Before revision:  An L-frame is the union of a vertical and a horizontal  segment that share one endpoint(corner of the L-frame). In light of the above discussion, we consider DS on the intersection graphs of L-frames. In this paper, we consider three restricted versions of the problem. First, we consider the version in which the corners of all input L-frames are anchored at a line with slope -1, and obtain a polynomial-time (2+\epsilon)-approximation .
After revision:  An L-frame is the union of a vertical and a horizontal segment that share an endpoint. As such, we also obtain a (2+\epsilon)-approximation .