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 \textit{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 \textit{et al}. [DISC'2020] provided a deterministic gathering algorithm of oblivious and silent robots on a circle in semi-synchronous (\textsc{SSync}) scheduler. Buchin \textit{et al}. [IPDPS(W)'2021] showed that, under full visibility, $\mathcal{OBLOT}$ robot model with \textsc{SSync} scheduler is incomparable to $\mathcal{FSTA}$ robot (robots are silent but have finite persistent memory) model with asynchronous (\textsc{ASync}) scheduler. Under limited visibility, this comparison is still unanswered. So, this work extends the work of Di Luna \textit{et al}. [DISC'2020] under \textsc{ASync} scheduler for $\mathcal{FSTA}$ robot model.
翻译:考虑一组美元移动实体, 称为机器人, 位于一个连续圆上运行, 也就是说, 所有机器人最初都在一个圆圈上的不同位置 。\ textit{ 收集} 问题要求设计一个分布式算法, 允许机器人在圆圈的某个点集合。 机器人是匿名、 相同和同质的。 机器人在圆形路径中以确定性 Look- Compute- Move 循环运作。 机器人在顺时针方向上达成一致 。 机器人的动作是僵硬的, 且其可见度有限 $, 也就是说, 每个机器人只能看到圆圈的角距离严格低于 美元。 [Dluna\ textitleit{ 收集算法 。 [DISC' slickr=mountal_ rolexmoudal_ rolates (\ textscrc) 。 [Buch\ flickr{ flick} frolick{ al} 。 [IPS] roudrlickr} room_roomt_ roudal_ roomot_ rol_ rol_ rol_ rol_ rol_ rolick_ rol_ rolick_ roxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx