Centerpoint theorems for wedges - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2009

Centerpoint theorems for wedges

Abstract

The Centerpoint Theorem states that, for any set S of n points in R(d), there exists a point p in R(d) such that every closed halfspace containing p contains at least [n/(d + 1)] points of S. We consider generalizations of the Centerpoint Theorem in which halfspaces are replaced with wedges (cones) of angle alpha. In R(2), we give bounds that are tight for all values of ff and give an O(n) time algorithm to find a point satisfying these bounds. We also give partial results for R(3) and, more generally, R(d).
Fichier principal
Vignette du fichier
1004-4082-1-PB.pdf (166.9 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00988186 , version 1 (07-05-2014)

Identifiers

Cite

Jeff Erickson, Ferran Hurtado, Pat Morin. Centerpoint theorems for wedges. Discrete Mathematics and Theoretical Computer Science, 2009, Vol. 11 no. 1 (1), pp.45--54. ⟨10.46298/dmtcs.464⟩. ⟨hal-00988186⟩

Collections

TDS-MACS
199 View
765 Download

Altmetric

Share

Gmail Facebook X LinkedIn More