  We study three covering problems in the plane. Our original motivation for
these problems come from trajectory analysis. The first is to decide whether a
given set of line segments can be covered by up to four unit-sized,
axis-parallel squares. The second is to build a data structure on a trajectory
to efficiently answer whether any query subtrajectory is coverable by up to
three unit-sized axis-parallel squares. The third problem is to compute a
longest subtrajectory of a given trajectory that can be covered by up to two
unit-sized axis-parallel squares.
