From Preemptive to Non-preemptive Speed-Scaling Scheduling

Bampis, Evripidis; Kononov, Alexander; Letsios, Dimitrios; Lucarelli, Giorgio; Nemparis, Ioannis

doi:10.1007/978-3-642-38768-5_14

Cited by 6 publications

(18 citation statements)

References 13 publications

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“…as Ω(( wmax w min ) α−1 ). In this direction, a (1 + wmax w min ) α−1 -approximation algorithm for the singleprocessor case has been presented in [8]. To overcome the above lower bound, all known constant-factor approximation algorithms for the single-processor problem [7,9,15] consider an initial partition of the time horizon into some specific intervals defined by the so-called landmarks.…”

Section: Previous Known Resultsmentioning

confidence: 99%

“…Note also that we generalize the machine environment and we pass from the homogeneous with different w i,j 's to the fully heterogeneous one. Our algorithm combines two basic ingredients: theB α (1 + ǫ) αapproximation algorithm of [9] for the fully heterogeneous preemptive non-migratory speedscaling problem and the (1 + wmax w min ) α -approximation algorithm of [8] for the single-processor non-preemptive speed-scaling problem. The first algorithm is used in order to assign the jobs to the processors, while the second one to get a non-preemptive schedule for each processor independently.…”

Section: Previous Known Resultsmentioning

confidence: 99%

“…Recently, an approximation algorithm of ratio (12(1 + ǫ)) α−1 is given in [15], improving the approximation ratio for any α > 25. Moreover, the relation between preemptive and non-preemptive schedules in the energy-minimization setting has been studied in [8]. The authors show that using as a lower bound the optimal preemptive solution, it is possible to obtain an approximation algorithm of ratio (1 + wmax w min ) α .…”

Section: Introductionmentioning

confidence: 99%

“…For homogeneous multiprocessors when preemptions are not allowed, an approximation algorithm with ratio m α ( m √ n) α−1 has been presented in [8] which uses as a lower bound the optimal preemptive solution. More recently, Cohen-Addad et al [15] proposed an algorithm of ratio (…”

Section: Introductionmentioning

confidence: 99%

“…Recall that in practice α is a small constant and usually α ∈ (1,3]. In [8], where the relation between preemptive and non-preemptive schedules has been explored, an example showing that their distance can be a factor of Ω(n α−1 ) have been proposed. A similar example was used in [15] to show that the standard configuration linear programming formulation has the same integrality gap.…”

Section: Introductionmentioning

confidence: 99%

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Speed-Scaling with No Preemptions

Bampis¹,

Letsios²,

Lucarelli³

2014

Algorithms and Computation

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We revisit the non-preemptive speed-scaling problem, in which a set of jobs have to be executed on a single or a set of parallel speed-scalable processor(s) between their release dates and deadlines so that the energy consumption to be minimized. We adopt the speedscaling mechanism first introduced in [Yao et al., FOCS 1995] according to which the power dissipated is a convex function of the processor's speed. Intuitively, the higher is the speed of a processor, the higher is the energy consumption. For the single-processor case, we improve the best known approximation algorithm by providing a (1+ǫ) αB α -approximation algorithm, whereB α is a generalization of the Bell number. For the multiprocessor case, we present an approximation algorithm of ratioB α ((1 + ǫ)(1 + wmax wmin )) α improving the best known result by a factor of ( 5 2 ) α−1 ( wmax wmin ) α . Notice that our result holds for the fully heterogeneous environment while the previous known result holds only in the more restricted case of parallel processors with identical power functions.

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Section: Previous Known Resultsmentioning

confidence: 99%

Section: Previous Known Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Speed-Scaling with No Preemptions

Bampis¹,

Letsios²,

Lucarelli³

2014

Algorithms and Computation

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Throughput Maximization in Multiprocessor Speed-Scaling

Angel

Bampis

Chau

et al. 2014

Algorithms and Computation

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We are given a set of n jobs that have to be executed on a set of m speed-scalable machines that can vary their speeds dynamically using the energy model introduced in [Yao et al., FOCS'95]. Every job j is characterized by its release date r j , its deadline d j , its processing volume p i,j if j is executed on machine i and its weight w j . We are also given a budget of energy E and our objective is to maximize the weighted throughput, i.e. the total weight of jobs that are completed between their respective release dates and deadlines. We propose a polynomial-time approximation algorithm where the preemption of the jobs is allowed but not their migration. Our algorithm uses a primal-dual approach on a linearized version of a convex program with linear constraints. Furthermore, we present two optimal algorithms for the non-preemptive case where the number of machines is bounded by a fixed constant. More specifically, we consider: (a) the case of identical processing volumes, i.e. p i,j = p for every i and j, for which we present a polynomial-time algorithm for the unweighted version, which becomes a pseudopolynomial-time algorithm for the weighted throughput version, and (b) the case of agreeable instances, i.e. for which r i ≤ r j if and only if d i ≤ d j , for which we present a pseudopolynomial-time algorithm. Both algorithms are based on a discretization of the problem and the use of dynamic programming.

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Energy-Efficient Algorithms for Non-preemptive Speed-Scaling

Cohen-Addad

Mathieu

et al. 2015

Approximation and Online Algorithms

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Abstract. We improve complexity bounds for energy-efficient speed scheduling problems for both the single processor and multi-processor cases. Energy conservation has become a major concern, so revisiting traditional scheduling problems to take into account the energy consumption has been part of the agenda of the scheduling community for the past few years [1]. We consider the energy minimizing speed scaling problem introduced by Yao et al. [20] where we wish to schedule a set of jobs, each with a release date, deadline and work volume, on a set of identical processors. The processors may change speed as a function of time and the energy they consume is the αth power of its speed. The objective is then to find a feasible schedule which minimizes the total energy used. We show that in the setting with an arbitrary number of processors where all work volumes are equal, there is a 2(1 + ε)(5(1 + ε)) α−1B α = Oα(1) approximation algorithm, whereBα is the generalized Bell number. This is the first constant factor algorithm for this problem. This algorithm extends to general unequal processor-dependent work volumes, up to losing a factor of ( (1+r)r 2 ) α in the approximation, where r is the maximum ratio between two work volumes. We then show this latter problem is APXhard, even in the special case when all release dates and deadlines are equal and r is 4. In the single processor case, we introduce a new linear programming formulation of speed scaling and prove that its integrality gap is at most 12 α−1 . As a corollary, we obtain a (12(1+ε)) α−1 approximation algorithm where there is a single processor, improving on the previous best bound of 2 α−1 (1 + ε) αB α when α ≥ 25.

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From Preemptive to Non-preemptive Speed-Scaling Scheduling

Cited by 6 publications

References 13 publications

Speed-Scaling with No Preemptions

Speed-Scaling with No Preemptions

Throughput Maximization in Multiprocessor Speed-Scaling

Energy-Efficient Algorithms for Non-preemptive Speed-Scaling

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