Worst-case and average-case approximations by simple randomized search heuristics

Abstract

In recent years, probabilistic analyses of algorithms have received increasing attention. Despite results on the average-case complexity and smoothed complexity of exact deterministic algorithms, little is known about the average-case behavior of randomized search heuristics (RSHs). In this paper, two simple RSHs are studied on a simple scheduling problem. While it turns out that in the worst case, both RSHs need exponential time to create solutions being significantly better than 4/3-approximate, an average-case analysis for two input distributions reveals that one RSH is convergent to optimality in polynomial time. Moreover, it is shown that for both RSHs, parallel runs yield a PRAS. © Springer-Verlag Berlin Heidelberg 2005.