SHARPER BOUNDS IN ADAPTIVE GROUP TESTING

Abstract

Adaptive group testing in the presence of a large percentage of defectives is best done by individual testing rather than by pooling. The fraction of items which must be defective to make individual testing optimal remains unknown, and is conjectured to be 1/3. In this paper it is shown that when the number of items is sufficiently large, and the fraction of defective items is at least $1/\log_{3/2}3$, individual testing is optimal.