Abstract
We investigate a preemptive semi-online scheduling problem. Jobs with sizes within a certain range [ 1 , r ] ( r ⩾ 1 ) arrive one by one to be scheduled on two uniform parallel processors with speed 1 and s ⩾ 1 , respectively. The objective is to minimize makespan. We characterize the optimal competitive ratio as a function of both s and r by devising a deterministic on-line scheduling algorithm along with a matching lower bound, which also holds for randomized algorithms.
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