Abstract
We consider one-by-one online scheduling on uniformly related machines. The input is a sequence of machines with different speeds and a sequence of jobs with different processing times. The output is a schedule which assigns the jobs to the machines; the completion time of a machine is the sum of the processing times of jobs assigned to it divided by its speed. The objective is to minimize the maximal completion time. The jobs arrive one by one and each has to be assigned to one machine immediately and irrevocably without the knowledge of the future jobs. We prove a new lower bound of 2.564 on the competitive ratio of deterministic online algorithms for this problem, improving the previous lower bound of 2.438.
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We are grateful to anonymous reviewers and György Dósa for helpful comments.
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Partially supported by the Center of Excellence—Inst. for Theor. Comp. Sci., Prague (project P202/12/G061 of GA ČR) and grant IAA100190902 of GA AV ČR.
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Ebenlendr, T., Sgall, J. A Lower Bound on Deterministic Online Algorithms for Scheduling on Related Machines Without Preemption. Theory Comput Syst 56, 73–81 (2015). https://doi.org/10.1007/s00224-013-9451-6
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DOI: https://doi.org/10.1007/s00224-013-9451-6