The Complexity of the Simplex Method

@article{Fearnley2015TheCO,
  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},
  year={2015}
}
  • 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
29 Citations
The Simplex Algorithm Is NP-Mighty
The Simplex Algorithm is NP-mighty
Theory of Local Search
Tropical aspects of linear programming
On the Complexity of Value Iteration
On the Length of Monotone Paths in Polyhedra.
The Complexity of All-switches Strategy Improvement
...
1
2
3
...

References

SHOWING 1-6 OF 6 REFERENCES
The simplex method is strongly polynomial for deterministic Markov decision processes
On Simplex Pivoting Rules and Complexity Theory
How easy is local search?
On the average number of steps of the simplex method of linear programming
  • S. Smale
  • Mathematics, Computer Science
  • Math. Program.
  • 1983
Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time
On the Complexity of the Policy Improvement Algorithm for Markov Decision Processes