Convex Hulls and Triangulations of Planar Point Sets on the Congested Clique

05/17/2023

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by   Jesper Jansson, et al.

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We consider geometric problems on planar n^2-point sets in the congested clique model. Initially, each node in the n-clique network holds a batch of n distinct points in the Euclidean plane given by O(log n)-bit coordinates. In each round, each node can send a distinct O(log n)-bit message to each other node in the clique and perform unlimited local computations. We show that the convex hull of the input n^2-point set can be constructed in O(min{ h,log n}) rounds, where h is the size of the hull, on the congested clique. We also show that a triangulation of the input n^2-point set can be constructed in O(log^2n) rounds on the congested clique.