On the Monge property of matrices (Q802638)

A square matrix \(A=(a_{ij})\) over a commutative linearly ordered group (G,*,\(\leq)\) is said to have the Monge property if \(a_{ii}*a_{kj}\leq a_{ij}*a_{ki}\) holds for all i and for all \(j,k>i\). The authors present an \(O(n^ 4)\) algorithm for checking whether the rows and columns of a given matrix can be permuted in such a way that the obtained matrix has the Monge property.