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

Consider a set of $n$ mobile entities, called robots, located and operating on a continuous circle, i.e., all robots are initially in distinct locations on a circle. The $\mathit{\text{gathering}}$ problem asks to design a distributed algorithm that allows the robots to assemble at a point on the circle. Robots are anonymous, identical, and homogeneous. Robots operate in a deterministic Look-Compute-Move cycle within the circular path. Robots agree on the clockwise direction. The robot’s movement is rigid and they have limited visibility $\pi$, i.e., each robot can only see the points of the circle which is at an angular distance strictly less than $\pi$ from the robot. Di Luna $\mathit{\text{et}}\mathit{\text{al}}$. [DISC’2020] provided a deterministic gathering algorithm of oblivious and silent robots on a circle in semi-synchronous ($\text{textsc}SSync$) scheduler. Buchin $\mathit{\text{et}}\mathit{\text{al}}$. [IPDPS(W)'2021] showed that, under full visibility, $\mathcal{O}\mathcal{B}\mathcal{L}\mathcal{O}\mathcal{T}$ robot model with $\text{textsc}SSync$ scheduler is incomparable to $\mathcal{F}\mathcal{S}\mathcal{T}\mathcal{A}$ robot (robots are silent but have finite persistent memory) model with asynchronous ($\text{textsc}ASync$) scheduler. Under limited visibility, this comparison is still unanswered. So, this work extends the work of Di Luna $\mathit{\text{et}}\mathit{\text{al}}$. [DISC’2020] under $\text{textsc}ASync$ scheduler for $\mathcal{F}\mathcal{S}\mathcal{T}\mathcal{A}$ robot model.