Smoothed analysis of termination of linear programming algorithms

We perform a smoothed analysis of a termination phase for linear programming algorithms. By combining this analysis with the smoothed analysis of Renegar’s condition number by Dunagan, Spielman and Teng (http://arxiv.org/abs/cs.DS/0302011) we show that the smoothed complexity of interior-point algorithms for linear programming isO(m3 log(m/σ)). In contrast, the best known bound on the worst-case complexity of linear programming is O(m3L), where L could be as large as m. We include an introduction to smoothed analysis and a tutorial on proof techniques that have been useful in smoothed analyses.