Minimum Vertex Cover in Rectangle Graphs

We consider the Vertex Cover problem in intersection graphs of axis-parallel rectangles on the plane. We present two algorithms: The first is an EPTAS for non-crossing rectangle families, rectangle families $\text{calR}$ where $R_1 \setminus R_2$isconnectedforeverypairofrectangles$R_1,R_2 \in \calR$. This algorithm extends to intersection graphs of pseudo-disks. The second algorithm achieves a factor of $(1.5+\epsilon )$ in general rectangle families, for any fixed $\epsilon >0$, and works also for the weighted variant of the problem. Both algorithms exploit the plane properties of axis-parallel rectangles in a non-trivial way.