Bounding the number of columns which appear only in positive pools

Abstract

d-separable, (d) over bar -separable and d-disjunct matrices are the major tools in constructing pooling designs which has many applications to DNA experiments, for example, the clone library screening problem. While there exists a simple decoding for d-disjunct matrices, only brute-force methods are known for the other two. In this paper we identify structures in these two matrices which lead to significant improvements for decoding.