Abstract
We consider a semi on-line version of the multiprocessor scheduling problem on three processors, where the total size of the tasks is known in advance. We prove a lower bound \(1+\frac{\sqrt{129}-9}{6}>1.3929\) on the competitive ratio of any algorithm and propose a simple algorithm with competitive ratio equal to 1.5. The performance is improved to \(1+\frac{8}{19}<1.4211\) by a preprocessing strategy. The latter algorithm is only 2% away from the lower bound.
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Z. Tuza is supported in part by the Hungarian Scientific Research Fund, OTKA grant T-049613.
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Angelelli, E., Speranza, M.G. & Tuza, Z. Semi on-line scheduling on three processors with known sum of the tasks. J Sched 10, 263–269 (2007). https://doi.org/10.1007/s10951-007-0023-y
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DOI: https://doi.org/10.1007/s10951-007-0023-y