Detecting Deficiencies: An Optimal Group Testing Algorithm

Abstract

The use of group testing to locate all instances of disease in a large population of blood samples was first considered seventy years ago. Since then, several methods have been used to approximate the minimum expected number of tests. The procedure presented here, in contrast to all previous ones, takes a constructive rather than a top-down approach. As far as could be verified, it offers the first proven solution to the problem of finding the minimum expected number of tests with a predetermined procedure. Computer results indicate that the algorithm has a Fibonacci-based pattern.