Abstract
Matroids can be defined by a lot of different concepts which are all theoretically equivalent. On the other hand, from a computational point of view, these concepts are quite different and can be classified into more or less powerful concepts. In this paper we give a complete analysis of the computational relations between various matroid concepts together with several extensions concerning combinations of concepts, general independence systems and calculations of the complexity of matroid properties with respect to various “oracles”. Of particular interest is the fact that matroids can be also axiomatically defined by a girth function and that the GIRTH oracle is significantly stronger than the more standard oracles.
Supported by Sonderforschungsbereich 21 (DFG), Institut für ökonometrie und Operations Research, Universität Bonn, W. Germany.
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References
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© 1981 The Mathematical Programming Society
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Hausmann, D., Korte, B. (1981). Algorithmic versus axiomatic definitions of matroids. In: König, H., Korte, B., Ritter, K. (eds) Mathematical Programming at Oberwolfach. Mathematical Programming Studies, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120924
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DOI: https://doi.org/10.1007/BFb0120924
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