Monotone eigenspace structure in max-min algebra

For a given n x n matrix A in a max-min algebra, the set of all increasing eigenvectors, in notation F-less than or equal to(A) is studied. It is shown that F-less than or equal to(A) is a union of at most 2(n-1) intervals, and an explicit formula for the intervals is given. Moreover, it is shown that the endpoints of these intervals can be computed in O(n(2)) time or in O(n) time, if an auxiliary n x n matrix C(A) has been previously computed. The results enable a complete description of the structure of the whole eigenspace F(A). (C) 2002 Elsevier Science Inc. All rights reserved.