On the Optimal Configuration of a Square Array Group Testing Algorithm

TL;DR

This paper derives exact formulas for the optimal configuration of a Square Array group testing algorithm, compares its efficiency to other schemes, and recommends its use based on Bayesian and minimax strategies.

Contribution

It provides the first exact analytical expressions for the optimal configuration of the A2 Square Array group testing scheme and evaluates its performance against other methods.

Findings

A2 GT scheme outperforms classical schemes in gain per specimen.

Optimal configuration formulas are explicitly derived.

Bayesian and minimax strategies favor group testing over individual testing.

Abstract

Up to date, only lower and upper bounds for the optimal configuration of a Square Array (A2) Group Testing (GT) algorithm are known. We establish exact analytical formulae and provide a couple of applications of our result. First, we compare the A2 GT scheme to several other classical GT schemes in terms of the gain per specimen attained at optimal configuration. Second, operating under objective Bayesian framework with the loss designed to attain minimum at optimal GT configuration, we suggest the preferred choice of the group size under natural minimal assumptions: the prior information regarding the prevalence suggests that grouping and application of A2 is better than individual testing. The same suggestion is provided for the Minimax strategy.