On the Optimal Pairwise Group Testing Algorithm

TL;DR

This paper thoroughly characterizes the probabilistic properties of the Pairwise Testing Algorithm, an optimal nested group testing method originally proposed in 1990, which had been largely overlooked in literature.

Contribution

It provides the first comprehensive probabilistic analysis of PTA, establishing its fundamental properties and filling a significant gap in the understanding of this optimal group testing procedure.

Findings

Provides an exhaustive characterization of PTA's probabilistic properties

Confirms the optimality of PTA within a specific probability range

Fills a gap in the literature by analyzing a previously underexplored algorithm

Abstract

Originally suggested for the blood testing problem by Dorfman in 1943, an idea of Group Testing (GT) has found many applications in other fields as well. Among many (binomial) GT procedures introduced since then, in 1990, Yao and Hwang proposed the Pairwise Testing Algorithm (PTA) and demonstrated that PTA is the \emph{unique} optimal nested GT procedure provided the probability of contamination lies in $\left[1-\frac{\sqrt{2}}{2},\frac{3-\sqrt{5}}{2}\right]$. Despite the fundamental nature of the result, PTA did not receive considerable attention in the literature. In particular, even its basic probabilistic properties remained unexplored. In this paper, we fill the gap by providing an exhaustive characterization of probabilistic PTA properties.