An optimal extension of the centerpoint theorem

DOI10.1016/j.comgeo.2007.10.004zbMath1169.65020OpenAlexW2100880759MaRDI QIDQ924064

Saurabh Ray, Nabil H. Mustafa

Publication date: 27 July 2009

Published in: Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.comgeo.2007.10.004

zbMATH Keywords

combinatorial geometrydiscrete geometryweak \(\epsilon\)-netscenterpoint theoremextremal methodshitting convex sets

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35)

Related Items (7)

Small strong epsilon nets ⋮ Improved bounds for discrete Voronoi games ⋮ An optimal generalization of the colorful Carathéodory theorem ⋮ On strong centerpoints ⋮ Discrete Voronoi games and \(\epsilon\)-nets, in two and three dimensions ⋮ Extending the centerpoint theorem to multiple points ⋮ The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Small weak epsilon-nets
• \(\epsilon\)-nets and simplex range queries
• Breakdown properties of location estimates based on halfspace depth and projected outlyingness
• New constructions of weak \(\varepsilon\)-nets
• Point Selections and Weak ε-Nets for Convex Hulls
• Separators for sphere-packings and nearest neighbor graphs
• Improved bounds on weak ε-nets for convex sets
• APPROXIMATING CENTER POINTS WITH ITERATIVE RADON POINTS

This page was built for publication: An optimal extension of the centerpoint theorem