Affiliation:
1. University of British Columbia, Vancouver BC
Abstract
Abstract
We prove that every set of n points in $\mathbb{R}^{3}$ spans O(n295/197+ε) unit distances. This is an improvement over the previous bound of O(n3/2), which was a natural barrier for this problem. A key ingredient in the proof is a new result for cutting circles in $\mathbb{R}^{3}$ into pseudo-segments.
Publisher
Oxford University Press (OUP)
Cited by
13 articles.
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