Smoothed Analysis of Algorithms: Why the Simplex Algorithm Usually Takes Polynomial Time
Abstract
We introduce the smoothed analysis of algorithms, which is a hybrid of the worstcase and averagecase analysis of algorithms. In smoothed analysis, we measure the maximum over inputs of the expected performance of an algorithm under small random perturbations of that input. We measure this performance in terms of both the input size and the magnitude of the perturbations. We show that the simplex algorithm has polynomial smoothed complexity.
 Publication:

arXiv eprints
 Pub Date:
 November 2001
 arXiv:
 arXiv:cs/0111050
 Bibcode:
 2001cs.......11050S
 Keywords:

 Computer Science  Data Structures and Algorithms;
 G.1.6
 EPrint:
 Revised. Improved statement of main theorem