Speed-Scaling with No Preemptions

Abstract

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 speed-scaling 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 $(1+\epsilon )^{\alpha }\tilde{B}_{\alpha }$-approximation algorithm, where $\tilde{B}_{\alpha }$ is a generalization of the Bell number. For the multiprocessor case, we present an approximation algorithm of ratio $\tilde{B}_{\alpha }((1+\epsilon )(1+\frac{w_{\max }}{w_{\min }}))^{\alpha }$ improving the best known result by a factor of $(\frac{5}{2})^{\alpha -1}(\frac{w_{\max }}{w_{\min }})^{\alpha }$. 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.

E. Bampis, D. Letsios and G. Lucarelli are partially supported by the project ALGONOW, co-financed by the European Union (European Social Fund - ESF) and Greek national funds, through the Operational Program “Education and Lifelong Learning”, under the program THALES and by the project Mathematical Programming and Non-linear Combinatorial Optimization under the program PGMO. D. Letsios is partially supported by the German Research Foundation, project AL-464/7-1. G. Lucarelli is supported by the project Moebus funded by ANR.