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Fast Nearest Neighbor Search for 𝓁_p Metrics

Authors Robert Krauthgamer , Nir Petruschka

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LIPIcs.SoCG.2026.66.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation β†’ Computational geometry
  • Theory of computation β†’ Nearest neighbor algorithms
Keywords
  • Nearest neighbor search
  • metric embeddings
  • 𝓁_p norm

Metrics

Abstract

The Nearest Neighbor Search (NNS) problem asks to design a data structure that preprocesses an n-point dataset X lying in a metric space β„³, so that given a query point q ∈ β„³, one can quickly return a point of X minimizing the distance to q. The efficiency of such a data structure is evaluated primarily by the amount of space it uses and the time required to answer a query. We focus on the fast query-time regime, which is crucial for modern large-scale applications, where datasets are massive and queries must be processed online, and is often modeled by query time poly(d log n) when β„³ is a d-dimensional normed space. Our main result is such a randomized data structure for NNS in 𝓁_p^d spaces, p > 2, that achieves p^{O(1) + log log p} approximation with fast query time and poly(dn) space. Our data structure improves, or is incomparable to, the state-of-the-art for the fast query-time regime from [Bartal and Gottlieb, TCS 2019] and [Krauthgamer, Petruschka and Sapir, FOCS 2025].

Cite As Get BibTex

Robert Krauthgamer and Nir Petruschka. Fast Nearest Neighbor Search for 𝓁_p Metrics. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 66:1-66:9, Schloss Dagstuhl – Leibniz-Zentrum fΓΌr Informatik (2026) https://doi.org/10.4230/LIPIcs.SoCG.2026.66

Author Details

Robert Krauthgamer
  • The Harry Weinrebe Professorial Chair of Computer Science, Weizmann Institute of Science, Rehovot, Israel
Nir Petruschka
  • Weizmann Institute of Science, Rehovot, Israel

Funding

  • Krauthgamer, Robert: Work partially supported by the Israel Science Foundation grant #1336/23.

Acknowledgements

We thank Shay Sapir and Asaf Petruschka for helpful discussions.

References

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