  We consider the $k$-center problem in which the centers are constrained to
lie on two lines. Given a set of $n$ weighted points in the plane, we want to
locate up to $k$ centers on two parallel lines. We present an $O(n\log^2 n)$
time algorithm, which minimizes the weighted distance from any point to a
center. We then consider the unweighted case, where the centers are constrained
to be on two perpendicular lines. Our algorithms run in $O(n\log^2 n)$ time
also in this case.
