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In the gathering problem, n autonomous robots have to meet on a single point.We consider the gathering of a closed chain of point-shaped, anonymous robotson a grid. The robots only have local knowledge about a constant number ofneighboring robots along the chain in both directions. Actions are performed inthe fully synchronous time model FSYNC. Every robot has a limited memory thatmay contain one timestamp of the global clock, also visible to its directneighbors. In this synchronous time model, there is no limited view gatheringalgorithm known to perform better than in quadratic runtime. The configurationsthat show the quadratic lower bound are closed chains. In this paper, wepresent the first sub-quadratic---in fact linear time---gathering algorithm forclosed chains on a grid.

Towards Gathering Robots with Limited View in Linear Time: The Closed Chain Case