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In this paper, we study the active time scheduling problem. We are given njobs with integral processing times each of which has an integral release timeand deadline. The goal is to schedule all the jobs on a machine that can workon b jobs simultaneously, and the objective is to minimize the number of timeslots for which the machine is active. The active time scheduling model wasintroduced by Chang et al. in the context of energy-efficient scheduling.Surprisingly, despite the development of a number of constant factorapproximation algorithms for the problem, the complexity of this fundamentalproblem had remained open. In this paper, we resolve this open problem and showthat the active time scheduling problem is indeed NP-complete.

NP-completeness of the Active Time Scheduling Problem