10.46298/dmtcs.464
https://dmtcs.episciences.org/464
Erickson, Jeff
Jeff
Erickson
Hurtado, Ferran
Ferran
Hurtado
Morin, Pat
Pat
Morin
0000-0003-0471-4118
Natural Sciences and Engineering Research Council of Canada
Centerpoint theorems for wedges
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).
episciences.org
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
2015-06-09
2009-01-01
2009-01-01
en
journal article
https://hal.science/hal-00988186v1
1365-8050
https://dmtcs.episciences.org/464/pdf
VoR
application/pdf
Discrete Mathematics & Theoretical Computer Science
Vol. 11 no. 1
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