Speed Scaling of Tasks with Precedence Constraints

We consider the problem of speed scaling to conserve energy in a multiprocessor setting where there are precedence constraints between tasks, and where the performance measure is the makespan. That is, we consider an energy bounded version of the classic problem Pm | prec | C _max. We extend the standard 3-field notation and denote this problem as Sm | prec, energy | C _max. We show that, without loss of generality, one need only consider constant power schedules. We then show how to reduce this problem to the problem Qm | prec | C _max to obtain a poly-log(m)-approximation algorithm. A preliminary version of this paper appears in Proceedings of the 3rd Workshop on Approximation and Online Algorithms (WAOA 2005). Research of K. Pruhs supported in part by NSF grants CCR-0098752, ANI-0123705, CNS-0325353, CCF-0448196, CCF-0514058, and IIS-0534531. Research of R. van Stee supported by Alexander von Humboldt-Stiftung.