Speed Scaling on Parallel Processors

In this paper we investigate dynamic speed scaling, a technique to reduce energy consumption in variable-speed microprocessors. While prior research has focused mostly on single processor environments, in this paper we investigate multiprocessor settings. We study the basic problem of scheduling a set of jobs, each specified by a release date, a deadline and a processing volume, on variable-speed processors so as to minimize the total energy consumption. We first settle the problem complexity if unit size jobs have to be scheduled. More specifically, we devise a polynomial time algorithm for jobs with agreeable deadlines and prove NP-hardness results if jobs have arbitrary deadlines. For the latter setting we also develop a polynomial time algorithm achieving a constant factor approximation guarantee. Additionally, we study problem settings where jobs have arbitrary processing requirements and, again, develop constant factor approximation algorithms. We finally transform our offline algorithms into constant competitive online strategies.