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

Distributed leader election and computation of local identifiers for programmable matter