Counting the onion

Authors:
Ketan Dalal
Affiliations:
School of Computer Science, McGill University, Montreal, Canada, H3A 2K6
Venue:
Random Structures & Algorithms
Year:
2004

Citing 0
Cited 4

Towards the semantic extraction of digital signatures for librarian image-identification purposes

Journal of the American Society for Information Science and Technology
Dynamic ham-sandwich cuts in the plane

Computational Geometry: Theory and Applications
Counting crossing-free structures

Proceedings of the twenty-eighth annual symposium on Computational geometry
CG_Hadoop: computational geometry in MapReduce

Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems

Quantified Score

Hi-index	0.00

Visualization

Abstract

Iteratively 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.