  In this paper, we study tropical-theoretic aspects of the ``rectification
algorithm'' on skew Young tableaux. It is shown that the algorithm is
interpreted as a time evolution of some tropical integrable system. By using
this fact, we construct a new combinatorial map that is essentially equivalent
to the rectification algorithm. Some of properties of the rectification can be
seen more clearly via this map. For example, the uniqueness of a rectification
boils down to an easy combinatorial problem. Our method is mainly based on the
two previous researches: the theory of geometric tableaux by Noumi-Yamada, and
the study on the relationship between jeu de taquin slides and the
ultradiscrete KP equation by Mikami and Katayama-Kakei.
