A lower bound for randomized on-line scheduling algorithms
Information Processing Letters
A lower bound for randomized on-line multiprocessor scheduling
Information Processing Letters
A Level Algorithm for Preemptive Scheduling
Journal of the ACM (JACM)
Preemptive Scheduling of Uniform Processor Systems
Journal of the ACM (JACM)
On-line load balancing for related machines
Journal of Algorithms
On randomized online scheduling
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A lower bound for on-line scheduling on uniformly related machines
Operations Research Letters
Preemptive on-line scheduling for two uniform processors
Operations Research Letters
An optimal algorithm for preemptive on-line scheduling
Operations Research Letters
Optimal preemptive on-line scheduling on uniform processors with non-decreasing speed ratios
Operations Research Letters
Randomized on-line scheduling on three processors
Operations Research Letters
Preemptive scheduling on a small number of hierarchical machines
Information and Computation
A Lower Bound for the On-Line Preemptive Machine Scheduling with lpNorm
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Semi-online preemptive scheduling: study of special cases
PPAM'09 Proceedings of the 8th international conference on Parallel processing and applied mathematics: Part II
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Our main result is an optimal online algorithm for preemptive scheduling on uniformly related machines with the objective to minimize makespan. The algorithm is deterministic, yet it is optimal even among all randomized algorithms. In addition, it is optimal for any fixed combination of speeds of the machines, and thus our results subsume all the previous work on various special cases. Together with a new lower bound it follows that the overall competitive ratio of this optimal algorithm is between 2.054 and e≈ 2.718.