License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.59
URN: urn:nbn:de:0030-drops-188849
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18884/
Blocki, Jeremiah ;
Grigorescu, Elena ;
Mukherjee, Tamalika ;
Zhou, Samson
How to Make Your Approximation Algorithm Private: A Black-Box Differentially-Private Transformation for Tunable Approximation Algorithms of Functions with Low Sensitivity
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.
BibTeX - Entry
@InProceedings{blocki_et_al:LIPIcs.APPROX/RANDOM.2023.59,
author = {Blocki, Jeremiah and Grigorescu, Elena and Mukherjee, Tamalika and Zhou, Samson},
title = {{How to Make Your Approximation Algorithm Private: A Black-Box Differentially-Private Transformation for Tunable Approximation Algorithms of Functions with Low Sensitivity}},
booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
pages = {59:1--59:24},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-296-9},
ISSN = {1868-8969},
year = {2023},
volume = {275},
editor = {Megow, Nicole and Smith, Adam},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2023/18884},
URN = {urn:nbn:de:0030-drops-188849},
doi = {10.4230/LIPIcs.APPROX/RANDOM.2023.59},
annote = {Keywords: Differential privacy, approximation algorithms}
}
|
Keywords: |
|
Differential privacy, approximation algorithms |
|
Collection: |
|
Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023) |
|
Issue Date: |
|
2023 |
|
Date of publication: |
|
04.09.2023 |
