On the exact upper bound for the multifit processor scheduling algorithm
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We consider the well-known problem of schedulingn independent tasks nonpre-emptively onm identical processors with the aim of minimizing the makespan. Coffman, Garey and Johnson  described an algorithm, MULTIFIT, based on techniques from binpacking, with better worst performance than the LPT algorithm and proved that it satisfies a bound of 1.22. It has been claimed by Friesen  that this bound can be improved upon to 1.2. However, we found his proof, in particular his lemma 4.9, difficult to understand. Yue, Kellerer and Yu  have presented the bound 1.2 in a simpler way. In this paper, we prove first that the bound cannot exceed 13/11 and then prove that it is exactly 13/11.
KeywordsSchedule Algorithm Independent Task Identical Processor Processor Schedule Processor Schedule Algorithm
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