On the Expected Number of k-sets of Coordinate-Wise Independent Points
msra
摘要
Let S be a set of n points in d dimensions. A k-set of S is a subset of size k that is the intersection of S with some open halfspace. This note shows that if the points of S are random, with a coordinate-wise independent distribution, then the expected number of k-sets of S is O((k log(en/k))d 1)2d/(d 1)!, as k logn ! 1, with a constant inde- pendent of the dimension.
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