Complete Visibility for Oblivious Robots in 풪(N) Time

We consider the distributed setting of N autonomous mobile robots that operate in Look-Compute-Move cycles following the classic oblivious robots model. We study the fundamental problem where starting from an arbitrary initial configuration, N autonomous robots reposition themselves to a convex hull formation on the plane where each robot is visible to all others (the Complete Visibility problem). We assume obstructed visibility, where a robot cannot see another robot if a third robot is positioned between them on the straight line connecting them. We provide the first \(\mathcal{O}(N)\) time algorithm for this problem in the fully synchronous setting. Our contribution is a significant improvement over the runtime of the only previously known algorithm for this problem which has a lower bound of \(\varOmega (N^2)\) in the fully synchronous setting. The proposed algorithm is collision-free – robots do not share positions and their paths do not cross.

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