Before revision:  Next, we consider the version, where all input L-frames intersect a vertical line , and prove APX-hardness of this version. Moreover, we prove NP-hardness of this version even in case the horizontal and vertical segments of each L-frame have the same length.
After revision:  Next, we consider the version, where all input L-frames intersect a vertical line . However, as we show, the problem is linear-time solvable in case the horizontal and vertical segments of each L-frame have the same length.