The rectilinear class Steiner tree problem for intervals on two parallel lines

We consider a generalization of the Rectilinear Steiner Tree problem, where our input is classes of required points instead of simple required points. Our task is to nd a minimum rectilinear tree connecting at least one point from each class. We prove that the version, where all required points lie on two parallel lines, called the Recti-linear Class Steiner Tree (channel) problem, is NP-hard. But we give a linear time algorithm for the case where the points of each required class are clustered, and the classes consist of non overlapping intervals of points.