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How to Make Your Approximation Algorithm Private: A Black-Box Differentially-Private Transformation for Tunable Approximation Algorithms of Functions with Low Sensitivity

Authors Jeremiah Blocki, Elena Grigorescu, Tamalika Mukherjee, Samson Zhou

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Author Details

Jeremiah Blocki
  • Purdue University, West Lafayette, IN, USA
Elena Grigorescu
  • Purdue University, West Lafayette, IN, USA
Tamalika Mukherjee
  • Purdue University, West Lafayette, IN, USA
Samson Zhou
  • University of California Berkeley, CA, USA
  • Rice University, Houston, TX, USA

Funding

  • Blocki, Jeremiah: Supported in part by NSF CCF-1910659, NSF CNS-1931443. and NSF CAREER award CNS-2047272.
  • Grigorescu, Elena: Supported in part by NSF CCF-1910659, NSF CCF-1910411, and NSF CCF-2228814.
  • Mukherjee, Tamalika: Supported in part by NSF CCF-1910659 and and NSF CCF-2228814.
  • Zhou, Samson: Work done in part while at Carnegie Mellon University and supported in part by a Simons Investigator Award and by NSF CCF-1815840.

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Jeremiah Blocki, Elena Grigorescu, Tamalika Mukherjee, and Samson Zhou. How to Make Your Approximation Algorithm Private: A Black-Box Differentially-Private Transformation for Tunable Approximation Algorithms of Functions with Low Sensitivity. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 59:1-59:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.59

Abstract

We develop a framework for efficiently transforming certain approximation algorithms into differentially-private variants, in a black-box manner. Specifically, our results focus on algorithms A that output an approximation to a function f of the form (1-α)f(x)-κ ≤ A(x) ≤ (1+α)f(x)+κ, where κ ∈ ℝ_{≥ 0} denotes additive error and α ∈ [0,1) denotes multiplicative error can be"tuned" to small-enough values while incurring only a polynomial blowup in the running time/space. We show that such algorithms can be made differentially private without sacrificing accuracy, as long as the function f has small "global sensitivity". We achieve these results by applying the "smooth sensitivity" framework developed by Nissim, Raskhodnikova, and Smith (STOC 2007). Our framework naturally applies to transform non-private FPRAS and FPTAS algorithms into ε-differentially private approximation algorithms where the former case requires an additional postprocessing step. We apply our framework in the context of sublinear-time and sublinear-space algorithms, while preserving the nature of the algorithm in meaningful ranges of the parameters. Our results include the first (to the best of our knowledge) ε-edge differentially-private sublinear-time algorithm for estimating the number of triangles, the number of connected components, and the weight of a minimum spanning tree of a graph whose accuracy holds with high probability. In the area of streaming algorithms, our results include ε-DP algorithms for estimating L_p-norms, distinct elements, and weighted minimum spanning tree for both insertion-only and turnstile streams. Our transformation also provides a private version of the smooth histogram framework, which is commonly used for converting streaming algorithms into sliding window variants, and achieves a multiplicative approximation to many problems, such as estimating L_p-norms, distinct elements, and the length of the longest increasing subsequence.

Subject Classification

ACM Subject Classification
  • Security and privacy → Usability in security and privacy
Keywords
  • Differential privacy
  • approximation algorithms

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