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On Simplex Pivoting Rules and Complexity Theory (1404.3320v1)
Published 12 Apr 2014 in cs.CC and cs.DS
Abstract: 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.