Identifying d positive clones in the presence of inhibitors

Farach et al. introduced the inhibitor model in pooling design, where existence of a single inhibitor clone in a pool dictates its outcome to be negative regardless of the existence of positive clones in the pool. Various sequential or multiround pooling designs have been given to identify all the positive clones under the inhibitor model. Recently, Hwang and Liu gave a (one round) pooling design for the inhibitor model which is error tolerant. More specifically, suppose the set of n clones to be screened contains up to d positive clones, up to r inhibitors and the pooling experiments can generate up to e errors, they show that a (d + r + 2e)-disjunct matrix does the job. In this paper, we give a pooling design for the case that among n clones exactly d are positive. We reduce the requirement of (d + r + 2e)-disjunctness to (d + r + e)-disjunctness, which would mean the saving of many pools. We also show how our design can be used to identify all positive clones when their number is, at most, d.