O(log n)-Time Uniform Circle Formation for Asynchronous Opaque Luminous Robots

We study the Uniform Circle Formation (UCF) problem for a distributed system of n robots which are required to displace on the vertices of a regular n-gon. We consider a well-studied model of autonomous, anonymous, mobile robots that act on the plane through Look-Compute-Move cycles. Moreover, robots are unaware of the cardinality of the system, they are punctiform, completely disoriented, opaque, and luminous. Collisions among robots are not tolerated. In the literature, the UCF problem has been solved for such a model by a deterministic algorithm in the asynchronous mode, using a constant amount of light colors and O(n) epochs in the worst case. In this paper, we provide an improved algorithm for solving the UCF problem for asynchronous robots, which uses O(log n) epochs still maintaining a constant amount of colors.