Given a 2D polygon, convex or nonconvex, maybe some holes (also small polygons) inside. How can we pack an (approximately) maximum number of identical rectangles in the polygon (the rectangle can not cover any hole)。
I know it is not an easy problem. But there are two advantages. The rectangles are identical, and the direction is fixed (the lengths of all rectangles are parallel to a given line). Therefore, the solution space is much smaller than the general case.
Is there any algorithm or literature concerning the problem or similar problems? I think the problem has wide applications, and maybe the "easiest" one among non-standard packing problems.
If there is any study on polygon without holes, it is also valuable for me. Thanks!