Threshold Group Testing on Inhibitor Model

Abstract

In classical group testing, one is given a population [Formula: see text] and an unknown subset [Formula: see text] of positive items, and the goal is to determine D by testing subsets of [Formula: see text]. Threshold group testing is a generalization of classical group testing, where the outcome of a group test is determined by the number of positive items in the test. In group testing on inhibitor model, inhibitors are the third type of item that dictate the test outcome to be negative regardless of how many positives are in the test. The threshold group testing on k-inhibitor model is a natural combination of threshold group testing and inhibitor model. In this article, we provide nonadaptive algorithms to conquer the threshold group testing on k-inhibitor model where error-tolerance is considered. Furthermore, we provide a two-stage algorithm to identify all inhibitors and find a g-approximate set.