Optimal and online preemptive scheduling on uniformly related machines

Ebenlendr, Tomáš; Sgall, Jiřį́

doi:10.1007/s10951-009-0119-7

Cited by 13 publications

(14 citation statements)

References 21 publications

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“…We do not know, however, what is its worst case value over all speed combinations. Nevertheless, using the fact that there exists an e-competitive randomized algorithm [5], we conclude that our (deterministic) algorithm is also e-competitive.…”

Section: Previous Results For Preemptive Online Schedulingmentioning

confidence: 82%

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Preemptive Online Scheduling: Optimal Algorithms for All Speeds

2008

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Our main result is an optimal online algorithm for preemptive scheduling on uniformly related machines with the objective to minimize makespan. The algorithm is deterministic, yet it is optimal even among all randomized algorithms. In addition, it is optimal for any fixed combination of speeds of the machines, and thus our results subsume all the previous work on various special cases. Together with a new lower bound it follows that the overall competitive ratio of this optimal algorithm is between 2.054 and e ≈ 2.718. We also give a complete analysis of the competitive ratio for three machines.

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Section: Previous Results For Preemptive Online Schedulingmentioning

confidence: 82%

“…For the general case, Ebenlendr and Sgall [5] obtained a 4-competitive deterministic algorithm and an e-competitive randomized algorithm, where e ≈ 2.718.…”

Section: Previous Results For Preemptive Online Schedulingmentioning

confidence: 99%

Preemptive Online Scheduling: Optimal Algorithms for All Speeds

2008

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“…This is a lower bound on the makespan, as the first term gives the minimal time when all the work can be completed using all the machines fully, and similarly the term for k is the minimal time when the work of the k largest jobs can be completed using the k fastest machines fully. The tightness of this bound follows from [10,8,5].…”

Section: Preliminariesmentioning

confidence: 94%

“…For a given valueT , Ψ contains all sequences with C * max [J ] =T . A 1-approximation semi-online algorithm is known for any s, see [5]. Known maximal job size, p max = p. For a given valuep, Ψ contains all sequences with max p j =p.…”

Section: Semi-online Restrictions and Previous Workmentioning

confidence: 99%

“…Even when we decide the completion time of a job, there are many ways to schedule it given the flexibility of preemptions. We choose a particular one based on the notion of a virtual machine from [5,4]. We define the ith virtual machine, denoted V i , so that at each time τ it contains the ith fastest machine among those real machines M 1 , M 2 , .…”

Section: The Optimal Algorithmmentioning

confidence: 99%

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Semi-Online Preemptive Scheduling: One Algorithm for All Variants

Ebenlendr

Sgall

2010

Theory Comput Syst

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Abstract. We present a unified optimal semi-online algorithm for preemptive scheduling on uniformly related machines with the objective to minimize the makespan. This algorithm works for all types of semi-online restrictions, including the ones studied before, like sorted (decreasing) jobs, known sum of processing times, known maximal processing time, their combinations, and so on. Based on the analysis of this algorithm, we derive some global relations between various semi-online restrictions and tight bounds on the approximation ratios for a small number of machines.

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