Abstract
We consider a semi-online multiprocessor scheduling problem with a given a set of identical machines and a sequence of jobs, the sum of whose processing times is known in advance. The jobs are to be assigned online to one of the machines and the objective is to minimize the makespan. The best known algorithm for this problem achieves a competitive ratio 1.6 (Cheng et al. in Theor Comput Sci 337:134–146, 2005). The best known lower bound is approximately 1.585 (Albers and Hellwig in Theor Comput Sci 443:1–9, 2012) if the number of machines tends to infinity. We present an elementary algorithm with competitive ratio equal to this lower bound. Thus, the algorithm is best possible if the number of machines tends to infinity.
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Acknowledgments
The authors are grateful to two anonymous referees for their helpful comments which helped to improve the presentation of the paper a lot. The research of the second author has been partially supported by Belarusian BRFFI Grant (Project F13K-078). The research of the third author has been partially supported by the LabEx PERSYVAL-Lab (ANR-11-LABX-0025) and by BRFFR-PICS project (PICS 5379).
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Kellerer, H., Kotov, V. & Gabay, M. An efficient algorithm for semi-online multiprocessor scheduling with given total processing time. J Sched 18, 623–630 (2015). https://doi.org/10.1007/s10951-015-0430-4
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DOI: https://doi.org/10.1007/s10951-015-0430-4