Privately Estimating Graph Parameters in Sublinear time

TL;DR

This paper develops differentially private algorithms that estimate key graph parameters like average degree, maximum matching size, and minimum vertex cover size in sublinear time, using a new sensitivity framework.

Contribution

It introduces a unifying sensitivity framework and provides the first differentially private sublinear algorithms for several fundamental graph parameters.

Findings

Achieved a private $(1+ ho)$-approximation for average degree with sublinear time.

First private sublinear algorithms for maximum matching size.

First private sublinear algorithms for minimum vertex cover size.

Abstract

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 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 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.