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research article

On the Adversarial Robustness of Locality-Sensitive Hashing in Hamming Space

Kapralov, Michael  
•
Makarov, Mikhail  
•
Sohler, Christian
June 9, 2025
Proceedings of the ACM on Management of Data

Locality-sensitive hashing (Indyk-Motwani'98) is a classical data structure for approximate nearest neighbor search. It allows, after a close to linear time preprocessing of the input dataset, to find an approximately nearest neighbor of any fixed query in sublinear time in the dataset size. The resulting data structure is randomized and succeeds with high probability for every fixed query independent of the randomness of the data structure. In many modern applications of nearest neighbor search the queries are, however, chosen adaptively. In this paper, we study the robustness of locality-sensitive hashing in Hamming space to adaptive queries. We present a simple adversary that can, under mild assumptions on the initial point set, provably find a query to the approximate near neighbor search data structure that the data structure fails on. Crucially, our adaptive algorithm finds the hard query exponentially faster than random sampling.

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Type
research article
DOI
10.1145/3725239
Author(s)
Kapralov, Michael  

École Polytechnique Fédérale de Lausanne

Makarov, Mikhail  

École Polytechnique Fédérale de Lausanne

Sohler, Christian
Date Issued

2025-06-09

Publisher

Association for Computing Machinery (ACM)

Published in
Proceedings of the ACM on Management of Data
Volume

3

Issue

2

Start page

1

End page

24

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
THL4  
Available on Infoscience
June 11, 2025
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/251212
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