We study popular local search and greedy algorithms for scheduling. The performance guarantee of these algorithms is well understood, but the worst-case lower bounds seem somewhat contrived and it is questionable if they arise in practical applications. To find out how robust these bounds are, we study the algorithms in the framework of smoothed analysis, in which instances are subject to some degree of random noise.
While the lower bounds for all scheduling variants with restricted machines are rather robust, we find out that the bounds are fragile for unrestricted machines. In particular, we show that the smoothed performance guarantee of the jump and the lex-jump algorithm are (in contrast to the worst case) independent of the number of machines. They are Theta(phi) and Theta(log(phi)), respectively, where 1/phi is a parameter measuring the magnitude of the perturbation. The latter immediately implies that also the smoothed price of anarchy is Theta(log(phi)) for routing games on parallel links. Additionally we show that for unrestricted machines also the greedy list scheduling algorithm has an approximation guarantee of Theta(log(phi)).
Fixed Point Computation: Beating Brute Force with Smoothed Analysis
Institute for Data, Econometrics, Algorithms, and Learning（数据、计量经济学、算法与学习研究所）；UIC（伊利诺伊大学芝加哥分校）；TTIC（丰田技术学院）；School of Computer Science Tel Aviv University（特拉维夫大学计算机科学学院）；EECS Department MIT（麻省理工学院电气工程与计算机科学系）；Department of Computer Science Yale University（耶鲁大学计算机科学系）
