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. [3] proposed an O(n 2 f (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.
We study the problem of scheduling a set of jobs with release dates, deadlines and processing requirements (or works) on parallel speed scalable processors so as to minimize the total energy consumption. We consider that both preemptions and migrations of jobs are allowed. For this problem, there exists an optimal polynomial-time algorithm which uses as a black box an algorithm for linear programming. Here, we formulate the problem as a convex program and we propose a combinatorial polynomial-time algorithm which is based on finding maximum flows. Our algorithm runs in O(nf (n) log U) time, where n is the number of jobs, U is the range of all possible values of processors' speeds divided by the desired accuracy and f (n) is the time needed for computing a maximum flow in a layered graph with O(n) vertices.
We consider the problem of scheduling on a single processor a given set of n jobs. Each job j has a workload w j and a release time r j . The processor can vary its speed and hibernate to reduce energy consumption. In a schedule minimizing overall consumed energy, it might be that some jobs complete arbitrarily far from their release time. So in order to guarantee some quality of service, we would like to impose a deadline d j = r j + F for every job j, where F is a guarantee on the flow time. We provide an O(n 3 ) algorithm for the more general case of agreeable deadlines, where jobs have release times and deadlines and can be ordered such that for every i < j, both r i ≤ r j and d i ≤ d j .
We consider the scheduling of an interval order precedence graph of unit execution time tasks with communication delays, release dates and deadlines. Tasks must be executed by a set of processors partitioned into K classes; each task requires one processor from a fixed class. The aim of this paper is to study the extension of the Leung-Palem-Pnueli (in short LPP) algorithm to this problem. The main result is to prove that the LPP algorithm can be extended to dedicated processors and monotone communication delays. It is also proved that the problem is NP-complete for two dedicated processors if communication delays are non monotone. Lastly, we show that list scheduling algorithm cannot provide a solution for identical processors.
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