BOUNDING THE NUMBER OF COLUMNS WHICH APPEAR ONLY IN POSITIVE POOLS

Abstract

$d$-separable, $\overline{d}$-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.