  We study the problem of scheduling a set of jobs with release dates,
deadlines and processing requirements (or works), on parallel speed-scaled
processors so as to minimize the total energy consumption. We consider that
both preemption and migration of jobs are allowed. An exact polynomial-time
algorithm has been proposed for this problem, which is based on the Ellipsoid
algorithm. Here, we formulate the problem as a convex program and we propose a
simpler polynomial-time combinatorial algorithm which is based on a reduction
to the maximum flow problem. Our algorithm runs in $O(nf(n)logP)$ time, where
$n$ is the number of jobs, $P$ is the range of all possible values of
processors' speeds divided by the desired accuracy and $f(n)$ is the complexity
of computing a maximum flow in a layered graph with O(n) vertices.
Independently, Albers et al. \cite{AAG11} proposed an $O(n^2f(n))$-time
algorithm exploiting the same relation with the maximum flow problem. We extend
our algorithm to the multiprocessor speed scaling problem with migration where
the objective is the minimization of the makespan under a budget of energy.
