A Better Algorithm for an Ancient Scheduling Problem

Karger, David R.; Phillips, Steven J.; Torng, Eric

doi:10.1006/jagm.1996.0019

Cited by 131 publications

(58 citation statements)

References 5 publications

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“…The first upper bound on the competitive ratio below 2 was 1.986 [6]. This upper bound was improved to 1.945 [24], then to 1.923 [2], and finally to 1.9201 [16].…”

Section: Previous Workmentioning

confidence: 96%

The Power of Reordering for Online Minimum Makespan Scheduling

Englert

Ozmen

Westermann

2008

2008 49th Annual IEEE Symposium on Foundations of Computer Science

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In the classic minimum makespan scheduling problem, we are given an input sequence of jobs with processing times. A scheduling algorithm has to assign the jobs to m parallel machines. The objective is to minimize the makespan, which is the time it takes until all jobs are processed. In this paper, we consider online scheduling algorithms without preemption. However, we do not require that each arriving job has to be assigned immediately to one of the machines. A reordering buffer with limited storage capacity can be used to reorder the input sequence in a restricted fashion so as to schedule the jobs with a smaller makespan. This is a natural extension of lookahead.We present an extensive study of the power and limits of online reordering for minimum makespan scheduling. As main result, we give, for m identical machines, tight and, in comparison to the problem without reordering, much improved bounds on the competitive ratio for minimum makespan scheduling with reordering buffers. Depending on m, the achieved competitive ratio lies between 4/3 and 1.4659. This optimal ratio is achieved with a buffer of size Θ(m). We show that larger buffer sizes do not result in an additional advantage and that a buffer of size Ω(m) is necessary to achieve this competitive ratio. Further, we present several algorithms for different buffer sizes. Among others, we introduce, for every buffer size k ∈ [1, (m + 1)/2], a (2 − 1/(m − k + 1))-competitive algorithm, which nicely generalizes the well-known result of Graham.For m uniformly related machines, we give a scheduling algorithm that achieves a competitive ratio of 2 with a reordering buffer of size m. Considering that the best known * Supported by DFG grant WE 2842/1. competitive ratio for uniformly related machines without reordering is 5.828, this result emphasizes the power of online reordering further more.

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“…The first upper bound on the competitive ratio below 2 was 1.986 [6]. This upper bound was improved to 1.945 [24], then to 1.923 [2], and finally to 1.9201 [16].…”

Section: Previous Workmentioning

confidence: 96%

The Power of Reordering for Online Minimum Makespan Scheduling

Englert

Ozmen

Westermann

2008

2008 49th Annual IEEE Symposium on Foundations of Computer Science

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“…The competitive ratio of that algorithm is 2 − 1/m. Since then there was a sequence of improvements on the performance of algorithms [4,26,1] and a sequence of lower bounds [5,1,20], and the best current results are an algorithm of competitive ratio 1.9201, designed by Fleischer and Wahl [17] and a lower bound of 1.88 given by Rudin [29]. For uniformly related machines there exist constant competitive algorithms, see [2,6].…”

Section: Resource Augmentationmentioning

confidence: 99%

Optimal On-Line Algorithms to Minimize Makespan on Two Machines with Resource Augmentation

Epstein

Ganot

2004

Approximation and Online Algorithms

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We study the problem of on-line scheduling on two uniformly related machines where the on-line algorithm has resources different from those of the off-line algorithm. We consider three versions of this problem, preemptive semi-online, non-preemptive on-line and preemptive on-line scheduling. For all these cases we design algorithms with best possible competitive ratios as functions of the machine speeds.

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“…Только в 1992 г. в [11] был предложен онлайн-алгоритм с мультипликативной ошибкой, не большей 1;986 для всех m > 70. Это значение затем было улучшено до 1;945, а затем и до 1;923 в работах [10] и [13]. Также было получено несколько результатов о нижних оценках для таких алгоритмов.…”

Section: Introductionunclassified

Об Онлайн-Алгоритмах Упаковки Прямоугольников В Несколько Полос

Zhuk¹

2007

Дискрет. матем.

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Исследуется задача об упаковке прямоугольников в несколько полос. Показано, что для этой задачи существуют онлайн-алгоритмы с асимптотической мультипликатив-ной ошибкой сколь угодно близкой к 2e, где e -основание натурального логарифма. Доказано, что ни один онлайн-алгоритм не может иметь асимптотическую мультипли-кативную ошибку меньше, чем e.

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A Better Algorithm for an Ancient Scheduling Problem

Cited by 131 publications

References 5 publications

The Power of Reordering for Online Minimum Makespan Scheduling

The Power of Reordering for Online Minimum Makespan Scheduling

Optimal On-Line Algorithms to Minimize Makespan on Two Machines with Resource Augmentation

Об Онлайн-Алгоритмах Упаковки Прямоугольников В Несколько Полос

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