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The computational complexity of matroid properties

Published online by Cambridge University Press:  24 October 2008

G. C. Robinson  and
D. J. A. Welsh
G. C. Robinson
Affiliation:
Merton College, Oxford
D. J. A. Welsh
Affiliation:
Merton College, Oxford
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Extract

Knuth (12) seems to have been the first to carry out non-trivial matroid operations on a computer. However, as he remarks, there are considerable computational difficulties. In this paper we examine in detail the computational complexity of some fundamental matroid properties. The model of computation is the Hausmann–Korte oracle machine introduced in (10), (11) to deal with properties of independence spaces and fixed point problems. It was these papers (10), (11) and (12) which motivated the present work. Basically, the problems we will be discussing are matroid analogues of low-level complexity problems for graphs. For an excellent survey of this we refer to the recent monograph of Bollobés ((3), chapter 8). We shall use the approach of (3), and Bollobaé;s and Eldridge(4) rather than the more general treatment of Hausmann and Korte (11).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 87 , Issue 1 , January 1980 , pp. 29 - 45
Copyright
Copyright © Cambridge Philosophical Society 1980

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References

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