Points and triangles in the plane and halving planes in space

Authors:
Boris Aronov;Bernard Chazelle;Herbert Edelsbrunner;Leonidas J. Guibas;Micha Sharir;Rephael Wenger
Affiliations:
DIMACS, Rutgers University;Department of Computer Science, Princeton University;Department of Computer Science, University of Illinois at Urbana-Champaign;DEC Systems Research Center and Computer Science Department, Stanford University;Courant Institute of Mathematical Sciences, New York University, and School of Mathematical Sciences, Tel Aviv University;DIMACS, Rutgers University
Venue:
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Year:
1990

Citing 5
Cited 1

The number of small semispaces of a finite set of points in the plane

Journal of Combinatorial Theory Series A
Power diagrams: properties, algorithms and applications

SIAM Journal on Computing
Algorithms in combinatorial geometry

Algorithms in combinatorial geometry
On the number of halving planes

SCG '89 Proceedings of the fifth annual symposium on 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

Voronoi diagrams—a survey of a fundamental geometric data structure

ACM Computing Surveys (CSUR)

Quantified Score

Hi-index	0.00

Visualization

Abstract

We prove that for any set S of n points in the plane and n3-&agr; triangles spanned by the points of S there exists a point (not necessarily of S) contained in at least n3-3&agr;/(512 log5 n) of the triangles. This implies that any set of n points in three-dimensional space defines at most 6.4n8/3 log5/3 n halving planes.