The Expected Number of Extreme Discs

Abstract: Given a finite set D of n planar discs whose centers are distributed randomly. We are interested in the expected number of extreme discs of the convex hull of D. We show that the expected number of extreme discs is at most O(log2n) for any distribution. This result can be used to derive expected complexity of convex hull algorithms. Keywords: Convex hull, computational geometry, expected number. Mathematics Subject Classification (2010): 65D18, 52A15, 51N05.