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Identification and Classification Problems on Pooling Designs for Inhibitor Models

Pooling designs are common tools to efficiently distinguish positive clones from negative clones in clone library screening. In some applications, there is a third type of clones called "inhibitors" whose effect is in a sense to obscure the positive clones in pools. Various inhibitor models have been proposed in the literature. We address the inhibitor problems of designing efficient nonadaptive procedures for both identification and classification problems, and improve previous results in three aspects: (1) The algorithm that is used to identify the positive clones works on a more general inhibitor model and has a polynomial-time decoding procedure that recovers the set of positives from the knowledge of the outcomes. (2) The algorithm that is used to classify all clones works in one-stage, i.e., all tests are arranged in advance without knowing the outcomes of other tests, along with a polynomial-time decoding procedure. (3) We extend our results to pooling designs on complexes where the property to be screened is defined on subsets of biological objects, instead of on individual ones.