Optimal energy trade-off schedules

Barcelo, Neal; Cole, Daniel G.; Letsios, Dimitrios; Nugent, Michael; Pruhs, Kirk

doi:10.1016/j.suscom.2013.01.007

Cited by 4 publications

(15 citation statements)

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“…[2] give a dynamic programming algorithm and deserve credit for introducing the notion of trade-off schedules. [13] give a polynomial-time 20 algorithm for recognizing an optimal schedule. They also showed that the optimal schedule evolves continuously as a function of the importance of energy, implying that a continuous homotopic algorithm is, at least in principle, possible.…”

Section: Related Resultsmentioning

confidence: 99%

“…They also showed that the optimal schedule evolves continuously as a function of the importance of energy, implying that a continuous homotopic algorithm is, at least in principle, possible. However, [13] was not able to provide any bound, even exponential, on the time of this algorithm, nor was [13] able to provide any way to discretize this algorithm.…”

Section: Related Resultsmentioning

confidence: 99%

“…To reemphasize, the prior literature [2,13,31] on our problem assumes that the set of allowable speeds is continuous. Our setting of discrete speeds both more closely models the current technology, and seems to be algorithmically more challenging.…”

Section: Related Resultsmentioning

confidence: 99%

“…Our setting of discrete speeds both more closely models the current technology, and seems to be algorithmically more challenging. In [13] the recognition of an optimal trade-off schedule in the continuous setting is essentially a direct consequence of the KKT conditions of the natural convex program, as it is observed that there is essentially only one degree of freedom for each job in any plausibly optimal schedule, and this degree of freedom can be recovered from the candidate schedule by looking at the speed that the job is run at. In the discrete setting, we shall see that there is again essentially only one degree of freedom for each job.…”

Section: Related Resultsmentioning

confidence: 99%

“…Using complementary slackness we find necessary and sufficient conditions for a candidate schedule to be optimal. Reminiscent of the approach used in the case of continuous speeds in [13], we then interpret these conditions in the following geometric manner. Each job j is associated with a linear function D α j j (t), which we call a dual line.…”

Section: Overviewmentioning

confidence: 99%

See 4 more Smart Citations

On the Complexity of Speed Scaling

Barcelo

Kling

Nugent

et al. 2015

Mathematical Foundations of Computer Science 2015

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It seems to be a corollary to the laws of physics that, all else being equal, higher performance devices are necessarily less energy efficient than lower performance devices. Conceptually there is an energy efficiency spectrum of design points, with high performance and low energy efficiency on one end, and low performance and high energy efficiency on the other end. As in most technologies, there is not a universal sweet spot for computer chips that is best for all situations. For example, there are situations when there are critical tasks to be done, when performance is more important than energy efficiency, and there are situations when there are no critical tasks, when energy efficiency may be more important than performance.Speed-scalable processors aim to resolve this conflict by allowing the operating system to dynamically choose the performance to energy trade-off. The resulting optimization problems involve scheduling jobs on such a processor and have conflicting dual objectives of quality of service and some energy related objective. This engenders many different optimization problems, depending on how one models the processor, the performance objective, and how one handles the dual objectives.In this thesis we map out a reasonably full landscape of all possible formulations, determining which assumptions drive computational tractability. Beyond identifying the individual computational complexities, we use algorithmics as a lens to study the combinatorial structure of such trade-off schedules. In particular, we give several general reductions which, in some sense, reduce the number of problems that are distinct in a complexity theoretic sense. We show that some problems, for which there are efficient algorithms on a fixed speed processor, are NP-hard. Finally, we present several primal-dual based polynomial time algorithms.iii 8 Let j be the green job. The set Ψ j := { 3, 4 } corresponds to the 2 execution intervals of j. The speeds at the border of the first execution interval, s ,3,j and s r,3,j , are both equal to s 2 . Similarly, the border speeds in the second execution interval, s ,4,j and s r,4,j , are both equal to s 1 . The value q ,j = 3 refers to the first and q r,j = 4 to the last execution interval of j. Finally, the indicator variables for j in the depicted example have the following values: y r,j (3) = y ,j (3) = 1 (borders at some release time), y r,j (4) = y ,j (4) = 0 (borders not at some release time), χ j (3) = 1 (not j's last execution interval), and χ j (4) = 0 (last execution interval of j). in the design process a car designer has to select a sweet spot on this spectrum as a design goal. There is seldom a uniquely defined sweet spot that is best for all situations, which is why both sports cars and economy cars are produced.Although information technology is no exception to this corollary, unlike other technologies, historically the sweet spot was invariably skewed towards the high performance low energy efficiency end of the spectrum. Energy consumption was simply not a first ...

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Section: Related Resultsmentioning

confidence: 99%

Section: Related Resultsmentioning

confidence: 99%

Section: Related Resultsmentioning

confidence: 99%

Section: Related Resultsmentioning

confidence: 99%

Section: Overviewmentioning

confidence: 99%

See 3 more Smart Citations

On the Complexity of Speed Scaling

Barcelo

Kling

Nugent

et al. 2015

Mathematical Foundations of Computer Science 2015

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Green Computing Algorithmics

Pruhs

2019

Lecture Notes in Computer Science

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Efficient Computation of Optimal Energy and Fractional Weighted Flow Trade-Off Schedules

et al. 2016

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We give a polynomial time algorithm to compute an optimal energy and fractional weighted flow trade-off schedule for a speed-scalable processor with discrete speeds. Our algorithm uses a geometric approach that is based on structural properties obtained from a primal-dual formulation of the problem. ACM Subject Classification F.2.2 Nonnumerical Algorithms and ProblemsKeywords and phrases scheduling, flow time, energy efficiency, speed scaling, primal-dual Digital Object Identifier 10.4230/LIPIcs.xxx.yyy.p IntroductionIt seems to be a universal law of technology in general, and information technology in particular, that higher performance comes at the cost of energy efficiency. Thus a common theme of green computing research is how to manage information technologies so as to obtain the proper balance between these conflicting goals of performance and energy efficiency. Here the technology we consider is a speed-scalable processor, as manufactured by the likes of Intel and AMD, that can operate in different modes, where each mode has a different speed and power consumption, and the higher speed modes are less energy-efficient in that they consume more energy per unit of computation. The management problem that we consider is how to schedule jobs on such a speed-scalable processor in order to obtain an optimal trade-off between a natural performance measure (fractional weighted flow) and the energy used. Our main result is a polynomial time algorithm to compute such an optimal trade-off schedule. We want to informally elaborate on the statement of our main result. Fully formal definitions can be found in Section 3. We need to explain how we model the processors, the jobs, a schedule, our performance measure, and the energy-performance trade-off: *

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Optimal energy trade-off schedules

Cited by 4 publications

References 12 publications

On the Complexity of Speed Scaling

On the Complexity of Speed Scaling

Green Computing Algorithmics

Efficient Computation of Optimal Energy and Fractional Weighted Flow Trade-Off Schedules

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