Nested Group Testing Procedures for Screening

TL;DR

This paper reviews adaptive nested group testing procedures designed to efficiently identify defective items among a set, minimizing the expected number of tests under probabilistic assumptions.

Contribution

It introduces and analyzes nested group testing strategies that adaptively optimize testing procedures for probabilistic defectiveness.

Findings

Nested procedures reduce the expected number of tests compared to non-adaptive methods.

The methods are effective under the probabilistic model with independent item defectiveness.

The approach provides a framework for efficient screening in large populations.

Abstract

This article reviews a class of adaptive group testing procedures that operate under a probabilistic model assumption as follows. Consider a set of $N$ items, where item $i$ has the probability $p$ ($p_i$ in the generalized group testing) to be defective, and the probability $1-p$ to be non-defective independent from the other items. A group test applied to any subset of size $n$ is a binary test with two possible outcomes, positive or negative. The outcome is negative if all $n$ items are non-defective, whereas the outcome is positive if at least one item among the $n$ items is defective. The goal is complete identification of all $N$ items with the minimum expected number of tests.