Differential privacy and Sublinear time are incompatible sometimes

TL;DR

This paper investigates the fundamental limitations of combining differential privacy with sublinear algorithms, proving that in some cases these two desirable properties cannot be achieved simultaneously.

Contribution

It establishes the first lower bounds demonstrating the incompatibility of differential privacy and sublinear time algorithms in certain problems.

Findings

Differential privacy and sublinear algorithms are sometimes fundamentally incompatible.

A simple problem based on one-way marginals illustrates this incompatibility.

No strictly sublinear-time differentially-private algorithm exists for the studied problem.

Abstract

Differential privacy and sublinear algorithms are both rapidly emerging algorithmic themes in times of big data analysis. Although recent works have shown the existence of differentially private sublinear algorithms for many problems including graph parameter estimation and clustering, little is known regarding hardness results on these algorithms. In this paper, we initiate the study of lower bounds for problems that aim for both differentially-private and sublinear-time algorithms. Our main result is the incompatibility of both the desiderata in the general case. In particular, we prove that a simple problem based on one-way marginals yields both a differentially-private algorithm, as well as a sublinear-time algorithm, but does not admit a ``strictly'' sublinear-time algorithm that is also differentially private.