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Orientation of matrices

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Mathematical Programming at Oberwolfach II

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 22))

Abstract

Camion proved that every real-valued matrix A can be transformed by pivoting operations and nonzero multiplications of columns into a nonnegative matrix. In this paper we describe a finite algorithm to make this transformation, based on the results of Camion. Our main result is that when A is a totally unimodular matrix this transformation can be made by a polynomial algorithm.

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References

  1. P. Camion, “Modules unimodulaires”, Journal of Combinatorial Theory 4 (1968) 301–362.

    Article  MathSciNet  MATH  Google Scholar 

  2. W.H. Cunningham, “Separating cocircuits in binary matroids”, Linear Algebra and Its Applications 43 (1982) 69–86.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Edmonds, Seminaire à l’Université de Grenoble (Grenoble, France, June 1981).

    Google Scholar 

  4. M. Grötschel, L. Lovasz and A. Schrijver, “The ellipsoid method and its consequences in combinatorial optimisation”, Combinatorica 1 (1981) 169–197.

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  5. A. Mandel, “The topology of oriented matroids”, Ph.D. Thesis, University of Waterloo (Waterloo, 1982).

    Google Scholar 

  6. M. Raco, Thèse 3ème Cycle, l’Université de Grenoble (Grenoble, France, June 1983).

    Google Scholar 

  7. P.D. Seymour, “Decomposition of regular matroids”, Journal of Combinatorial Theory B28 (1980) 305–359.

    Article  MathSciNet  MATH  Google Scholar 

  8. W.T. Tutte, “Lecutres on matroids”, Journal of Research, National Bureau of Standards B69 (1965) 1–47.

    MathSciNet  MATH  Google Scholar 

  9. D.J.A. Welsh, Matroid theory (Academic Press, New York, 1976).

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Laboratoire Artemis, U.S.M.G., B.P. 68, 38402 St, Martin D’Heres Cedex, France

    J. Fonlupt & M. Raco

Authors
  1. J. Fonlupt
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  2. M. Raco
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Editor information

Bernhard Korte Klaus Ritter

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© 1984 The Mathematical Programming Society, Inc.

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Fonlupt, J., Raco, M. (1984). Orientation of matrices. In: Korte, B., Ritter, K. (eds) Mathematical Programming at Oberwolfach II. Mathematical Programming Studies, vol 22. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121010

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  • DOI: https://doi.org/10.1007/BFb0121010

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00914-3

  • Online ISBN: 978-3-642-00915-0

  • eBook Packages: Springer Book Archive

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