Improved bound for k-sets in three dimensions

Micha Sharir; Shakhar Smorodinsky; Gabor Tardos

doi:10.1145/336154.336173

Improved bound for k-sets in three dimensions

Micha Sharir, Shakhar Smorodinsky, Gabor Tardos

Research output: Contribution to conference › Paper › peer-review

9 Scopus citations

Abstract

The problem of determining tight asymptotic bounds on the maximum number of k-sets is one of the most challenging open problems in combinatorial geometry. It is a widely studied problem due to its importance in analyzing geometric algorithms. The maximum number of k-sets in a set of n points in three dimensions is proven O(nk^3/2). This improves substantially the best known upper bound of O(nk^5/3).

Original language	English
Pages	43-49
Number of pages	7
DOIs	https://doi.org/10.1145/336154.336173
State	Published - 1 Jan 2000
Externally published	Yes
Event	16th Annual Symposium on Computational Geometry - Hong Kong, Hong Kong Duration: 12 Jun 2000 → 14 Jun 2000

Conference

Conference	16th Annual Symposium on Computational Geometry
City	Hong Kong, Hong Kong
Period	12/06/00 → 14/06/00

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Computational Mathematics

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10.1145/336154.336173

Cite this

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abstract = "The problem of determining tight asymptotic bounds on the maximum number of k-sets is one of the most challenging open problems in combinatorial geometry. It is a widely studied problem due to its importance in analyzing geometric algorithms. The maximum number of k-sets in a set of n points in three dimensions is proven O(nk3/2). This improves substantially the best known upper bound of O(nk5/3).",

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N2 - The problem of determining tight asymptotic bounds on the maximum number of k-sets is one of the most challenging open problems in combinatorial geometry. It is a widely studied problem due to its importance in analyzing geometric algorithms. The maximum number of k-sets in a set of n points in three dimensions is proven O(nk3/2). This improves substantially the best known upper bound of O(nk5/3).

AB - The problem of determining tight asymptotic bounds on the maximum number of k-sets is one of the most challenging open problems in combinatorial geometry. It is a widely studied problem due to its importance in analyzing geometric algorithms. The maximum number of k-sets in a set of n points in three dimensions is proven O(nk3/2). This improves substantially the best known upper bound of O(nk5/3).

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DO - 10.1145/336154.336173

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T2 - 16th Annual Symposium on Computational Geometry

Y2 - 12 June 2000 through 14 June 2000

ER -

Improved bound for k-sets in three dimensions

Abstract

Conference

ASJC Scopus subject areas

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