TY - GEN
T1 - On center regions and balls containing many points
AU - Smorodinsky, Shakhar
AU - Sulovský, Marek
AU - Wagner, Uli
PY - 2008/8/4
Y1 - 2008/8/4
N2 - We study the disk containment problem introduced by Neumann-Lara and Urrutia and its generalization to higher dimensions. We relate the problem to centerpoints and lower centerpoints of point sets. Moreover, we show that for any set of n points in ℝd, there is a subset A ⊆ S of size [d+3/2] such that any ball containing A contains at least roughly 4/5ed 3n points of S. This improves previous bounds for which the constant was exponentially small in d. We also consider a generalization of the planar disk containment problem to families of pseudodisks.
AB - We study the disk containment problem introduced by Neumann-Lara and Urrutia and its generalization to higher dimensions. We relate the problem to centerpoints and lower centerpoints of point sets. Moreover, we show that for any set of n points in ℝd, there is a subset A ⊆ S of size [d+3/2] such that any ball containing A contains at least roughly 4/5ed 3n points of S. This improves previous bounds for which the constant was exponentially small in d. We also consider a generalization of the planar disk containment problem to families of pseudodisks.
UR - http://www.scopus.com/inward/record.url?scp=48249135435&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-69733-6_36
DO - 10.1007/978-3-540-69733-6_36
M3 - Conference contribution
AN - SCOPUS:48249135435
SN - 3540697322
SN - 9783540697329
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 363
EP - 373
BT - Computing and Combinatorics - 14th Annual International Conference, COCOON 2008, Proceedings
T2 - 14th Annual International Conference on Computing and Combinatorics, COCOON 2008
Y2 - 27 June 2008 through 29 June 2008
ER -