Circle formation by asynchronous opaque robots on infinite grid

Abstract

This paper presents a distributed algorithm for circle formation problem under the infinite grid environment by asynchronous mobile opaque robots. Initially all the robots are acquiring distinct positions and they have to form a circle over the grid. Movements of the robots are restricted only along the grid lines. They do not share any global co-ordinate system. Robots are controlled by an asynchronous adversarial scheduler that operates in Look-Compute-Move cycles. The robots are indistinguishable by their nature, do not have any memory of their past configurations and previous actions. We consider the problem under luminous model, where robots communicate via lights, other than that they do not have any external communication system. Our protocol solves the  circle formation problem using seven colors. A subroutine of our algorithm also solves the line formation problem using three colors.