We revisit the non-preemptive speed-scaling problem, in which a set of jobs
have to be executed on a single or a set of parallel speed-scalable
processor(s) between their release dates and deadlines so that the energy
consumption to be minimized. We adopt the speed-scaling mechanism first
introduced in [Yao et al., FOCS 1995] according to which the power dissipated
is a convex function of the processor's speed. Intuitively, the higher is the
speed of a processor, the higher is the energy consumption. For the
single-processor case, we improve the best known approximation algorithm by
providing a (1+Ï”)αB~αâ-approximation algorithm,
where B~뱉 is a generalization of the Bell number. For the
multiprocessor case, we present an approximation algorithm of ratio
B~αâ((1+Ï”)(1+wminâwmaxââ))α
improving the best known result by a factor of
(25â)αâ1(wminâwmaxââ)α. Notice that our
result holds for the fully heterogeneous environment while the previous known
result holds only in the more restricted case of parallel processors with
identical power functions