Author

Nir Petruschka

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Preprint Aug 2026

Towards Lower Bounds for Geometric Spanners in High Dimension

We study the stretch--size tradeoff for geometric spanners in high-dimensional $\ell_p$ spaces. Our main contribution is a simple proof of a lower bound shown by Har-Peled, Indyk, and Sidiropoulos [SODA 2013]: Every $2$-hop $t$-spanner of the pointset $\{0,1\}^d$ under $\ell_2$ norm has at least $(2^d)^{1+\Omega(1/t^2)...

Robert Krauthgamer, Nir Petruschka · 0 citations

Conference Aug 2026

Fast Metric Decompositions in High Dimension

The algorithm constructs a new sparse neighborhood cover that is based on geometric properties of $\ell_\infty$ and utilizes recent reductions between covers and decompositions, and the techniques have additional applications to spanners and nearest-neighbor search.

Robert Krauthgamer, Asaf Petruschka, Nir Petruschka · Embedded Systems and Applica... · 0 citations