We study a preemptive semi-online scheduling problem. Jobs with
non-increasing weights 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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