Abstract
Minimizing the total completion time has practical application in providing the best quality of service. We consider energy and time constrained task scheduling for minimized total completion time and minimized total energy consumption. We show that there is a polynomial time algorithm to find a nonpreemptive schedule with the minimum total completion time for a given total energy consumption constraint. Similarly, there is a polynomial time algorithm to find a nonpreemptive schedule with the minimum total energy consumption for a given total completion time constraint.
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