Sergio Cabello: Separation of two points with minimum number of segments

Let S be a set of segments in the plane and let x,y be two points in the plane. We consider the following optimization problem: find the smallest subset S' of S, such that any path from x to y crosses some segment of S'. Can this problem be solved in polynomial time, or is it NP-hard?

Joint work with Helmut Alt, Pannos Giannopulos, and Christian Knauer.