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Distinct distances in homogeneous sets

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Published:08 June 2003Publication History

ABSTRACT

We show that the number of distinct distances in a well-distributed set of n points in Rd is O (n2/d-1/d2) which is not far from the best known upper bound O(n2/d).

References

  1. Aronov, Pach, Sharir, and Tardos. Distinct distances in three and higher dimensions. Manuscript, 2003.Google ScholarGoogle Scholar
  2. Clarkson, Edelsbrunner, Guibas, Sharir, and Welzl. Combinatorial complexity bounds for arrangements of curves and spheres. Discrete and Computational Geometry, 5, 1990.Google ScholarGoogle Scholar
  3. Erdos. On sets of distances of n points. Amer. Math. Monthly, 53:248--250, 1946.Google ScholarGoogle ScholarCross RefCross Ref
  4. Iosevich. Curvature, combinatorics, and the fourier transform. Notices of the American Mathematical Society, 48, 2001.Google ScholarGoogle Scholar
  5. Solymosi, Tardos, and Toth. The k most frequent distances in the plane. Discrete and Computational Geometry, 28, 2002.Google ScholarGoogle Scholar
  6. Solymosi and Toth. Distinct distances in the plane. Discrete and Computational Geometry, 25, 2001.Google ScholarGoogle Scholar

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  1. Distinct distances in homogeneous sets

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    • Published in

      cover image ACM Conferences
      SCG '03: Proceedings of the nineteenth annual symposium on Computational geometry
      June 2003
      398 pages
      ISBN:1581136633
      DOI:10.1145/777792

      Copyright © 2003 ACM

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      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 8 June 2003

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      Acceptance Rates

      SCG '03 Paper Acceptance Rate42of118submissions,36%Overall Acceptance Rate625of1,685submissions,37%

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