We show that there are simplex pivoting rules for which it is PSPACE-complete to tell if a particular basis will appear on the algorithm's path. Such rules cannot be the basis of a strongly polynomial algorithm, unless P = PSPACE. We conjecture that the same can be shown for most known variants of the simplex method. However, we also point out that Dantzig's shadow vertex algorithm has a polynomial path problem. Finally, we discuss in the same context randomized pivoting rules. © 2014 Springer International Publishing Switzerland.
CITATION STYLE
Adler, I., Papadimitriou, C., & Rubinstein, A. (2014). On simplex pivoting rules and complexity theory. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8494 LNCS, pp. 13–24). Springer Verlag. https://doi.org/10.1007/978-3-319-07557-0_2
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