On Order Types of Random Point Sets
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Let P be a set of n random points chosen uniformly in the unit square. In this paper, 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 1/n^3+ϵ without changing its order type. Second, we study algorithms for determining the order type of a point set in terms of the the number of coordinate bits they require to know. We give an algorithm that requires on average 4n 2 n + O(n) bits to determine the order type of P, and show that any algorithm requires at least 4n 2 n -- O(n n) bits. Both results extend to more general models of random point sets.
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