The Complexity of the Simplex Method

  title={The Complexity of the Simplex Method},
  author={John Fearnley and Rahul Savani},
  journal={Proceedings of the forty-seventh annual ACM symposium on Theory of Computing},
  • John Fearnley, Rahul Savani
  • Published 2015
  • Computer Science, Mathematics
  • Proceedings of the forty-seventh annual ACM symposium on Theory of Computing
The simplex method is a well-studied and widely-used pivoting method for solving linear programs. When Dantzig originally formulated the simplex method, he gave a natural pivot rule that pivots into the basis a variable with the most violated reduced cost. In their seminal work, Klee and Minty showed that this pivot rule takes exponential time in the worst case. We prove two main results on the simplex method. Firstly, we show that it is PSPACE-complete to find the solution that is computed by… Expand
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