Finding all essential terms of a characteristic maxpolynomial

Let us denote a ⊕ b = max(a,b) and a ⊗ b = a + b for a, b ∈ oR = R ∪ {-∞} and extend this pair of operations to matrices and vectors in the same way as in linear algebra. We present an O(n2(m + n log n)) algorithm for finding all essential terms of the max-algebraic characteristic polynomial of an n × n matrix over oR with m finite 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}, find a k × k principal submatrix of A whose assignment problem value is maximum.