# Sketch-Flip-Merge: Mergeable Sketches for Private Distinct Counting

arXiv: https://arxiv.org/abs/2302.02056 · HTML: https://mlsanity.com/paper/2302.02056/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Feb 2023.

## Built on by (most cited first, 2 of 2)

- [PAPAYA Federated Analytics Stack: Engineering Privacy, Scalability and Practicality](https://mlsanity.com/paper/2412.02340/) (2024)
- [DPSW-Sketch: A Differentially Private Sketch Framework for Frequency Estimation over Sliding Windows (Technical Report)](https://mlsanity.com/paper/2406.07953/) (2024)

## Abstract (arXiv)

Data sketching is a critical tool for distinct counting, enabling multisets to be represented by compact summaries that admit fast cardinality estimates. Because sketches may be merged to summarize multiset unions, they are a basic building block in data warehouses. Although many practical sketches for cardinality estimation exist, none provide privacy when merging. We propose the first practical cardinality sketches that are simultaneously mergeable, differentially private (DP), and have low empirical errors. These introduce a novel randomized algorithm for performing logical operations on noisy bits, a tight privacy analysis, and provably optimal estimation. Our sketches dramatically outperform existing theoretical solutions in simulations and on real-world data.