Tracing a single user (Q850073)

Denote \(g(n,r)\) the maximum possible cardinality of a family of subsets of an \(n\)-element underlying set so that given a union of at most \(r\) members, one can identify at least one of the members. This has a close connection with the so-called group testing problem applied to design DNA chips in molecular biology. The paper shows that \(g(n,r)=2^{\Theta({n \over r})}.\) The main contribution of the paper is a new lower bound for \(g(n,r)\).