Computing an eigenvector of an inverse Monge matrix in max–plus algebra

The problem of computing an eigenvector of an inverse Monge matrix in max–plus algebra is addressed. For a general matrix, the problem can be solved in at most O(n3)O(n3) time. This note presents an O(n2)O(n2) algorithm for computing one max–plus algebraic eigenvector of an inverse Monge matrix A. It is assumed that A is irreducible.