The computation of a Gröbner basis of a polynomial ideal is known to be exponential space complete. We revisit the algorithm by Kühnle and Mayr using recent improvements of various degree bounds. The result is an algorithm which is exponential in the ideal dimension (rather than the number of indeterminates).Furthermore, we provide an incremental version of the algorithm which is independent of the knowledge of degree bounds. Using a space-efficient implementation of Buchberger's S-criterion, the algorithm can be implemented such that the space requirement only depends on the size of the representation and the Gröbner basis degrees of the problem instance (instead of the worst case), and thus is much lower in average.
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