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Section: New Results


On Order Types of Random Point Sets

Participant : Marc Glisse.

In collaboration with Olivier Devillers and Xavier Goaoc (Inria team Gamble) and Philippe Duchon (LaBRI, Université de Bordeaux).

Let P be a set of n random points chosen uniformly in the unit square. In this paper [41], we examine the typical resolution of the order type of P. First, we show that with high probability, P can be rounded to the grid of step 1n3+ϵ without changing its order type. Second, we study algorithms for determining the order type of a point set in terms of the number of coordinate bits they require to know. We give an algorithm that requires on average 4nlog2n+O(n) bits to determine the order type of P, and show that any algorithm requires at least 4nlog2n-O(nloglogn) bits. Both results extend to more general models of random point sets.