Before revision:  Surprisingly, for simple and widely used objects such as rectangles, the problem is NP-hard even when all the rectangles are "anchored" at a  line with slope -1. It is easy to see that for the anchored rectangles , the problem reduces to one with even simpler objects: L-frames .
After revision:  Surprisingly, for simple and widely used objects such as rectangles, the problem is NP-hard even when all the rectangles are "anchored" at a line with slope -1 (Pandit, CCCG 2017). In this paper, we first show that for any \epsilon>0, there exists a (2+\epsilon)-approximation algorithm for the MDS problem on "diagonal-anchored" rectangles, providing the first O(1)-approximation for the problem on a non-trivial subclass of rectangles. It is not hard to see that for the anchored rectangles , the problem reduces to one with even simpler objects: L-frames .