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.

翻译：差分隐私与亚线性算法皆是大数据分析时代快速兴起的算法范式。尽管近期研究已证明图参数估计与聚类等诸多问题存在具备差分隐私特性的亚线性算法，但关于此类算法的困难性结果仍鲜为人知。本文首次系统研究同时满足差分隐私与亚线性时间要求的算法下界问题。我们的核心结论表明：在一般情形下，这两个理想特性具有内在不兼容性。具体而言，我们证明基于单向边际量的基础问题既存在差分隐私算法，也存在亚线性时间算法，却无法同时实现兼具差分隐私特性与"严格"亚线性时间复杂度的算法。