Finding all essential terms of a characteristic maxpolynomial

Let us denote a⊕ b=max(a; b) and a⊗ b= a+ b for a; b∈R=R ∪ {−∞} and extend this pair of operations to matrices and vectors in the same way as in linear algebra. We present an O(n(m + n log n)) algorithm for 8nding all essential terms of the max-algebraic characteristic polynomial of an n × n matrix over R with m 8nite elements. In the cases when all terms are essential, this algorithm also solves the following problem: Given an n × n matrix A and k ∈{1; : : : ; n}, 8nd a k×k principal submatrix of A whose assignment problem value is maximum. ? 2003 Elsevier B.V. All rights reserved.