Broadcastings and digit tilings on three-dimensional torus networks

A tiling in a finite abelian group H is a pair of subsets of H such that any h∈H can be uniquely represented as t+l where and l∈L. This paper studies a finite analogue of self-affine tilings in Euclidean spaces and applies it to a problem of broadcasting on circuit switched networks. We extend the tiling argument of Peters and Syska [Joseph G. Peters, Michel Syska, Circuit switched broadcasting in torus networks, IEEE Trans. Parallel Distrib. Syst., 7 (1996) 246–255] to 3-dimensional torus networks.