Follow Up on Detecting Deficiencies: An Optimal Group Testing Algorithm

TL;DR

This paper critiques and clarifies claims made in a 2017 article on an optimal group testing algorithm, correcting misconceptions and highlighting well-established results in the literature.

Contribution

The author provides clarifications, corrections, and commentary on Zimmerman’s 2017 claims about optimal group testing algorithms, reaffirming established facts.

Findings

Zimmerman's claims are contradicted by existing literature

Corrections are provided for mistaken claims in Zimmerman (2017)

Clarifications reinforce well-known group testing principles

Abstract

In a recent volume of Mathematics Magazine (Vol. 90, No. 3, June 2017) there is an interesting article by Seth Zimmerman, titled Detecting Deficiencies: An Optimal Group Testing Algorithm. The claim in the summary is contradictory to well-known facts reported in the group- testing literature, which is easily verified, beginning with the work by Sobel and Groll (1959), which was cited by S. Zimmerman himself. Therefore, I feel compelled to offer a number of comments and clarifications. In addition, I have made some correction of mistaken claim made by Zimmerman (2017).