Gathering on a Circle with Limited Visibility by Anonymous Oblivious Robots
Giuseppe A. Di Luna, Ryuhei Uehara, Giovanni Viglietta, and Yukiko, Yamauchi

TL;DR
This paper investigates the gathering problem for anonymous, oblivious robots on a circle with limited visibility, providing algorithms for full visibility and impossibility results for limited visibility, using novel probabilistic techniques.
Contribution
It introduces a distributed algorithm for gathering with full visibility and proves impossibility for limited visibility, employing a new probabilistic approach in robot pattern formation.
Findings
Gathering is possible when robots can see the entire circle (visibility $ heta= ext{pi}$).
Gathering is impossible when visibility is limited to $ heta extless ext{pi/2}$, regardless of initial asymmetry.
A novel probabilistic technique based on random perturbations is used for impossibility proofs.
Abstract
A swarm of anonymous oblivious mobile robots, operating in deterministic Look-Compute-Move cycles, is confined within a circular track. All robots agree on the clockwise direction (chirality), they are activated by an adversarial semi-synchronous scheduler (SSYNCH), and an active robot always reaches the destination point it computes (rigidity). Robots have limited visibility: each robot can see only the points on the circle that have an angular distance strictly smaller than a constant from the robot's current location, where (angles are expressed in radians). We study the Gathering problem for such a swarm of robots: that is, all robots are initially in distinct locations on the circle, and their task is to reach the same point on the circle in a finite number of turns, regardless of the way they are activated by the scheduler. Note that, due to the…
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