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In this work we study the problem of scheduling tasks with dependencies inmultiprocessor architectures where processors have different speeds. We presentthe preemptive algorithm "Save-Energy" that given a schedule of tasks it postprocesses it to improve the energy efficiency without any deterioration of themakespan. In terms of time efficiency, we show that preemptive scheduling in anasymmetric system can achieve the same or better optimal makespan than in asymmetric system. Motivited by real multiprocessor systems, we investigatearchitectures that exhibit limited asymmetry: there are two essentiallydifferent speeds. Interestingly, this special case has not been studied in thefield of parallel computing and scheduling theory; only the general case wasstudied where processors have $K$ essentially different speeds. We present thenon-preemptive algorithm ``Remnants'' that achieves almost optimal makespan. Weprovide a refined analysis of a recent scheduling method. Based on thisanalysis, we specialize the scheduling policy and provide an algorithm of $(3 +o(1))$ expected approximation factor. Note that this improves the previous bestfactor (6 for two speeds). We believe that our work will convince researchersto revisit this well studied scheduling problem for these simple, yetrealistic, asymmetric multiprocessor architectures.

Energy and Time Efficient Scheduling of Tasks with Dependencies on Asymmetric Multiprocessors