Before revision:  It is easy to see that for the anchored rectangles , the problem reduces to one with even simpler objects: L-frames . An L-frame is the union of a vertical and a horizontal  segment that share one endpoint(corner of the L-frame).
After revision:  It is easy to see that for the anchored rectangles , the problem reduces to one with even simpler objects: L-frames : the union of a vertical and a horizontal segment that share one endpoint(corner of the L-frame).