Distinct distances in three and higher dimensions

Boris Aronov, János Pach, Micha Sharir, G. Tardos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

Improving an old result of Clarkson et al., we show that the number of distinct distances determined by a set P of n points in three-dimensional space is Ω(n77/141-ε) = Ω(n0.546), for any ε > 0. Moreover, there always exists a point p ∈ P from which there are at least these many distinct distances to the remaining elements of P. The same result holds for points on the three-dimensional sphere. As a consequence, we obtain analogous results in higher dimensions.

Original languageEnglish
Title of host publicationConference Proceedings of the Annual ACM Symposium on Theory of Computing
Pages541-546
Number of pages6
Publication statusPublished - 2003
Event35th Annual ACM Symposium on Theory of Computing - San Diego, CA, United States
Duration: Jun 9 2003Jun 11 2003

Other

Other35th Annual ACM Symposium on Theory of Computing
CountryUnited States
CitySan Diego, CA
Period6/9/036/11/03

Keywords

  • Distinct distances
  • Incidences
  • Point configurations

ASJC Scopus subject areas

  • Software

Cite this

Aronov, B., Pach, J., Sharir, M., & Tardos, G. (2003). Distinct distances in three and higher dimensions. In Conference Proceedings of the Annual ACM Symposium on Theory of Computing (pp. 541-546)

Distinct distances in three and higher dimensions. / Aronov, Boris; Pach, János; Sharir, Micha; Tardos, G.

Conference Proceedings of the Annual ACM Symposium on Theory of Computing. 2003. p. 541-546.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Aronov, B, Pach, J, Sharir, M & Tardos, G 2003, Distinct distances in three and higher dimensions. in Conference Proceedings of the Annual ACM Symposium on Theory of Computing. pp. 541-546, 35th Annual ACM Symposium on Theory of Computing, San Diego, CA, United States, 6/9/03.
Aronov B, Pach J, Sharir M, Tardos G. Distinct distances in three and higher dimensions. In Conference Proceedings of the Annual ACM Symposium on Theory of Computing. 2003. p. 541-546
Aronov, Boris ; Pach, János ; Sharir, Micha ; Tardos, G. / Distinct distances in three and higher dimensions. Conference Proceedings of the Annual ACM Symposium on Theory of Computing. 2003. pp. 541-546
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