Scheduling on same-speed processors with at most one downtime on each machine

Grigoriu, Liliana; Friesen, Donald K.

doi:10.1016/j.disopt.2010.04.003

Cited by 5 publications

(7 citation statements)

References 15 publications

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“…For example, an ordering where all time slots before the downtimes are considered first and all time slots after the downtimes are considered afterwards can be used. This strategy is similar to that of the LPT-based algorithm from [13]. While attempting to prove upper bounds for schedule durations of algorithms, it may happen that no set of weights can be used to cover all cases when proving certain properties.…”

Section: Resultsmentioning

confidence: 95%

“…In the proof of the bound's tightness from [12], the fact that there are multiple downtimes is not used, and so the bound is tight in the class of polynomial algorithms assuming that P ̸ = NP even if there can only be at most one downtime on each machine [13]. The case of uniform processors is more general than the case of same-speed processors, and so, assuming that P ̸ = NP, no polynomial algorithm can achieve a bound that is better than 3/2 for the problem we consider.…”

Section: Bound Tightnessmentioning

confidence: 96%

“…Scheduling on same-speed processors with at most one downtime on each machine was considered in [13], where an LPTbased algorithm which finishes within 3/2 times the optimal (smallest possible) maximum completion time (of a schedule) or 3/2 times the latest end of a downtime was given. There it is also shown that it is NP-hard to obtain a better bound, which follows from a proof presented in [12], which was made for the case when there may be multiple fixed jobs on one machine.…”

Section: Introductionmentioning

confidence: 99%

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Scheduling on uniform processors with at most one downtime on each machine

Grigoriu

Friesen

2015

Discrete Optimization

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a b s t r a c tWe consider the problem of scheduling a given set of tasks on uniform processors with predefined periods of unavailability, with the aim of minimizing the maximum completion time.We give a simple polynomial MULTIFIT-based algorithm, the schedules of which finish within 1.5 times the maximum between the latest end of a downtime and the end of the optimal schedule, when there is at most one downtime on each machine. Even when all processors have the same processing speed, it is NP-hard to obtain schedules that obey better bounds for this problem.

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Section: Resultsmentioning

confidence: 95%

Section: Bound Tightnessmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

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Scheduling on uniform processors with at most one downtime on each machine

Grigoriu

Friesen

2015

Discrete Optimization

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“…We discuss this in more detail in Section 4.2. To obtain approximation results for scheduling with unavailability periods in this context, assumptions about the downtimes were made such as the assumption that only a fraction of the processors can be unavailable at the same time [1,2], or by comparing the generated schedule to the latest among the end of an optimal schedule or the latest end of a downtime, thus essentially considering scheduling with fixed jobs [3,4].…”

Section: Introductionmentioning

confidence: 99%

“…Polynomial-time approximation algorithms for this problem that achieve the worst-case approximation bound of 1.5 were given for the general problem in [6]. For the case where there is at most one fixed job on each machine, significanlty simpler heuristics with lower time complexities resembling the largest processing time algorithm (LPT) [7] for identical processors and the MULTIFIT algorithm [8] for uniform processors also achieve this bound [3,4].…”

Section: Introductionmentioning

confidence: 99%

Approximation for Scheduling on Parallel Machines with Fixed Jobs or Unavailability Periods

Grigoriu¹

2020

Scheduling Problems - New Applications and Trends

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We survey results that address the problem of non-preemptive scheduling on parallel machines with fixed jobs or unavailability periods with the purpose of minimizing the maximum completion time. We consider both identical and uniform processors, and also address the special case of scheduling on nonsimultaneous parallel machines, which may start processing at different times. The discussed results include polynomial-time approximation algorithms that achieve the best possible worst-case approximation bound of 1.5 in the class of polynomial algorithms unless P = NP for scheduling on identical processors with at most one fixed job on each machine and on uniform machines with at most one fixed job on each machine. The presented heuristics have similarities with the LPT algorithm or the MULTIFIT algorithm and they are fast and easy to implement. For scheduling on nonsimultaneous machines, experiments suggest that they would perform well in practice. We also include references to the relevant work in this area that contains more complex algorithms. We then discuss the main methods of argument used in the approximation bound proofs for the simple heuristics, and comment upon current challenges in this area by describing aspects of related practical problems from the automotive industry.

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Multiprocessor Scheduling with Availability Constraints

Grigoriu

2013

Operations Research Proceedings

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We consider the problem of scheduling a given set of tasks on multiple processors with predefined periods of unavailability, with the aim of minimizing the maximum completion time. Since this problem is strongly NP-hard, polynomial approximation algorithms are being studied for its solution. Among these, the best known are LPT (largest processing time first) and Multifit with their variants. We give a Multifit-based algorithm, FFDL Multifit, which has an optimal worstcase performance in the class of polynomial algorithms for same-speed processors with at most two downtimes on each machine, and for uniform processors with at most one downtime on each machine, assuming that P = N P. Our algorithm finishes within 3/2 the maximum between the end of the last downtime and the end of the 5 Example showing that the 3/2 bound is asymptotically tight. .. .. 22 CHAPTER I

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Scheduling on same-speed processors with at most one downtime on each machine

Cited by 5 publications

References 15 publications

Scheduling on uniform processors with at most one downtime on each machine

Scheduling on uniform processors with at most one downtime on each machine

Approximation for Scheduling on Parallel Machines with Fixed Jobs or Unavailability Periods

Multiprocessor Scheduling with Availability Constraints

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