On the monge property of matrices

Abstract

A square matrix A = ( a ij ) over a commutative linearly ordered group ( G, ∗, ⩽) is said to have the Monge property if a ii ∗ a kj⩽ a ij ∗ a ki holds for all i and for all j, k> i. We 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.