Speed-scaling with no Preemptions

TL;DR

This paper improves approximation algorithms for non-preemptive speed-scaling problems, minimizing energy consumption on single and multiple processors with heterogeneous environments, by leveraging convex power functions and advanced mathematical bounds.

Contribution

It introduces improved approximation algorithms for non-preemptive speed-scaling on heterogeneous processors, extending previous results to more general environments.

Findings

Single-processor approximation ratio improved to $(1+\epsilon)^{\alpha}\tilde{B}_{\alpha}$.

Multiprocessor approximation ratio improved, accommodating heterogeneity.

Results hold for fully heterogeneous environments, unlike previous work.

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.