Efficient pooling designs and screening performance in group testing for two type defectives

TL;DR

This paper develops efficient pooling designs and a belief propagation algorithm for group testing scenarios involving two types of defectives, improving testing efficiency and accuracy.

Contribution

It introduces a novel belief propagation algorithm and pooling strategies specifically for two-type defective group testing, extending prior single-type models.

Findings

The belief propagation algorithm effectively estimates defectives.

Pooling designs reduce the number of tests needed.

Simulation results demonstrate improved performance.

Abstract

Group testing is utilized in the case when we want to find a few defectives among large amount of items. Testing n items one by one requires n tests, but if the ratio of defectives is small, group testing is an efficient way to reduce the number of tests. Many research have been developed for group testing for a single type of defectives. In this paper, we consider the case where two types of defective A and B exist. For two types of defectives, we develop a belief propagation algorithm to compute marginal posterior probability of defectives. Furthermore, we construct several kinds of collections of pools in order to test for A and B. And by utilizing our belief propagation algorithm, we evaluate the performance of group testing by conducting simulations.