In this thesis, we consider the problem of finding the largest area convex rectilinear polygon which is contained in a given rectilinear polygon with N vertices.
We show that this problem can be solved in O(N) time and space when the given rectilinear polygon is monotone. We also consider the query mode problem for the monotone separable rectilinear polygon and give an O($log^2$N) query time algorithm.
In addition to these algorithms, an O(N$log^3$N) time algorithm for finding the largest subrectangle of a rectilinear polygon is presented.