Author

Tian Zhang

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Preprint Sep 2026

Fast Geometric Spanners via Approximate Nearest Neighbor Search

We study the problem of constructing metric spanners in general metric spaces in subquadratic time when given blackbox access to a fast algorithm for batch approximate nearest neighbor search. In particular, we show the following results for any metric space $\mathsf{M} = ([n], \mathsf{d})$ with aspect ratio $\Delta$ a...

Alexandr Andoni, M. Páez, Krish Singal et al. · 0 citations

Preprint Sep 2026

Approximate Nearest Neighbor in Ultra-High Dimensional $\ell_\infty$

One may preserve all pairwise distances of an $n$ point dataset up to a factor of $O(c)$ by computing distances on only $n^{1+1/c}$ coordinates by computing distances on only $n^{1+1/c}$ coordinates.

Nathan White, Tian Zhang · 0 citations