Complexity and inapproximability for problems of finding minimum set of stabbing objects on geometric graphs

We consider a problem of seeking minimum set of stabbing objects for straight line segments which are edges of geometric graph $G.$ In our talk we give some complexity and inapproximability results (integrality gap lower bounds) for these problems considered both in the case of an arbitrary and planar graph $G$ where class of stabbers is restricted to disks of fixed positive radius and to straight lines of an arbitrary orientation.