Optimal Nested Test Plan for Combinatorial Quantitative Group Testing

TL;DR

This paper derives the optimal nested test plan for quantitative group testing, providing a closed-form solution that outperforms existing methods in accuracy and efficiency, with applications in anomaly detection and spectrum sensing.

Contribution

The paper establishes the first closed-form solution for the optimal nested test plan in quantitative group testing, proving its order optimality.

Findings

Optimal nested test plan derived in closed form

Order optimality of the plan as population size grows

Significant improvement over existing sampling-based methods in simulations

Abstract

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.