Fast Nearest Neighbor Search for $\ell_p$ Metrics
Robert Krauthgamer, Nir Petruschka

TL;DR
This paper introduces a randomized data structure for approximate nearest neighbor search in spaces with p>2, achieving fast query times and improved approximation guarantees suitable for large-scale applications.
Contribution
It presents a novel data structure for NNS in spaces with p>2, offering faster query times and competitive approximation ratios compared to previous methods.
Findings
Achieves NNS with p>2 in poly(dn) space.
Provides approximation factor of p^{O(1)+\u221a{\u2212}log p}.
Outperforms or matches state-of-the-art in fast query regimes.
Abstract
The Nearest Neighbor Search (NNS) problem asks to design a data structure that preprocesses an -point dataset lying in a metric space , so that given a query point , one can quickly return a point of minimizing the distance to . 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 . Our main result is such a randomized data structure for NNS in spaces, , that achieves approximation with fast query time and space. Our data structure improves, or is incomparable to, the state-of-the-art for the…
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Taxonomy
TopicsData Management and Algorithms · Computational Geometry and Mesh Generation · Advanced Image and Video Retrieval Techniques
