A Fully Polynomial-Time Approximation Scheme for Speed Scaling with a Sleep State

We study classical deadline-based preemptive scheduling of jobs in a computing environment equipped with both dynamic speed scaling and sleep state capabilities: Each job is specified by a release time, a deadline and a processing volume, and has to be scheduled on a single, speed-scalable processor...

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Vydáno v:Algorithmica Ročník 81; číslo 9; s. 3725 - 3745
Hlavní autoři: Antoniadis, Antonios, Huang, Chien-Chung, Ott, Sebastian
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 16.09.2019
Springer Nature B.V
Springer Verlag
Témata:
Algorithm Analysis and Problem Complexity
Algorithms
Approximation
Complexity
Computational Geometry
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Algorithms
Data Structures and Information Theory
Energy consumption
Lower bounds
Mathematical analysis
Mathematics of Computing
Microprocessors
Polynomials
Preempting
Production scheduling
Scaling
Schedules
Sleep
Theory of Computation
Approximation algorithms
Polynomial-time approximation scheme
Energy efficiency
ISSN:0178-4617, 1432-0541
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Shrnutí:We study classical deadline-based preemptive scheduling of jobs in a computing environment equipped with both dynamic speed scaling and sleep state capabilities: Each job is specified by a release time, a deadline and a processing volume, and has to be scheduled on a single, speed-scalable processor that is supplied with a sleep state. In the sleep state, the processor consumes no energy, but a constant wake-up cost is required to transition back to the active state. In contrast to speed scaling alone, the addition of a sleep state makes it sometimes beneficial to accelerate the processing of jobs in order to transition the processor to the sleep state for longer amounts of time and incur further energy savings. The goal is to output a feasible schedule that minimizes the energy consumption. Since the introduction of the problem by Irani et al. (ACM Trans Algorithms 3(4), 2007 ), its exact computational complexity has been repeatedly posed as an open question (see e.g. Albers and Antoniadis in ACM Trans Algorithms 10(2):9,  2014 ; Baptiste et al. in ACM Trans Algorithms 8(3):26, 2012 ; Irani and Pruhs in SIGACT News 36(2):63–76, 2005 ). The currently best known upper and lower bounds are a 4 / 3-approximation algorithm and NP-hardness due to Albers and Antoniadis ( 2014 ) and Kumar and Shannigrahi (CoRR, 2013 . arXiv:1304.7373 ), respectively. We close the aforementioned gap between the upper and lower bound on the computational complexity of speed scaling with sleep state by presenting a fully polynomial-time approximation scheme for the problem. The scheme is based on a transformation to a non-preemptive variant of the problem, and a discretization that exploits a carefully defined lexicographical ordering among schedules.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-019-00596-3