Abstract
We consider online scheduling on m parallel-batch machines to minimize the makespan where the batch capacity is unbounded. The processing time of a job becomes known only upon its arrival. We give an improved lower bound 1 + α m on the competitive ratio, where α m is the positive solution of the equation α m 2 + m α m − 1 = 0 , and establish a best possible online algorithm matching this lower bound. We also provide a new lower bound 3/2 on the competitive ratio for dense-algorithms, and present a best possible dense-algorithm matching this lower bound.
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