Cellular automata rules solving the wireless sensor network coverage problem

The problem of an optimal coverage of a wireless sensor network area is considered. To solve this problem, a Cellular Automata (CA) approach is proposed. More specifically, the objective is to find CA rules which are able to cover the 2D space by a minimum number of so-called "Sensor Tiles". A sensor tile consists of a von Neumann neighborhood of range 2 centered at sensor "point" and surrounded by 12 sensing "pixels". Two probabilistic CA rules were designed that can perform this task. Results of an experimental study show that the first rule evolves very fast stable sub-optimal coverings, starting from a random configuration. The second rule finds optimal coverings, however it needs much more time for their evolution. The results are supported by a theoretical study on von Neumann neighborhoods and borrowing either from heuristics or from the spectral theory of circulant graphs.