Abstract
In this paper, we investigate the online scheduling problem on two uniform machines, where the last job of each machine can be reassigned after all jobs have been assigned. The objective is to minimize the makespan. We prove that the classical List Scheduling algorithm with the competitive ratio s + 1 s is optimal for s ≥ 1 + 5 2 , where s is the speed ratio between the two machines. Also, we prove the lower bound s + 1 for 1 ≤ s < 1 + 5 2 and design an algorithm that matches the bound.
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