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Differential Privacy and Sublinear Time Are Incompatible Sometimes

Authors Jeremiah Blocki , Hendrik Fichtenberger , Elena Grigorescu , Tamalika Mukherjee

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ACM Subject Classification
  • Theory of computation → Theory of database privacy and security
  • Theory of computation → Streaming, sublinear and near linear time algorithms
  • Security and privacy → Privacy-preserving protocols
Keywords
  • differential privacy
  • sublinear algorithms
  • sublinear-time algorithms
  • one-way marginals
  • lower bounds

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Abstract

Differential privacy and sublinear algorithms are both rapidly emerging algorithmic themes in times of big data analysis. Although recent works have shown the existence of differentially private sublinear algorithms for many problems including graph parameter estimation and clustering, little is known regarding hardness results on these algorithms. In this paper, we initiate the study of lower bounds for problems that aim for both differentially-private and sublinear-time algorithms. Our main result is the incompatibility of both the desiderata in the general case. In particular, we prove that a simple problem based on one-way marginals yields both a differentially-private algorithm, as well as a sublinear-time algorithm, but does not admit a "strictly" sublinear-time algorithm that is also differentially private.

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Jeremiah Blocki, Hendrik Fichtenberger, Elena Grigorescu, and Tamalika Mukherjee. Differential Privacy and Sublinear Time Are Incompatible Sometimes. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 19:1-19:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.19

Author Details

Jeremiah Blocki
  • Purdue University, West Lafayette, IN, USA
Hendrik Fichtenberger
  • Google Research, Zürich, Switzerland
Elena Grigorescu
  • University of Waterloo, ON, Canada
Tamalika Mukherjee
  • Columbia University, New York, NY, USA

Funding

  • Blocki, Jeremiah: Supported in part by NSF CAREER Award CNS-2047272, and NSF Award CCF-1910659.
  • Grigorescu, Elena: Funded in part by NSF CCF-1910659, NSF CCF-2205811, and NSF CCF-2228814.
  • Mukherjee, Tamalika: Funded in part by NSF CCF-1910659, NSF CCF-2205811, and NSF CCF-2228814. Supported in part by Amazon through the Columbia Center of Artificial Intelligence Technology, a Google Cyber NYC Award, and DARPA under contract number W911NF2110371. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the United States Government or DARPA.

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