  The problem of attaining energy efficiency in distributed systems is of
importance, but a general, non-domain-specific theory of energy-minimal
scheduling is far from developed. In this paper, we classify the problems of
energy-minimal scheduling and present theoretical foundations of the same. We
derive results concerning energy-minimal scheduling of independent jobs in a
distributed system with functionally similar machines with different working
and idle power ratings. The machines considered in our system can have
identical as well as different speeds. If the jobs can be divided into
arbitrary parts, we show that the minimum-energy schedule can be generated in
linear time and give exact scheduling algorithms. For the cases where jobs are
non-divisible, we prove that the scheduling problems are NP-hard and also give
approximation algorithms for the same along with their bounds.
