Year: 2025
Type: article
Abstract: 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.
DOI: 10.1145/3725239
Authors: Michael Kapralov, Mikhail Makarov, Christian Sohler
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4411141627