Author:
KAPLAN HAIM,MATOUŠEK JIŘÍ,SAFERNOVÁ ZUZANA,SHARIR MICHA
Abstract
We show that the number of unit distances determined bynpoints in ℝ3isO(n3/2), slightly improving the bound of Clarkson, Edelsbrunner, Guibas, Sharir and Welzl [5], established in 1990. The new proof uses the recently introduced polynomial partitioning technique of Guth and Katz [12]. While this paper was still in a draft stage, a similar proof of our main result was posted to the arXiv by Joshua Zahl [28].
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science
Reference28 articles.
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4. [28] Zahl J. (2011) An improved bound on the number of point-surface incidences in three dimensions. arXiv:1104.4987. First posted (v1) 26 April 2011; revised and corrected 22 September 2011.
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