Non-unique probe selection and group testing

A minimization problem that has arisen from the study of non-unique probe selection with group testing technique is as follows: Given a binary matrix, find a d-disjunct submatrix with the minimum number of rows and the same number of columns. We show that when every probe hybridizes to at most two viruses, i.e., every row contains at most two 1s, this minimization is still MAX SNP-complete, but has a polynomial-time approximation with performance ratio 1 + 2 / (d + 1). This approximation is constructed based on an interesting result that the above minimization is polynomial-time solvable when every probe hybridizes to exactly two viruses.