Distinct distances in homogeneous sets

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Distinct distances in homogeneous sets

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Annual Symposium on Computational Geometry archive
Proceedings of the nineteenth annual symposium on Computational geometry table of contents

San Diego, California, USA

SESSION: Combinatorial geometry table of contents

Pages: 104 - 105

Year of Publication: 2003

ISBN:1-58113-663-3

Authors

Jazsef Solymosi	University of California, San Diego, La Jolla, California
Van H. Vu	University of California, San Diego, La Jolla, California

Sponsors

SIGACT: ACM Special Interest Group on Algorithms and Computation Theory
SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques
ACM: Association for Computing Machinery

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 4, Downloads (12 Months): 17, Citation Count: 2

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ABSTRACT

We show that the number of distinct distances in a well-distributed set of n points in R^d is O (n^2/d-1/d²) which is not far from the best known upper bound O(n^2/d).

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	Aronov, Pach, Sharir, and Tardos. Distinct distances in three and higher dimensions. Manuscript, 2003.
	2	Kenneth L. Clarkson , Herbert Edelsbrunner , Leonidas J. Guibas , Micha Sharir , Emo Welzl, Combinatorial complexity bounds for arrangements of curves and spheres, Discrete & Computational Geometry, v.5 n.2, p.99-160, 1990 [doi>10.1007/BF02187783]
	3	Erdos. On sets of distances of n points. Amer. Math. Monthly, 53:248--250, 1946.
	4	Iosevich. Curvature, combinatorics, and the fourier transform. Notices of the American Mathematical Society, 48, 2001.
	5	Solymosi, Tardos, and Toth. The k most frequent distances in the plane. Discrete and Computational Geometry, 28, 2002.
	6	Solymosi and Toth. Distinct distances in the plane. Discrete and Computational Geometry, 25, 2001.

CITED BY 2

	Boris Aronov , János Pach , Micha Sharir , Gábor Tardos, Distinct distances in three and higher dimensions, Proceedings of the thirty-fifth annual ACM symposium on Theory of computing, June 09-11, 2003, San Diego, CA, USA
	Boris Aronov , János Pach , Micha Sharir , Gábor Tardos, Distinct Distances in Three and Higher Dimensions, Combinatorics, Probability and Computing, v.13 n.3, p.283-293, May 2004