Abstract
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.
Highlights
Energy consumption is a major issue in our days
This later approach has been adopted in the seminal paper of Yao et al (1995) who considered the problem of scheduling a set of jobs with release dates and deadlines on a single processor so that the total energy is minimized, under the so-called speed scaling model in which the speed of a processor can be varied over time and the power consumption is a convex function of the processor’s speed
Our objective is to find a schedule with minimum energy consumption so that every job is entirely executed between its release date and its deadline
Summary
Energy consumption is a major issue in our days. Great efforts are devoted to the reduction of energy dissipation in computing environments ranging from small portable devices to large data centers. Chen et al (2004) initiated the study of the multiprocessor speed scaling problem of minimizing the energy and they proposed a greedy algorithm for the basic setting in which all jobs have the same release date and deadline. Pruhs et al (2008) studied the problem of optimizing performance without exceeding a fixed budget of energy Their objective was total flow time minimization and they presented an optimal polynomial-time algorithm for instances with unit-work jobs. Chan et al (2009) proposed an online algorithm for maximizing the throughput and minimizing the energy of a set of jobs which have to be executed by a processor whose speed is bounded above Their algorithm has constant competitive ratio in terms of both objectives. To our work, Albers et al (2011) proposed another optimal algorithm for the same problem which explores the relation of the problem with maximum flow
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