On a couple of unresolved group testing conjectures

Abstract

In the recent review published in 2019, Malinovsky and Albert conjectured analytical formulae of the optimal sample sizes for the modified Dorfman and Sterrett 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 their hypotheses analitically thereby filling in the present gap.

Keywords:

• Probabilistic group testing
• Sterrett scheme
• Dorfman scheme
• optimal configuration

Acknowledgments

We are grateful to the anonymous referee for constructive remarks given during the peer review process. These remarks enabled us to remove several inconsistencies contained in the initial manuscript and end up with a version of our results precisely matching the hypothesis announced by Malinovsky and Albert (2019).

Notes

1 For example, the American Red Cross makes use of Dorfman scheme for the screening of blood donations for HIV and hepatitis Dodd et al. (2002) whereas, in Lithuania, Dorfman scheme is currently applied to test for COVID-19 employees of larger firms and pupils attending public schools Alonderytė (2021).

2 This needs some reasoning yet we omit the details.