| Summary: | Iteratively computing and discarding a set of convex hulls creates a structure known as an "onion". In this thesis, we show that the expected number of layers of a convex hull onion for n uniformly and independently distributed points in a disk is theta( n23 ). Additionally, we show that in general the bound is theta( n2d+1 ) for points distributed in a d-dimensional ball. Further, we show that this bound holds more generally for any fixed, bounded, full-dimensional shape with a non-empty interior. The results of this thesis were published in Random Structures and Algorithms (2004) [1].
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