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 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 Ω(N 2 ) in the fully synchronous setting. The proposed algorithm is collision-free – robots do not share positions and their paths do not cross.
CITATION STYLE
Sharma, G., Busch, C., & Mukhopadhyay, S. (2019). Complete visibility for oblivious robots in O(N) Time. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11028 LNCS, pp. 67–84). Springer Verlag. https://doi.org/10.1007/978-3-030-05529-5_5
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