On the generic Cut–Point detection procedure in the Binomial Group Testing

Abstract

Initially announced by Dorfman in 1943 for medical screening, (Binomial) Group Testing (BGT) was quickly recognized as a useful probabilistic tool in many other fields: quality control, communications and networking, engineering, statistics, etc. To apply any particular BGT procedure effectively, one first of all needs to know an important operating characteristic, the so called Optimal Cut-Point (OCP), describing the limits of its applicability. The determination of the latter is often a complicated task. In this work, we provide a generic algorithm suitable for a wide class of the BGT procedures and demonstrate its applicability by example. The way we do it exhibits independent interest since we link the BGT to seemingly unrelated field — the bifurcation theory.