A resolvable r × c grid-block packing and its application to DNA library screening

For a v-set V, let A be a collection of r × c arrays with elements in V. A pair (V, A) is called an r × c grid-block packing if every two distinct points i and j in V occur together at most once in the same row or in the same column of arrays in A. And an r × c grid-block packing (V, A) is said to be resolvable if the collection of arrays A can be partitioned into sub-classes R₁, R₂, ..., R_t such that every point of V is contained in precisely one array of each class. These packings have originated from the use of DNA library screening. In this paper, we give some constructions of resolvable r × c grid-block packings and give a brief survey of their application to DNA library screening.