eng
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
2009-01-01
Vol. 11 no. 1
10.46298/dmtcs.464
464
journal article
Centerpoint theorems for wedges
Jeff Erickson
Ferran Hurtado
Pat Morin
https://orcid.org/0000-0003-0471-4118
General
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).
https://dmtcs.episciences.org/464/pdf
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]