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d-separable, 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.

BOUNDING THE NUMBER OF COLUMNS WHICH APPEAR ONLY IN POSITIVE POOLS