Note on generalized group testing

In this note, we present a new adaptive algorithm for generalized group testing, which is asymptotically optimal if $d=o({\log }_2\mathrm{\mid }E\mathrm{\mid })$, $E$ is a set of potentially contaminated sets, $d$ is a maximal size of elements of $E$. Also, we design a 3-stage algorithm, which is asymptotically optimal for $d=2$.