The optimal procedures for quantitative group testing

Abstract

Suppose we have exactly two defective elements in a set and we are going to identify these two defectives from the set by a series of group testings while the feedback for each testing subset is the number of the defective elements contained in this subset. Let T( n) be the minimal number of tests which will definitely identify the two defective elements from a set with size n. In this paper, we obtain several inequalities about T( n), and prove the convergence of { T(n) ln n }. In particular, we show that the golden section method is not a good approximation for T( n) as n is large.