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DOI: 10.4230/LIPIcs.FORC.2025.15

Differentially Private High-Dimensional Approximate Range Counting, Revisited

Authors: Martin Aumüller, Fabrizio Boninsegna, and Francesco Silvestri

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract

Locality Sensitive Filters are known for offering a quasi-linear space data structure with rigorous guarantees for the Approximate Near Neighbor search (ANN) problem. Building on Locality Sensitive Filters, we derive a simple data structure for the Approximate Near Neighbor Counting (ANNC) problem under differential privacy (DP). Moreover, we provide a simple analysis leveraging a connection with concomitant statistics and extreme value theory. Our approach produces a simple data structure with a tunable parameter that regulates a trade-off between space-time and utility. Through this trade-off, our data structure achieves the same performance as the recent findings of Andoni et al. (NeurIPS 2023) while offering better utility at the cost of higher space and query time. In addition, we provide a more efficient algorithm under pure ε-DP and elucidate the connection between ANN and differentially private ANNC. As a side result, the paper provides a more compact description and analysis of Locality Sensitive Filters for Fair Near Neighbor Search, improving a previous result in Aumüller et al. (TODS 2022).

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Martin Aumüller, Fabrizio Boninsegna, and Francesco Silvestri. Differentially Private High-Dimensional Approximate Range Counting, Revisited. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 15:1-15:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aumuller_et_al:LIPIcs.FORC.2025.15,
  author =	{Aum\"{u}ller, Martin and Boninsegna, Fabrizio and Silvestri, Francesco},
  title =	{{Differentially Private High-Dimensional Approximate Range Counting, Revisited}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{15:1--15:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.15},
  URN =		{urn:nbn:de:0030-drops-231426},
  doi =		{10.4230/LIPIcs.FORC.2025.15},
  annote =	{Keywords: Differential Privacy, Locality Sensitive Filters, Approximate Range Counting, Concominant Statistics}
}

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Differentially Private High-Dimensional Approximate Range Counting, Revisited

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