2026-07-22T08:26:36Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:18884 2024-03-06T11:02:50Z ddc:004 open_access

How to Make Your Approximation Algorithm Private: A Black-Box Differentially-Private Transformation for Tunable Approximation Algorithms of Functions with Low Sensitivity Blocki, Jeremiah Grigorescu, Elena Mukherjee, Tamalika Zhou, Samson Differential privacy approximation algorithms 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Jeremiah Blocki and Elena Grigorescu and Tamalika Mukherjee and Samson Zhou 2023 Is Part Of LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX/RANDOM.2023.59 urn:nbn:de:0030-drops-188849 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.59 eng https://creativecommons.org/licenses/by/4.0/legalcode