We improve the space bound for streaming approximation of Diameter but also of Farthest Neighbor queries, Minimum Enclosing Ball and its Coreset, in high-dimensional Euclidean spaces. In particular, our deterministic streaming algorithms store O(ε−2log(ε1)) points. This improves by a factor of ε−1 the previous space bound of Agarwal and Sharathkumar (SODA 2010), while offering a simpler and more complete argument. We also show that storing Ω(ε−1) points is necessary for a (2+ε)-approximation of Farthest Pair or Farthest Neighbor queries.
@article{arxiv.2505.16720,
title = {Streaming Diameter of High-Dimensional Points},
author = {Magnús M. Halldórsson and Nicolaos Matsakis and Pavel Veselý},
journal= {arXiv preprint arXiv:2505.16720},
year = {2025}
}