A combinatorial result on points and circles on the plane
Discrete Mathematics
Some extremal results on circles containing points
Discrete & Computational Geometry
A combinatorial result about points and balls in Euclidean space
Discrete & Computational Geometry
A note on the circle containment problem
Discrete & Computational Geometry
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Lectures on Discrete Geometry
Selecting Points that are Heavily Covered by Pseudo-Circles, Spheres or Rectangles
Combinatorics, Probability and Computing
Algorithms for center and Tverberg points
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
A Lower Bound for the Rectilinear Crossing Number
Graphs and Combinatorics
On a Geometric Generalization of the Upper Bound Theorem
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
A theorem of bárány revisited and extended
Proceedings of the twenty-eighth annual symposium on Computational geometry
| Hi-index | 0.00 |
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 npoints in , there is a subset A茂戮驴 Sof size $\lfloor \frac{d+3}{2}\rfloor$ such that any ball containing Acontains at least roughly $\frac{4}{5ed^3}n$ 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.