Abstract: Let $X$ be a simple region (e.g., a simple polygon), and let $Q$ be a set of points in $X$. Let $O$ be any fixed convex object such as a disk, an axis-parallel square, etc. An $O$-cover of $Q$ with respect to $X$ is a set of homothetic copies of $O$ such that their union covers $Q$ and is contained in $X$. We present a scheme for computing a minimum size $O$-cover of $Q$ with respect to $X$, for any fixed convex object $O$ in polynomial time. In particular, a disk cover of $Q$ with respect to $X$, can be computed in polynomial time. This is a joint work with Matya Katz