Asynchronous Gathering of Finite Memory Robots on a Circle under Limited Visibility

The gathering of robots is a fundamental problem and has been extensively studied in the area of distributed computing. Consider a set of [Formula: see text] mobile entities, called robots, located and operating on a continuous circle of fixed radius. All robots are initially in distinct locations on a circle. The gathering problem asks to design a distributed algorithm that allows the robots to assemble at a single point on the circle. Robots are anonymous, identical, and homogeneous. They have finite memory and operate in a deterministic Look-Compute-Move cycle within the circular path. Robots agree on the clockwise direction. The robots’ movement is rigid and they have limited visibility [Formula: see text], i.e., each robot can only see the points of the circle which is at an angular distance strictly less than [Formula: see text] from the robot. Di Luna et al. [DISC’2020] provided a deterministic gathering algorithm of oblivious and silent robots on a circle under semi-synchronous (SSync) scheduler with [Formula: see text] visibility. Now considering asynchronous scheduler, to the best of our knowledge, there is no work that solves this problem. So, here in this work, we have proposed a deterministic algorithm that gathers [Formula: see text] robots on a circle having [Formula: see text] visibility and finite memory under asynchronous scheduler.