Minimum vertex cover in rectangle graphs

We consider the Minimum 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 R where R1∖R2 is connected for every pair of rectangles R1,R2∈R. This algorithm extends to intersection graphs of pseudo-disks. The second algorithm achieves a factor of (1.5+ε) in general rectangle families, for any fixed ε>0, and works also for the weighted variant of the problem. Both algorithms exploit the plane properties of axis-parallel rectangles in a novel way.