A Survey on Approximation Algorithms for Scheduling with Machine Unavailability

Diedrich, Florian; Jansen, Klaus; Schwarz, Ulrich M.; Trystram, Denis

doi:10.1007/978-3-642-02094-0_3

Cited by 13 publications

(8 citation statements)

References 47 publications

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“…which is true by (7). That completes the proof of the fact that [max{L 1 , L 2 }, min{U 1 , U 2 , U 3 }] = ∅ and therefore the proof of our upper bound.…”

Section: Appendicessupporting

confidence: 65%

“…A lot less research addresses uncertainty about the machine environment, particularly, where the processing speeds of machines change in an unforeseeable manner. The majority of such research focuses on the special case of scheduling with unknown non-availability periods, that is, machines break down temporarily [2,7] or permanently [16]. Arbitrarily changing machine speeds have been considered for scheduling on a single machine [9].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Speed-Robust Scheduling -- Sand, Bricks, and Rocks

Éberlé¹,

Hoeksma²,

Megow³

et al. 2020

Preprint

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The speed-robust scheduling problem is a two-stage problem where, given m machines, jobs must be grouped into at most m bags while the processing speeds of the machines are unknown. After the speeds are revealed, the grouped jobs must be assigned to the machines without being separated. To evaluate the performance of algorithms, we determine upper bounds on the worst-case ratio of the algorithm's makespan and the optimal makespan given full information. We refer to this ratio as the robustness factor. We give an algorithm with a robustness factor 2 − 1/m for the most general setting and improve this to 1.8 for equal-size jobs. For the special case of infinitesimal jobs, we give an algorithm with an optimal robustness factor equal to e/(e − 1) ≈ 1.58. The particular machine environment in which all machines have either speed 0 or 1 was studied before by Stein and Zhong (SODA 2019). For this setting, we provide an algorithm for scheduling infinitesimal jobs with an optimal robustness factor of (1 + √ 2)/2 ≈ 1.207. It lays the foundation for an algorithm matching the lower bound of 4/3 for equal-size jobs.

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“…which is true by (7). That completes the proof of the fact that [max{L 1 , L 2 }, min{U 1 , U 2 , U 3 }] = ∅ and therefore the proof of our upper bound.…”

Section: Appendicessupporting

confidence: 65%

Section: Introductionmentioning

confidence: 99%

Speed-Robust Scheduling -- Sand, Bricks, and Rocks

Éberlé¹,

Hoeksma²,

Megow³

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…[12,20,21,26]. Despite a history of more than 30 years, only recently the first constant approximation for min w j C j was derived by Epstein et al [14].…”

Section: Previous Workmentioning

confidence: 99%

Dual Techniques for Scheduling on a Machine with Varying Speed

Megow

Verschae

2013

Automata, Languages, and Programming

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We study scheduling problems on a machine with varying speed. Assuming a known speed function we ask for a cost-efficient scheduling solution. Our main result is a PTAS for minimizing the total weighted completion time in this setting. This also implies a PTAS for the closely related problem of scheduling to minimize generalized global cost functions. The key to our results is a re-interpretation of the problem within the wellknown two-dimensional Gantt chart: instead of the standard approach of scheduling in the time-dimension, we construct scheduling solutions in the weight-dimension.We also consider a dynamic problem variant in which deciding upon the speed is part of the scheduling problem and we are interested in the tradeoff between scheduling cost and speed-scaling cost, which is typically the energy consumption. We observe that the optimal order is independent of the energy consumption and that the problem can be reduced to the setting where the speed of the machine is fixed, and thus admits a PTAS. Furthermore, we provide an FPTAS for the NP-hard problem variant in which the machine can run only on a fixed number of discrete speeds. Finally, we show how our results can be used to obtain a (2+ε)-approximation for scheduling preemptive jobs with release dates on multiple identical parallel machines.

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“…Scheduling with limited machine availability, and more generally with arbitrarily varying machine capacity or speed, is a subfield of machine scheduling that has been studied for more than twenty years; see, e.g., the surveys [9,28,32,37]. Different objective functions, stochastic fluctuations, as well as the offline problem with known machine availability periods have been investigated.…”

Section: Introductionmentioning

confidence: 99%

Universal Sequencing on an Unreliable Machine

Mestre

Megow

2015

Encyclopedia of Algorithms

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We consider scheduling on an unreliable machine that may experience unexpected changes in processing speed or even full breakdowns. We aim for a universal solution that performs well without adaptation for any possible machine behavior. Our objective is to minimize w j f (C j ) for any non-decreasing, nonnegative, differentiable cost function f (C j ). We design a deterministic algorithm that finds a universal scheduling sequence with a solution value within 4 times the value of an optimal clairvoyant algorithm that knows the machine behavior in advance. A randomized version of this algorithm attains in expectation a ratio of e. We also show that both results are best possible among all universal solutions. Our algorithms can be adapted to run in polynomial time with slightly increased cost.When jobs have individual release dates, the situation changes drastically. Even if all weights are equal, there are instances for which any universal solution is a factor of Ω(log n/ log log n) worse than an optimal sequence for any unbounded cost function. Motivated by this hardness, we study the special case when the processing time of each job is proportional to its weight. We present a non-trivial algorithm with a small constant performance guarantee.

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A Survey on Approximation Algorithms for Scheduling with Machine Unavailability

Cited by 13 publications

References 47 publications

Speed-Robust Scheduling -- Sand, Bricks, and Rocks

Speed-Robust Scheduling -- Sand, Bricks, and Rocks

Dual Techniques for Scheduling on a Machine with Varying Speed

Universal Sequencing on an Unreliable Machine

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