Brief Announcement: Gathering in Linear Time: A Closed Chain of Disoriented and Luminous Robots with Limited Visibility

This work focuses on the following question related to the Gathering problem of n autonomous, mobile robots in the Euclidean plane: Is it possible to solve Gathering of disoriented robots with limited visibility in \(o(n^2)\) fully synchronous rounds ( Open image in new window )? The best known algorithm considering the \(\mathcal {OBLOT}\) model (oblivious robots) needs \(\varTheta \left( n^2\right) \) rounds [6]. The lower bound for this algorithm even holds in a simplified closed chain model, where each robot has exactly two neighbors and the chain connections form a cycle. The only existing algorithms achieving a linear number of rounds for disoriented robots assume robots that are located on a two dimensional grid [1] and [5]. Both algorithms consider the \(\mathcal {LUMINOUS}\) model.