Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time

@article{Spielman2001SmoothedAO,
  title={Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time},
  author={D. Spielman and S. Teng},
  journal={J. ACM},
  year={2001},
  volume={51},
  pages={385-463}
}
We introduce the smoothed analysis of algorithms, which is a hybrid of the worst-case and average-case analysis of algorithms. Essentially, we study the performance of algorithms under small random perturbations of their inputs. We show that the shadow-vertex simplex algorithm has polynomial smoothed complexity. 
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