Power-Saving Scheduling for Weakly Dynamic Voltage Scaling Devices

We study the problem of non-preemptive scheduling to minimize energy consumption for devices that allow dynamic voltage scaling. Specifically, consider a device that can process jobs in a non-preemptive manner. The input consists of (i) the set R of available speeds of the device, (ii) a set J of jobs, and (iii) a precedence constraint Π among J . Each job j in J , defined by its arrival time aj , deadline dj , and amount of computation cj , is supposed to be processed by the device at a speed in R. Under the assumption that a higher speed means higher energy consumption, the power-saving scheduling problem is to compute a feasible schedule with speed assignment for the jobs in J such that the required energy consumption is minimized. This paper focuses on the setting of weakly dynamic voltage scaling, i.e., speed change is not allowed in the middle of processing a job. To demonstrate that this restriction on many portable power-aware devices introduces hardness to the power-saving scheduling problem, we prove that the problem is NP-hard even if aj = aj′ and dj = dj′ hold for all j, j′ ∈ J and |R| = 2. If |R| < ∞, we also give fully polynomial-time approximation schemes for two cases of the general NP-hard problem: (a) all jobs share a common arrival time, and (b) Π = ∅ and for any j, j′ ∈ J , aj ≤ aj′ implies dj ≤ dj′ . To the best of our knowledge, there is no previously known approximation algorithm for any special case of theNP-hard problem.