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Bounding the Size of an Almost-Equidistant Set in Euclidean Space

  • ANDREY KUPAVSKII (a1), NABIL H. MUSTAFA (a2) and KONRAD J. SWANEPOEL (a3)

Abstract

A set of points in d-dimensional Euclidean space is almost equidistant if, among any three points of the set, some two are at distance 1. We show that an almost-equidistant set in ℝd has cardinality O(d4/3).

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The work of Andrey Kupavskii was supported by Russian Foundation for Basic Research grant 18-01-00355.

The work of Nabil H. Mustafa in this paper has been supported by the grant ANR SAGA (JCJC-14-CE25-0016-01).

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Bounding the Size of an Almost-Equidistant Set in Euclidean Space

  • ANDREY KUPAVSKII (a1), NABIL H. MUSTAFA (a2) and KONRAD J. SWANEPOEL (a3)

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