Speed-Scaling with No Preemptions

We revisit the non-preemptive speed-scaling problem, in which a set of jobs have to be executed on a single or a set of parallel speed-scalable processor(s) between their release dates and deadlines so that the energy consumption to be minimized. We adopt the speedscaling mechanism first introduced in [Yao et al., FOCS 1995] according to which the power dissipated is a convex function of the processor’s speed. Intuitively, the higher is the speed of a processor, the higher is the energy consumption. For the single-processor case, we improve the best known approximation algorithm by providing a (1+ǫ)αB̃α-approximation algorithm, where B̃α is a generalization of the Bell number. For the multiprocessor case, we present an approximation algorithm of ratio B̃α((1 + ǫ)(1 + wmax wmin ))α improving the best known result by a factor of ( 2 )(w wmin )α. Notice that our result holds for the fully heterogeneous environment while the previous known result holds only in the more restricted case of parallel processors with identical power functions.