We consider offline scheduling algorithms that incorporate speed scaling to address the bicriteria problem of minimizing energy consumption and a scheduling metric. For makespan, we give linear-time algorithms to compute all non-dominated solutions for the general uniprocessor problem and for the multiprocessor problem when every job requires the same amount of work. We also show that the multiprocessor problem becomes NP-hard when jobs can require different amounts of work. For total flow, we show that the optimal flow corresponding to a particular energy budget cannot be exactly computed on a machine supporting arithmetic and the extraction of roots. This hardness result holds even when scheduling equal-work jobs on a uniprocessor. We do, however, extend previous work by to give an arbitrarily-good approximation for scheduling equal-work jobs on a multiprocessor.
We survey recent research that has appeared in the theoretical computer science literature on algorithmic problems related to power management. We will try to highlight some open problem that we feel are interesting. This survey places more concentration on lines of research of the authors: managing power using the techniques of speed scaling and power-down which are also currently the dominant techniques in practice.