Open Shop Scheduling to Minimize Finish Time

Gonzalez, Teofilo F.; Sahni, Sartaj

doi:10.1145/321978.321985

Cited by 613 publications

(327 citation statements)

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“…Note that the network flow approach we just recalled enables to minimize the max-stretch with preemption on one machine. Following the work of Gonzalez and Sahni [19], Lawler and Labetoulle [23] present a scheme to build in polynomial-time a preemptive schedule of makespan C for a set of jobs J 1 , ..., J n of null release dates (∀j, r j = 0), under the condition that Linear System (3) has a solution. This system simply states that: a. all jobs must be fully processed (Equation (3a)); b. the whole processing of a job cannot take a time larger than C (Equation (3b)); c. the whole utilization time of a machine cannot be longer than a time C (Equation (3c)).…”

Section: Minimizing the Maximum Weighted Flow With Preemption (But Nomentioning

confidence: 99%

Minimizing the stretch when scheduling flows of divisible requests

Legrand

Vivien

2008

J Sched

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In this paper, we consider the problem of scheduling distributed biological sequence comparison applications. This problem lies in the divisible load framework with negligible communication costs. Thus far, very few results have been proposed in this model. We discuss and select relevant metrics for this framework: namely max-stretch and sum-stretch. We explain the relationship between our model and the preemptive uni-processor case, and we show how to extend algorithms that have been proposed in the literature for the uni-processor model to the divisible multi-processor problem domain. We recall known results on closely related problems, we show how to minimize the max-stretch on unrelated machines either in the divisible load model or with preemption, we derive new lower bounds on the competitive ratio of any on-line algorithm, we present new competitiveness results for existing algorithms, and we develop several new on-line heuristics. We also address the Pareto optimization of max-stretch. Then, we extensively study the performance of these algorithms and heuristics in realistic scenarios. Our study shows that all previously proposed guaranteed heuristics for max-stretch for the uni-processor model prove to be inefficient in practice. In contrast, we show our on-line algorithms based on linear programming to be near-optimal solutions for maxstretch. Our study also clearly suggests heuristics that are efficient for both metrics, although a combined optimization is in theory not possible in the general case.Keywords: Bioinformatics, heterogeneous computing, scheduling, divisible load, linear programming, stretch RésuméDans ce rapport, nous nous intéressonsà l'ordonnancement d'applications comparant de manière distribuée des séquences biologiques. Ce problème se situe dans le domaine des tâches divisibles avec coûts de communications négli-geables. Jusqu'à présent, très peu de résultats ontété publiés pour ce modèle. Nous discutons et sélectionnons des métriques appropriées pour notre cadre de travail,à savoir le max-stretch et le sum-stretch. Nous expliquons les relations entre notre modèle et le cadre mono-processeur avec préemption, et nous montrons commentétendre au cadre des tâches divisibles sur multi-processeur les algorithmes proposés dans la littérature pour le cas mono-processeur avec pré-emption. Nous rappelons les résultats connus pour des problématiques proches, nous montrons comment minimiser le max-stretch sur des machines non corrélées (que les tâches soient divisibles ou simplement préemptibles), nous obtenons de nouvelles bornes inférieures de compétitivité pour tout algorithme on-line, nous présentons de nouveaux résultats de compétitivité pour des algorithms de la littérature, et nous proposons de nouvelles heuristiques on-line. Nous nous intéressonségalement au problème de la minimisation Pareto du max-stretch. Ensuite, nousétudions, de manière extensive, les performances de tous ces algorithmes et de toutes ces heuristiques, et ce dans un cadre réa-liste. Notreétude montre que les ...

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Section: Minimizing the Maximum Weighted Flow With Preemption (But Nomentioning

confidence: 99%

Minimizing the stretch when scheduling flows of divisible requests

Legrand

Vivien

2008

J Sched

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“…Problem F 3|op ≤ 2|C max remains NP-hard in the strong sense Neumytov and Sevastianov (1993), while the complexity status of problem O3|op ≤ 2|C max is still open. Problem O3| |C max is NP-hard in the ordinary sense, as proved by Gonzalez and Sahni (1976). It is still unknown whether problem Om| |C max with a fixed number of machines m ≥ 3 is NP-hard in the strong sense.…”

Section: Shop Problems: a Reviewmentioning

confidence: 99%

“…Several linear time algorithms are known for problem O2| |C max , the historically the first belongs to Gonzalez and Sahni (1976). Each of the two-machine mixed shop and super shop problems admits an O(n log n)-time algorithm, see Masuda et al (1985) and Strusevich (1991), respectively.…”

Section: Shop Problems: a Reviewmentioning

confidence: 99%

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An approximation algorithm for the three-machine scheduling problem with the routes given by the same partial order

Quibell

Strusevich

2014

Computers & Industrial Engineering

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“…If the distribution is non-preemptive, the second stage is trivial. The problem of construction of an optimal schedule, associated with the given distribution, was thoroughly investigated in [13]. The concept of an open shop, introduced in this paper, is almost the same as that of a distribution.…”

Section: Preliminariesmentioning

confidence: 99%

Task Distributions on Multiprocessor Systems

Shchepin

Vakhania²

2000

Theoretical Computer Science: Exploring New Frontiers of Theoretical Informatics

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Abstract. We consider the problem of scheduling of n independent jobs on m unrelated machines to minimize the max(t 1, t2, ..., tm), ti being the completion time of machine i. In [1] was suggested a polynomial 2-approximation algorithm for this problem. It was also proved that there can exist no polynomial 1.5-approximation algorithm unless P = NP . Here we improve this earlier performance bound 2 to 2 − 1 m . In [1] is also proved a general rounding theorem, which allows to construct in polynomial time 1-job approximations to the optimum, i.e. schedules with an absolute bound equal to the largest job processing time. We also improve this result and obtain (1 − 1 m )-job approximation to optimal.

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Open Shop Scheduling to Minimize Finish Time

Cited by 613 publications

References 1 publication

Minimizing the stretch when scheduling flows of divisible requests

Minimizing the stretch when scheduling flows of divisible requests

An approximation algorithm for the three-machine scheduling problem with the routes given by the same partial order

Task Distributions on Multiprocessor Systems

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