{"ID":2823426,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2601.00272","arxiv_id":"2601.00272","title":"Efficient Algorithms for Adversarially Robust Approximate Nearest Neighbor Search","abstract":"We study the Approximate Nearest Neighbor (ANN) problem under a powerful adaptive adversary that controls both the dataset and a sequence of $Q$ queries. Primarily, for the high-dimensional regime of $d = ω(\\sqrt{Q})$, we introduce a sequence of algorithms with progressively stronger guarantees. We first establish a novel connection between adaptive security and \\textit{fairness}, leveraging fair ANN search to hide internal randomness from the adversary with information-theoretic guarantees. To achieve data-independent performance, we then reduce the search problem to a robust decision primitive, solved using a differentially private mechanism on a Locality-Sensitive Hashing (LSH) data structure. This approach, however, faces an inherent $\\sqrt{n}$ query time barrier. To break the barrier, we propose a novel concentric-annuli LSH construction that synthesizes these fairness and differential privacy techniques. The analysis introduces a new method for robustly releasing timing information from the underlying algorithm instances and, as a corollary, also improves existing results for fair ANN. In addition, for the low-dimensional regime $d = O(\\sqrt{Q})$, we propose specialized algorithms that provide a strong ``for-all'' guarantee: correctness on \\textit{every} possible query with high probability. We introduce novel metric covering constructions that simplify and improve prior approaches for ANN in Hamming and $\\ell_p$ spaces.","short_abstract":"We study the Approximate Nearest Neighbor (ANN) problem under a powerful adaptive adversary that controls both the dataset and a sequence of $Q$ queries. Primarily, for the high-dimensional regime of $d = ω(\\sqrt{Q})$, we introduce a sequence of algorithms with progressively stronger guarantees. We first establish a no...","url_abs":"https://arxiv.org/abs/2601.00272","url_pdf":"https://arxiv.org/pdf/2601.00272v1","authors":"[\"Alexandr Andoni\",\"Themistoklis Haris\",\"Esty Kelman\",\"Krzysztof Onak\"]","published":"2026-01-01T09:23:19Z","proceeding":"cs.DS","tasks":"[\"cs.DS\"]","methods":"[]","has_code":false}