  It is shown that the four-gluon scattering amplitude for N=4 supersymmetric
Yang-Mills theory in the planar limit can be written, in both the weak- and
strong-coupling limits, as a reggeized amplitude, with a parent trajectory and
an infinite number of daughter trajectories. This result relies crucially on
the fact that the leading IR-divergence and the finite log^2(s/t)-dependent
piece of the amplitude are characterized by the same function for all values of
the coupling, as conjectured by Bern, Dixon, and Smirnov, and proved by Alday
and Maldacena in the strong-coupling limit. We use the Alday-Maldacena result
to determine the strong-coupling Regge trajectory.
