Algorithm Engineering: 4th International Workshop, WAE 2000 Saarbrücken, Germany, September 5–8, 2000 Proceedings

We present the first comprehensive experimental study of online algorithms for Graham’s scheduling problem. In Graham’s scheduling problem, which is a fundamental and extensively studied problem in scheduling theory, a sequence of jobs has to be scheduled on m identical parallel machines so as to minimize the makespan. Graham gave an elegant algorithm that is (2−1/m)-competitive. Recently a number of new online algorithms were developed that achieve competitive ratios around 1.9. Since competitive analysis can only capture the worst case behavior of an algorithm a question often asked is: Are these new algorithms geared only towards a pathological case or do they perform better in practice, too? We address this question by analyzing the algorithms on various job sequences. We have implemented a general testing environment that allows a user to generate jobs, execute the algorithms on arbitrary job sequences and obtain a graphical representation of the results. In our actual tests, we analyzed the algorithms (1) on real world jobs and (2) on jobs generated by probability distributions. It turns out that the performance of the algorithms depends heavily on the characteristics of the respective work load. On job sequences that are generated by standard probability distributions, Graham’s strategy is clearly the best. However, on the real world jobs the new algorithms often outperform Graham’s strategy. Our experimental study confirms theoretical results and gives some new insights into the problem. In particular, it shows that the techniques used by the new online algorithms are also interesting from a practical point of view.