Group Testing with Multiple Mutually-Obscuring Positives

Group testing is a frequently used tool to identify an unknown set of defective (positive) elements out of a large collection of elements by testing subsets (pools) for the presence of defectives. Various models have been studied in the literature. The most studied case concerns only two types (defective and non-defective) of elements in the given collection. This paper studies a novel and natural generalization of group testing, where more than one type of defectives are allowed with an additional assumption that certain obscuring phenomena occur among different types of defectives. This paper proposes some algorithms for this problem, trying to optimize different measures of performance: the total number of tests required, the number of stages needed to perform all tests and the decoding complexity.