# A Fast Binary Splitting Approach to Non-Adaptive Group Testing

arXiv: https://arxiv.org/abs/2006.10268 · HTML: https://mlsanity.com/paper/2006.10268/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jun 2020.

## Built on by (most cited first, 5 of 5)

- [A Fast Binary Splitting Approach for Non-Adaptive Learning of ErdHos--R'enyi Graphs](https://mlsanity.com/paper/2511.17240/) (2025)
- [Concomitant Group Testing](https://mlsanity.com/paper/2309.04221/) (2023)
- [Matrix Completion in Group Testing: Bounds and Simulations](https://mlsanity.com/paper/2501.13780/) (2025)
- [Efficient Support Recovery of Mixtures of Sparse Linear Classifiers with Fewer Measurements](https://mlsanity.com/paper/2609.32176/) (2026)
- [Non-Adaptive Learning of Sparse ErdHos--R'enyi Graphs via Affine Splitting](https://mlsanity.com/paper/2609.33704/) (2026)

## Abstract (arXiv)

In this paper, we consider the problem of noiseless non-adaptive group testing under the for-each recovery guarantee, also known as probabilistic group testing. In the case of n items and k defectives, we provide an algorithm attaining high-probability recovery with O(k log n) scaling in both the number of tests and runtime, improving on the best known O(k2 log k · log n) runtime previously available for any algorithm that only uses O(k log n) tests. Our algorithm bears resemblance to Hwang's adaptive generalized binary splitting algorithm (Hwang, 1972); we recursively work with groups of items of geometrically vanishing sizes, while maintaining a list of "possibly defective" groups and circumventing the need for adaptivity. While the most basic form of our algorithm requires Omega(n) storage, we also provide a low-storage variant based on hashing, with similar recovery guarantees.