A RESOLVABLE $ r\times c$ GRID-BLOCK PACKING AND ITS APPLICATION TO DNA LIBRARY SCREENING

Abstract

For a $v$-set $V$, let ${\cal A}$ be a collection of $r \times c$ arrays with elements in $V$. A pair $(V, {\cal A})$ is called an {\it $r\times c$ 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 ${\cal A}$. And an $r\times c$ grid-block packing $(V, {\cal A})$ is said to be {\it resolvable} if the collection of arrays ${\cal A}$ can be partitioned into sub-classes $\boldsymbol{R}_1$, $\boldsymbol{R}_2$, $\ldots$, $\boldsymbol{R}_t$ 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 $r\times c$ grid-block packings and give a brief survey of their application to DNA library screening.