On-line scheduling revisited

Fleischer, Rudolf; Wahl, Michaela

doi:10.1002/1099-1425(200011/12)3:6<343::aid-jos54>3.0.co;2-2

Cited by 133 publications

(41 citation statements)

References 13 publications

(16 reference statements)

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“…A long list of improved algorithms has since been published. The best heuristic known for this problem is due to Fleischer and Wahl (2000). They designed an algorithm with competitive ratio smaller than 1.9201 when the number of machines tends to infinity.…”

Section: Introductionmentioning

confidence: 99%

An efficient algorithm for semi-online multiprocessor scheduling with given total processing time

Kellerer

Котов

Gabay

2015

J Sched

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International audienceWe consider a semi-online multiprocessor scheduling problem with a given a set of identical machines and a sequence of jobs, the sum of whose processing times is known in advance. The jobs are to be assigned online to one of the machines and the objective is to minimize the makespan. The best known algorithm for this problem achieves a competitive ratio 1.6 (Cheng et al. in Theor Comput Sci 337:134–146, 2005). The best known lower bound is approximately 1.585 (Albers and Hellwig in Theor Comput Sci 443:1–9, 2012) if the number of machines tends to infinity. We present an elementary algorithm with competitive ratio equal to this lower bound. Thus, the algorithm is best possible if the number of machines tends to infinity

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Section: Introductionmentioning

confidence: 99%

An efficient algorithm for semi-online multiprocessor scheduling with given total processing time

Kellerer

Котов

Gabay

2015

J Sched

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“…Despite major efforts, the exact competitive ratio for the non-preemptive case is still an open problem, but since Rudin [26] gave a lower bound of 1.880, it is clear that the competitive ratio is significantly worse than the one for preemptive scheduling. The best upper bound on the competitive ratio of nonpreemptive scheduling known so far is 1.920 due to Fleischer and Wahl [19].…”

Section: Non-preemptive Schedulingmentioning

confidence: 99%

An overview of some results for reordering buffers

Englert

2011

Comput Sci Res Dev

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Lookahead is a classic concept in the theory of online scheduling. An online algorithm without lookahead has to process tasks as soon as they arrive and without any knowledge about future tasks. With lookahead, this strict assumption is relaxed. There are different variations on the exact type of information provided to the algorithm under lookahead but arguably the most common one is to assume that, at every point in time, the algorithm has knowledge of the attributes of the next k tasks to arrive. This assumption is justified by the fact that, in practice, tasks may not always strictly arrive one-by-one and therefore, a certain number of tasks are always waiting in a queue to be processed.In recent years, so-called reordering buffers have been studied as a sensible generalization of lookahead. The basic idea is that, in problem settings where the order in which the tasks are processed is not important, we can permit a scheduling algorithm to choose to process any task waiting in the queue. This stands in contrast to lookahead, where the algorithm has knowledge of all the tasks in the queue but still has to process them in the order they arrived. We discuss some of the results for reordering buffers for different scheduling problems.

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“…In addition, (10) implies that x k + y k = x k+1 for k < m, and x m + y m = m i=1 s i α i−1 = S/R. Using also the fact that y 1 = s m = x 2 , the left-hand side of the linear combination given by (9) is equal to q 1 (y 1 + y 2 + · · · + y m ) + q 2 (x 2 + y 2 + · · · + y m ) + q 3 (x 3 + y 3 + · · · + y m ) + · · · + q m (x m + y m ) = (q 1 + · · · + q m ) S R .…”

Section: Special Casesmentioning

confidence: 99%

“…For non-preemptive scheduling, tight results are known only for two related or three identical machines. Even for deterministic algorithms on m identical machines, there still remains a small gap between the lower bound of 1.880 [18] and the upper bound of 1.923 [10], and a much larger gap for uniformly related machines, where the current bounds are 2.438 and 5.828 [2].…”

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confidence: 99%

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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On-line scheduling revisited

Cited by 133 publications

References 13 publications

An efficient algorithm for semi-online multiprocessor scheduling with given total processing time

An efficient algorithm for semi-online multiprocessor scheduling with given total processing time

An overview of some results for reordering buffers

Preemptive Online Scheduling: Optimal Algorithms for All Speeds

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