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Title: Privately Estimating Graph Parameters in Sublinear Time
We initiate a systematic study of algorithms that are both differentially-private and run in sublinear time for several problems in which the goal is to estimate natural graph parameters. Our main result is a differentially-private $(1+\rho)$-approximation algorithm for the problem of computing the average degree of a graph, for every $\rho>0$. The running time of the algorithm is roughly the same (for sparse graphs) as its non-private version proposed by Goldreich and Ron (Sublinear Algorithms, 2005). We also obtain the first differentially-private sublinear-time approximation algorithms for the maximum matching size and the minimum vertex cover size of a graph. An overarching technique we employ is the notion of \emph{coupled global sensitivity} of randomized algorithms. Related variants of this notion of sensitivity have been used in the literature in ad-hoc ways. Here we formalize the notion and develop it as a unifying framework for privacy analysis of randomized approximation algorithms.
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Mikołaj Boja´nczyk, Emanuela Merelli
Award ID(s):
1931443 1910659 1910411
Publication Date:
Journal Name:
49th International Colloquium on Automata, Languages, and Programming (ICALP 2022).
Sponsoring Org:
National Science Foundation
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