Privately Estimating Graph Parameters in Sublinear Time

Authors Jeremiah Blocki, Elena Grigorescu, Tamalika Mukherjee

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Jeremiah Blocki
  • Department of Computer Science, Purdue University, West Lafayette, IN, USA
Elena Grigorescu
  • Department of Computer Science, Purdue University, West Lafayette, IN, USA
Tamalika Mukherjee
  • Department of Computer Science, Purdue University, West Lafayette, IN, USA


We thank several anonymous reviewers for their valuable feedback on a preliminary version of this work. We thank Soheil Behnezhad for bringing to our attention the subtlety in the analysis of [Krzysztof Onak et al., 2012], first discovered by [Yu Chen et al., 2020], and finally resolved in his recent work [Soheil Behnezhad, 2021]. We also thank Jakub Tetek for bringing up several points for clarification, which we have incorporated in the current version.

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Jeremiah Blocki, Elena Grigorescu, and Tamalika Mukherjee. Privately Estimating Graph Parameters in Sublinear Time. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 26:1-26:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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+ρ)-approximation algorithm for the problem of computing the average degree of a graph, for every ρ > 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 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.

Subject Classification

ACM Subject Classification
  • Security and privacy → Privacy-preserving protocols
  • Theory of computation → Streaming, sublinear and near linear time algorithms
  • differential privacy
  • sublinear time
  • graph algorithms


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