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Computational relations between various definitions of matroids and independence systems

  • Integer Programming
  • Conference paper
  • First Online:
Optimization Techniques

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 23))

  • 172 Accesses

Abstract

The paper analyses the computational relations between well known concepts in the theory of matroids and independence systems. It is shown that these concepts although known to be theoretically equivalent are not computationally equivalent. In particular the girth concept in matroid theory is "stronger" than concepts like independence, rank or basis.

Supported by Sonderforschungsbereich 21 (DFG).

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References

  1. D. Hausmann, B. Korte: Algorithmic versus axiomatic definitions of matroids. Report 79141-OR, Institut für Ökonometrie und Operations Research, University of Bonn, Bonn, W. Germany (1979).

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  2. D. Hausmann, B. Korte: The relative strength of oracles for independence systems. Report 79143-OR, Institut für Ökonometrie und Operations Research, University of Bonn, Bonn, W. Germany (1979).

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  3. L. Matthews: Closure in independence systems. Report 7894-OR, Institut für Ökonometrie und Operations Research, University of Bonn, Bonn, W. Germany (1978).

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  4. G.C. Robinson, D.J.A Welsh: The computational complexity of matroid properties. Working paper (1979).

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  5. R. von Randow: Introduction to the Theory of Matroids. Springer Verlag. Berlin, Heidelberg, New York (1975).

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  6. D.J.A. Welsh: Matroid Theory. Academic Press. London, New York, San Francisco (1978).

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Authors and Affiliations

  1. Institut für Ökonometrie und Operations Research, Universität Bonn, W. Germany

    D. Hausmann & B. Korte

Authors
  1. D. Hausmann
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  2. B. Korte
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Editor information

K. Iracki K. Malanowski S. Walukiewicz

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© 1980 Springer-Verlag

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Hausmann, D., Korte, B. (1980). Computational relations between various definitions of matroids and independence systems. In: Iracki, K., Malanowski, K., Walukiewicz, S. (eds) Optimization Techniques. Lecture Notes in Control and Information Sciences, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006604

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  • DOI: https://doi.org/10.1007/BFb0006604

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10081-2

  • Online ISBN: 978-3-540-38253-9

  • eBook Packages: Springer Book Archive

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