Exponentially Fast Collaborative Broadcasting in 3D Space

Broadcasting stands as a vital function within wireless sensor networks (WSNs), where nodes disseminate messages throughout the entire network, radiating in all possible directions. Our focus lies on the issue of three-dimensional broadcasting, involving n sensors/robots positioned uniformly across a three-dimensional space. We propose an exponentially fast hybrid collaborative broadcasting algorithm in three-dimensional space "growing ball" through successive propagation steps. We study the effect of various parameters such as the density of the growing ball (ρ), distance (d), the energy emitted by node (Eemit), and ϵ used by the collaborative broadcast. Our approach is based on the idea of dividing the 3D space into two halves that reduce mathematical intricacy. The number of nodes Nk in the k^th step of the growing ball is the factor of (1+ϵ)^k implies the exponential fast broadcast.