On a Couple of Unresolved Group Testing Conjectures

TL;DR

This paper rigorously proves and refines conjectured formulas for optimal sample sizes in modified Dorfman and Sterret group testing schemes, addressing previously unresolved theoretical questions.

Contribution

It provides the first rigorous proofs and refinements of the conjectured optimal sample size formulas in group testing schemes.

Findings

Confirmed the conjectured formulas analytically.

Refined the formulas for better accuracy.

Filled the gap in the theoretical understanding of group testing.

Abstract

In the recent review published in 2019, Malinovsky and Albert conjectured analytical formulae of the optimal sample sizes for the modified Dorfman and Sterret group testing schemes and verified the validity of the formulae numerically within a broad range. However, the authors pointed out that they were unable to give a rigorous proof of the stated conjectures. In this note, we affirm and refine their hypotheses analitically thereby filling in the present gap.