Local, private, efficient protocols for succinct histograms

Raef Bassily, Adam Smith

Research output: Chapter in Book/Report/Conference proceedingConference contribution

294 Scopus citations


We give efficient protocols and matching accuracy lower bounds for frequency estimation in the local model for differential privacy. In this model, individual users randomize their data themselves, sending differentially private reports to an untrusted server that aggregates them. We study protocols that produce a succinct histogram representation of the data. A succinct histogram is a list of the most frequent items in the data (often called "heavy hitters") along with estimates of their frequencies; the frequency of all other items is implicitly estimated as 0. If there are n users whose items come from a universe of size d, our protocols run in time polynomial in n and log(d). With high probability, they estimate the accuracy of every item up to error O(√ log(d)/(∈2n)). Moreover, we show that this much error is necessary, regardless of computational efficiency, and even for the simple setting where only one item appears with significant frequency in the data set. Previous protocols (Mishra and Sandler, 2006; Hsu, Khanna and Roth, 2012) for this task either ran in time Ω(d) or had much worse error (about 6√log(d)/(∈2n)), and the only known lower bound on error was Ω(1/√n). We also adapt a result of McGregor et al (2010) to the local setting. In a model with public coins, we show that each user need only send 1 bit to the server. For all known local protocols (including ours), the transformation preserves computational efficiency.

Original languageEnglish (US)
Title of host publicationSTOC 2015 - Proceedings of the 2015 ACM Symposium on Theory of Computing
PublisherAssociation for Computing Machinery
Number of pages9
ISBN (Electronic)9781450335362
StatePublished - Jun 14 2015
Event47th Annual ACM Symposium on Theory of Computing, STOC 2015 - Portland, United States
Duration: Jun 14 2015Jun 17 2015

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017


Other47th Annual ACM Symposium on Theory of Computing, STOC 2015
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Software


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