An O( n2) algorithm for maximum cycle mean of Monge matrices in max-algebra - Gavalec, Martin; Plávka, Ján (Discrete Applied Mathematics, 2003)
An O( n 2) algorithm is described for computing the maximum cycle mean (eigenvalue) for n× n matrices, A=( a ij ) fulfilling Monge property, a ij + a kl ⩽ a il + a kj for any i< k, j< l. The algorithm computes the value λ( A)=max( a i 1 i 2 + a i 2 i 3 +⋯+ a i k i 1 )/ k over all cyclic permutations ( i 1, i 2,…, i k ) of subsets of the set {1,2,…, n}. A similar result is presented for matrices with inverse Monge property. The standard algorithm for the general case works in O( n 3) time.