Given a simple polygon $P$ having $n$ vertices, compute a minimum area star-shaped simple polygon $P^*$ that contains $P$ and has as its vertices a subset of those of $P$ (the restricted problem). (A set $S$ is star-shaped with respect to point $z\in S$ if for every point $w\in S$ the line segment $(z, w)$ is contained in $S$. We say that $S$ is star-shaped if it is star-shaped with respect to some point $z$, and we refer to such a point $z$ as a center point of $S$)