Adjoint Separating Systems

Abstract

Combinatorial group testing is a method that could be used to efficiently test many individuals for diseases like COVID-19 by pooling and testing their samples. This paper develops ideas concerning separating systems as an initial theoretical framework for studying combinatorial group testing methods. A system of subsets of a finite set S is called separating if it enables to separate individual elements of S, i.e., for any two different aspects of S there is a set in the system containing just one of them. In this paper, we present an easy and flexible method to construct “small” separating systems on “large” sets from “large” separating systems on “small” sets. The point is that small systems are practical for saving time and money, while large ones are much easier to construct.