Preemptive Online Scheduling: Optimal Algorithms for All Speeds

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. We also give a complete analysis of the competitive ratio for three machines. T. Ebenlendr and J. Sgall partially supported by Institutional Research Plan No. AV0Z10190503, by Inst. for Theor. Comp. Sci., Prague (project 1M0545 of MŠMT ČR), grant 201/05/0124 of GA ČR, and grant IAA1019401 of GA AV ČR. W. Jawor supported by NSF grants CCF-0208856 and OISE-0340752.