On Simplex Pivoting Rules and Complexity Theory

@inproceedings{Adler2014OnSP,
  title={On Simplex Pivoting Rules and Complexity Theory},
  author={I. Adler and C. Papadimitriou and A. Rubinstein},
  booktitle={IPCO},
  year={2014}
}
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. 
18 Citations
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