In max algebra it is well known that the sequence of max algebraic powers , with an irreducible square matrix, becomes periodic after a finite transient time , and the ultimate period is equal to the cyclicity of the critical graph of .
In this connection, we study computational complexity of the following problems: (1) for a given , compute a periodic power with and , (2) for a given , find the ultimate period of . We show that both problems can be solved by matrix squaring in operations. The main idea is to apply an appropriate diagonal similarity scaling , called visualization scaling, and to study the role of cyclic classes of the critical graph.