On Simplex Pivoting Rules and Complexity Theory
Computational Complexity
2014-04-15 v1 Data Structures and Algorithms
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.
Cite
@article{arxiv.1404.3320,
title = {On Simplex Pivoting Rules and Complexity Theory},
author = {Ilan Adler and Christos Papadimitriou and Aviad Rubinstein},
journal= {arXiv preprint arXiv:1404.3320},
year = {2014}
}
Comments
To appear in IPCO 2014