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Generating Maximum Members of Independence Systems

  • Reinhardt Euler
Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 157)

Abstract

Given an independence system J over a finite set N= {1,...,n} a relation “ Γ ” is defined for sets X ⊆ N of a fixed cardinality k. This leads to “regular“ systems, which are independence systems having the additional property : Xεj,XΓ => Yε J. The concept of “ Γ -bases” is applied and a criterion to recognize regular systems having matroidal structure is developed. Based on these results an algorithm for the construction of all Γ -bases of independence or regular systems is introduced.

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References

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    C.P. Bruter : Eléments de la Théorie des Matroides ; Springer-Verlag, Berlin-Heidelberg-New York, 1974Google Scholar
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    Die Bestimmung maximaler Elemente in monotonen Mengensystemen; Report No. 7761-OR , Institut für Ökonometrie und Operations Research, Universität Bonn, September 1977Google Scholar
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    P.L. Hammer, E.L. Johnson , U.N. Peled : Regular o-1 Programs ; Cahiers du Centre d’Etudes de Recherche Opérationelle, 16 (1974) 267–276Google Scholar
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    R. v.Randow :Introduction to the Theory of Matroids ; Springer-Verlag, Berlin-Heidelberg-New York, 1975Google Scholar
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    L.A. Wolsey : Faces for a Linear Inequality in o-1 Variables ; Mathematical Programming 8 (1975) 165–178Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Reinhardt Euler
    • 1
  1. 1.Institut für Ökonometrie und Operations ResearchUniversität BonnBonnGermany

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