Error-Tolerant Pooling Designs with Inhibitors

Pooling designs are used in clone library screening to efficiently distinguish positive clones from negative clones. Mathematically, a pooling design is just a nonadaptive group testing scheme which has been extensively studied in the literature. In some applications, there is a third category of clones called "inhibitors" whose effect is to neutralize positives. Specifically, the presence of an inhibitor in a pool dictates a negative outcome even though positives are present. Sequential group testing schemes, which can be modified to three-stage schemes, have been proposed for the inhibitor model, but it is unknown whether a pooling design (a one-stage scheme) exists. Another open question raised in the literature is whether the inhibitor model can treat unreliable pool outcomes. In this paper, we answer both open problems by giving a pooling design, as well as a two-stage scheme, for the inhibitor model with unreliable outcomes. The number of pools required by our schemes are quite comparable to the three-stage scheme.