Smoothed analysis of termination of linear programming algorithms

被引:27
|
作者
Spielman, DA [1 ]
Teng, SH
机构
[1] MIT, Dept Math, Cambridge, MA 02139 USA
[2] Boston Univ, Dept Comp Sci, Boston, MA 02215 USA
关键词
smoothed analysis; linear programming; interior-point algorithms; condition numbers;
D O I
10.1007/s10107-003-0448-9
中图分类号
TP31 [计算机软件];
学科分类号
081202 ; 0835 ;
摘要
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 is O(m(3) log(m/sigma)). In contrast, the best known bound on the worst-case complexity of linear programming is O(m(3) L), 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.
引用
收藏
页码:375 / 404
页数:30
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