Brief Announcement: A QPTAS for Non-preemptive Speed-scaling.

Modern processors typically allow dynamic speed-scaling offering an effective trade-off between high throughput and energy efficiency. In a classical model, a processor/machine runs at speed s when consuming power sα where α >1 is a constant. Yao et al. [FOCS 1995] studied the problem of completing all jobs before their deadlines on a single machine with the minimum energy in their seminal work and gave a nice polynomial time algorithm. The influential work has been extended to various settings. In particular, the problem has been extensively studied in the presence of multiple machines as multi-core processors have become dominant computing units. However, when jobs must be scheduled non-preemptively, our understanding of the problem remains fairly unsatisfactory. Often, preempting a job is prohibited since it could be very costly. Previously, a O((wmax wmin)α)-approximation was known for the non-preemptive setting where wmax and wmin denote the maximum and minimum job sizes, respectively. Even when there is only one machine, the best known approximation factor had a dependency on α. In this paper, for any fixed α >1 and ε >0, we give the first (1+ε)-approximation for this problem on multiple machines which runs in nO(polylog (n)) time where n is the number of jobs to be scheduled.