Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Points and triangles in the plane and halving planes in space
Discrete & Computational Geometry
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
Selecting Heavily Covered Points
SIAM Journal on Computing
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
The Clarkson–Shor Technique Revisited and Extended
Combinatorics, Probability and Computing
On Center Regions and Balls Containing Many Points
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Coloring geometric range spaces
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
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In this paper we prove several point selection theorems concerning objects ‘spanned’ by a finite set of points. For example, we show that for any set $P$ of $n$ points in $\R^2$ and any set $C$ of $m \,{\geq}\, 4n$ distinct pseudo-circles, each passing through a distinct pair of points of $P$, there is a point in $P$ that is covered by (i.e., lies in the interior of) $\Omega(m^2/n^2)$ pseudo-circles of $C$. Similar problems involving point sets in higher dimensions are also studied.Most of our bounds are asymptotically tight, and they improve and generalize results of Chazelle, Edelsbrunner, Guibas, Hershberger, Seidel and Sharir [8], where weaker bounds for some of these cases were obtained.