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Interval Matrices with Monge Property

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Abstract

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

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Department of Applied Mathematics, Charles University, Malostranské nám. 2/25, 118 00, Praha 1, Czech Republic

    Martin Černý

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  1. Martin Černý
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Correspondence to Martin Černý.

Additional information

Cordially dedicated to Dr. Vladimir G. Deineko.

The research has been supported by the Czech Science Foundation Grant P403-18-04735S.

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Černý, M. Interval Matrices with Monge Property. Appl Math 65, 619–643 (2020). https://doi.org/10.21136/AM.2020.0370-19

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  • DOI: https://doi.org/10.21136/AM.2020.0370-19

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