k-Circle Formation and k-epf by Asynchronous Robots

For a given positive integer k, the k-circle formation problem asks set of autonomous, asynchronous robots to form disjoint circles having k each at distinct locations, centered fixed points in Euclidean plane. The are identical, anonymous, oblivious, and they operate Look–Compute–Move cycles. This paper studies its relationship with k-epf problem, generalized version embedded pattern which exactly reach remain point. First, is studied setting where have an agreement on common direction orientation one axes. We characterized all configurations values for deterministically unsolvable this setting. remaining deterministic distributed algorithm has been proposed, order solve problem. It proved that initial robot positions, if solvable then also solvable. shown by modifying proposed algorithm, can be solved deterministically.