Abstract
We study a preemptive semi-online scheduling problem. Jobs with non-increasing sizes arrive one by one to be scheduled on two uniformly related machines. We analyze the algorithms as a function of the speed ratio ( q⩾1) between the two machines. We design algorithms of optimal competitive ratio for all values of q, and show that for q>2, idle time needs to be introduced. This is the first preemptive scheduling problem over list, where idle time is provably required.
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