader-election framework for 3D amoebot systems that simultaneously handles holes, the full lattice symmetry group including reflections, and crash-recovery faults. We outline (i) a randomized fault-tolerant leader election algorithm based on Borůvka-style merging of candidate-rooted trees combined with a coordinate-based solitude-verification, and (ii) a deterministic approach for assorted local orientations that simulates a virtual instance for each possible orientation in the symmetry group and breaks residual symmetries via a centroid-guided movement phase. Logarithmic-size coordinates are streamed or stored distributively, preserving constant local memory, while crashes are handled by rerooting so failures partition trees without destroying the global competition structure.