Asynchronous Gathering of Robots with Finite Memory on a Circle under Limited Visibility
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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 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 π, i.e., each robot can only see the points of the circle which is at an angular distance strictly less than π from the robot. Di Luna et al. [DISC'2020] provided a deterministic gathering algorithm of oblivious and silent robots on a circle in semi-synchronous (SSync) scheduler. Buchin et al. [IPDPS(W)'2021] showed that, under full visibility, 𝒪ℬℒ𝒪𝒯 robot model with SSync scheduler is incomparable to ℱ𝒮𝒯𝒜 robot (robots are silent but have finite persistent memory) model with asynchronous (ASync) scheduler. Under limited visibility, this comparison is still unanswered. So, this work extends the work of Di Luna et al. [DISC'2020] under ASync scheduler for ℱ𝒮𝒯𝒜 robot model.
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