  Given a convex polygon $P$ with $k$ vertices and a polygonal domain $Q$
consisting of polygonal obstacles with total size $n$ in the plane, we study
the optimization problem of finding a largest similar copy of $P$ that can be
placed in $Q$ without intersecting the obstacles. We improve the time
complexity for solving the problem to $O(k^2n^2\lambda_4(k)\log{n})$. This is
progress of improving the previously best known results by Chew and Kedem
[SoCG89, CGTA93] and Sharir and Toledo [SoCG91, CGTA94] on the problem in more
than 25 years.
