On Simplex Pivoting Rules and Complexity Theory

  • Ilan Adler
  • Christos Papadimitriou
  • Aviad Rubinstein
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8494)


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.


linear programming the simplex method computational complexity 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Ilan Adler
    • 1
  • Christos Papadimitriou
    • 1
  • Aviad Rubinstein
    • 1
  1. 1.University of CaliforniaBerkeleyUSA

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