Counting the onion
Copyright policy )Counting the onion
AbstractIteratively computing and discarding a set of convex hulls creates a structure known as an “onion.” In this paper, we show that the expected number of layers of a convex hull onion for n uniformly and independently distributed points in a disk is Θ(n2/3). Additionally, we show that in general the bound is Θ(n2/(d+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 nonempty interior. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004
- McGill University Canada
Combinatorial probability, Random convex sets and integral geometry (aspects of convex geometry), convex depth, probability analysis, Geometric probability and stochastic geometry, convex hull, onion
Combinatorial probability, Random convex sets and integral geometry (aspects of convex geometry), convex depth, probability analysis, Geometric probability and stochastic geometry, convex hull, onion
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