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.
|Number of pages||6|
|Journal||Conference Proceedings of the Annual ACM Symposium on Theory of Computing|
|State||Published - 2003|
|Event||35th Annual ACM Symposium on Theory of Computing - San Diego, CA, United States|
Duration: 9 Jun 2003 → 11 Jun 2003
- Distinct distances
- Point configurations