Circle formation by asynchronous opaque robots on infinite grid

Abstract

This paper presents a distributed algorithm for the Circle Formation problem under the infinite grid environment by asynchronous mobile opaque robots. Initially, all of the robots acquire distinct positions, and they must form a circle over the grid. The movements of the robots are only restricted along the grid lines; they do not share any global coordinate system. The robots are controlled by an asynchronous adversarial scheduler that operates in Look-Compute-Move cycles. The robots are indistinguishable by their nature, and they do not have any memory of their past configurations nor previous actions. We consider the problem under a luminous model, where robots communicate via lights; other than that, they do not have any external communication systems. Our protocol solves the Circle Formation problem using seven colors. A subroutine of our algorithm also solves the Line Formation problem using three colors