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A constructive method to recognize the total unimodularity of a matrix

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Summary

A necessary and sufficient condition for a matrix to be totally unimodular is developed in this note. This condition in turn provides a constructive method to recognize the total unimodularity or otherwise of any matrixC with elements 0, 1 or −1.

Zusammenfassung

In diesem Beitrag wird eine notwendige und hinreichende Bedingung für die vollständige Unimodularität einer Matrix entwickelt. Diese Bedingung führt zu einer brauchbaren Methode, mit der für jede beliebige Matrix C mit den Elementen 0, 1, −1 bestimmt werden kann, ob sie vollständig unimodular ist oder nicht.

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References

  • Heller, I., andC. B. Tompkins: An extension of a Theorem of Dantzig's, in: Linear Inequalities and Related Systems, Annals of Mathematics Studies, No.38, 247–254. Princeton, New Jersey, USA, 1956.

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  • Hoffman, A. J., andJ. B. Kruskal: Integral boundary points of convex Polyhedra, in: Linear Inequalities and Related Systems, Annals of Mathematics Studies, No.38, 223–246. Princeton, New Jersey, USA, 1956.

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Raghavachari, M. A constructive method to recognize the total unimodularity of a matrix. Zeitschrift für Operations Research 20, 59–61 (1976). https://doi.org/10.1007/BF01916748

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  • DOI: https://doi.org/10.1007/BF01916748

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