# Optimal Nested Test Plan for Combinatorial Quantitative Group Testing

arXiv: https://arxiv.org/abs/1407.2283 · HTML: https://mlsanity.com/paper/1407.2283/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2014.

## Built on by (most cited first, 4 of 4)

- [Distributed Reconstruction of Noisy Pooled Data](https://mlsanity.com/paper/2204.07491/) (2022)
- [Efficient Approximate Recovery from Pooled Data Using Doubly Regular Pooling Schemes](https://mlsanity.com/paper/2303.00043/) (2023)
- [On a Near-Optimal & Efficient Algorithm for the Sparse Pooled Data Problem](https://mlsanity.com/paper/2312.14588/) (2023)
- [Learning to Ask: Decision Transformers for Adaptive Quantitative Group Testing](https://mlsanity.com/paper/2509.01723/) (2025)

## Abstract (arXiv)

We consider the quantitative group testing problem where the objective is to identify defective items in a given population based on results of tests performed on subsets of the population. Under the quantitative group testing model, the result of each test reveals the number of defective items in the tested group. The minimum number of tests achievable by nested test plans was established by Aigner and Schughart in 1985 within a minimax framework. The optimal nested test plan offering this performance, however, was not obtained. In this work, we establish the optimal nested test plan in closed form. This optimal nested test plan is also order optimal among all test plans as the population size approaches infinity. Using heavy-hitter detection as a case study, we show via simulation examples orders of magnitude improvement of the group testing approach over two prevailing sampling-based approaches in detection accuracy and counter consumption. Other applications include anomaly detection and wideband spectrum sensing in cognitive radio systems.