Amortized efficiency of list update and paging rules
Communications of the ACM
On the performance of on-line algorithms for partition problems
Acta Cybernetica
An on-line scheduling heuristic with better worst case ratio than Graham's list scheduling
SIAM Journal on Computing
A better lower bound for on-line scheduling
Information Processing Letters
A lower bound for randomized on-line scheduling algorithms
Information Processing Letters
New algorithms for an ancient scheduling problem
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
Scheduling Parallel Machines On-line
SIAM Journal on Computing
A better algorithm for an ancient scheduling problem
Journal of Algorithms
Better bounds for online scheduling
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A lower bound for randomized on-line multiprocessor scheduling
Information Processing Letters
Scheduling to minimize average completion time: off-line and on-line algorithms
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
An experimental study of LP-based approximation algorithms for scheduling problems
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the Workshop on Job Scheduling Strategies for Parallel Processing
IPPS '95 Proceedings of the Workshop on Job Scheduling Strategies for Parallel Processing
Proceedings of the Workshop on Job Scheduling Strategies for Parallel Processing
IPPS '96 Proceedings of the Workshop on Job Scheduling Strategies for Parallel Processing
Developments from a June 1996 seminar on Online algorithms: the state of the art
Expected Makespans for Largest-First Multiprocessor Scheduling
Performance '84 Proceedings of the Tenth International Symposium on Computer Performance Modelling, Measurement and Evaluation
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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 schedulingtheory, 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 analyzingthe 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.