Better Differentially Private Approximate Histograms and Heavy Hitters using the Misra-Gries Sketch

Lebeda, Christian Janos; Tětek, Jakub

doi:10.1145/3584372.3588673

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2024

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Cited by 4 publications

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Differential Private Histogram Publication with Background Knowledge

Xue

2024

2024 IEEE 48th Annual Computers, Software, and Applications Conference (COMPSAC)

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Differential Private Histogram Publication with Background Knowledge

Xue

2024

2024 IEEE 48th Annual Computers, Software, and Applications Conference (COMPSAC)

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DPSW-Sketch: A Differentially Private Sketch Framework for Frequency Estimation over Sliding Windows

Wang,

Chen

2024

Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining

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Streaming Algorithms with Few State Changes

Jayaram,

Woodruff,

Zhou

2024

Proc. ACM Manag. Data

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In this paper, we study streaming algorithms that minimize the number of changes made to their internal state (i.e., memory contents). While the design of streaming algorithms typically focuses on minimizing space and update time, these metrics fail to capture the asymmetric costs, inherent in modern hardware and database systems, of reading versus writing to memory. In fact, most streaming algorithms write to their memory on every update, which is undesirable when writing is significantly more expensive than reading. This raises the question of whether streaming algorithms with small space and number of memory writes are possible. We first demonstrate that, for the fundamental F p moment estimation problem with p ≥ 1, any streaming algorithm that achieves a constant factor approximation must make Ω(n 1-1/p ) internal state changes, regardless of how much space it uses. Perhaps surprisingly, we show that this lower bound can be matched by an algorithm which also has near-optimal space complexity. Specifically, we give a (1+ε)-approximation algorithm for F p moment estimation that use a near-optimal ~O ε (n 1-1/p ) number of state changes, while simultaneously achieving near-optimal space, i.e., for p∈[1,2), our algorithm uses poly(log n,1/ε) bits of space for, while for p>2, the algorithm uses ~O ε (n 1-1/p ) space. We similarly design streaming algorithms that are simultaneously near-optimal in both space complexity and the number of state changes for the heavy-hitters problem, sparse support recovery, and entropy estimation. Our results demonstrate that an optimal number of state changes can be achieved without sacrificing space complexity.

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Better Differentially Private Approximate Histograms and Heavy Hitters using the Misra-Gries Sketch

Cited by 4 publications

References 18 publications

Differential Private Histogram Publication with Background Knowledge

Differential Private Histogram Publication with Background Knowledge

DPSW-Sketch: A Differentially Private Sketch Framework for Frequency Estimation over Sliding Windows

Streaming Algorithms with Few State Changes

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