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 vertical bar prec vertical bar C-max. We extend the standard 3-field notation and denote this problem as Sm vertical bar prec, energy vertical bar Cmax. 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 vertical bar prec vertical bar C-max to obtain a poly-log( m)approximation algorithm.