Interval matrices with Monge property

TL;DR

This paper extends the Monge property to interval matrices, defining strong and weak classes, exploring their properties, characterizations, and closure, and generalizing an algorithm for permutation-based Monge matrix recognition.

Contribution

It introduces a novel generalization of the Monge property for interval matrices, including characterizations, properties, and an algorithmic approach.

Findings

Characterization of strong Monge property for interval matrices

Polynomial and necessary conditions for weak Monge property

Algorithm for permuting matrices to achieve Monge property

Abstract

We generalize Monge property of real matrices for interval matrices. We define two classes of interval matrices with Monge property - in a strong and in a weak sense. We study fundamental properties of both classes. We show several different characterizations of the strong Monge property. For weak Monge property we give a polynomial characterization and several sufficient and necessary conditions. For both classes we study closure properties. We further propose a generalization of an algorithm by Deineko \& Filonenko which for a given matrix returns row and column permutations such that the permuted matrix is Monge if the permutations exist.