Algorithmic Issues in Energy-Efficient Computation

In this paper, we introduce a model for the speed scaling setting in the framework of explorable uncertainty. In the model, each job has a release time, a deadline and an unknown workload that can be revealed to the algorithm only after executing a query that induces a given additional job-dependent load. Alternatively, the job may be executed without any query, but in that case its workload is equal to a given upper bound. This assumption is motivated for instance in applications like code optimization, or file compression. We study the problem of minimizing the overall energy consumption for executing all the jobs in their time windows. We also consider the related problem of minimizing the maximum speed used by the algorithm. We present lower and upper bounds for both the offline case, where all the jobs are known in advance, and the online case, where the jobs arrive over time. We start with the single machine setting and we finally deal with the more general case where multiple identical parallel machines are available.

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“…[2,3,5,6,[9][10][11][12][13]21], and surveys, e.g. [1,8,19], have been appeared. In [27], each job has…”

Section: Related Workmentioning

confidence: 99%

Speed Scaling with Explorable Uncertainty

Bampis

Dogeas

Kononov

et al. 2021

Proceedings of the 33rd ACM Symposium on Parallelism in Algorithms and Architectures

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“…Without providing a comprehensive list of results of this type, we refer an interested reader to the survey papers by Albers (2009Albers ( , 2010a and Bampis (2016).…”

Section: Related Workmentioning

confidence: 99%

Models and algorithms for energy-efficient scheduling with immediate start of jobs

Shioura

Shakhlevich

Strusevich

et al. 2017

J Sched

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We study a scheduling model with speed scaling for machines and the immediate start requirement for jobs. Speed scaling improves the system performance, but incurs the energy cost. The immediate start condition implies that each job should be started exactly at its release time. Such a condition is typical for modern Cloud computing systems with abundant resources. We consider two cost functions, one that represents the quality of service and the other that corresponds to the cost of running. We demonstrate that the basic scheduling model to minimize the aggregated cost function with n jobs is solvable in O(n log n) time in the singlemachine case and in O(n 2 m) time in the case of m parallel machines. We also address additional features, e.g., the cost of job rejection or the cost of initiating a machine. In the case of a single machine, we present algorithms for minimizing one of the cost functions subject to an upper bound on the value of the other, as well as for finding a Pareto-optimal solution.

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“…Other variants of this problem have been studied, for example the multi-processor case (Demaine et al 2007) or the case when jobs have agreeable deadlines (Angel et al 2012(Angel et al , 2014. (See the survey in Bampis (2016) for more information. )…”

Section: Introductionmentioning

confidence: 99%

Scheduling with gaps: new models and algorithms

Chrobák

Golin

Lam

et al. 2021

J Sched

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We consider scheduling problems for unit jobs with release times, where the number or size of the gaps in the schedule is taken into consideration, either in the objective function or as a constraint. Except for several papers on minimum-energy scheduling, there is no work in the scheduling literature that uses performance metrics depending on the gap structure of a schedule. One of our objectives is to initiate the study of such scheduling problems. We focus on the model with unit-length jobs. First we examine scheduling problems with deadlines, where we consider two variants of minimum-gap scheduling: maximizing throughput with a budget for the number of gaps and minimizing the number of gaps with a throughput requirement. We then turn to other objective functions. For example, in some scenarios gaps in a schedule may be actually desirable, leading to the problem of maximizing the number of gaps. A related problem involves minimizing the maximum gap size. The second part of the paper examines the model without deadlines, where we focus on the tradeoff between the number of gaps and the total or maximum flow time. For all these problems we provide polynomial time algorithms, with running times ranging from $$O(n\log n)$$ O ( n log n ) for some problems to $$O(n^7)$$ O ( n 7 ) for other. The solutions involve a spectrum of algorithmic techniques, including different dynamic programming formulations, speed-up techniques based on searching Monge arrays, searching $$X+Y$$ X + Y matrices, or implicit binary search. Throughout the paper, we also draw a connection between gap scheduling problems and their continuous analogues, namely hitting set problems for intervals of real numbers. As it turns out, for some problems the continuous variants provide insights leading to efficient algorithms for the corresponding discrete versions, while for other problems completely new techniques are needed to solve the discrete version.

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Algorithmic Issues in Energy-Efficient Computation

Abstract: International audienc

Cited by 7 publications

References 43 publications

Speed Scaling with Explorable Uncertainty

Speed Scaling with Explorable Uncertainty

Models and algorithms for energy-efficient scheduling with immediate start of jobs

Scheduling with gaps: new models and algorithms

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