On the Approximability of Multiprocessor Task Scheduling Problems

Miranda, Antônio Carlos de; Torres, Luz; Chen, Jianer

doi:10.1007/3-540-36136-7_36

Cited by 4 publications

(1 citation statement)

References 20 publications

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“…If the number of computing nodes is fixed, then a Polynomial Time Approximation Scheme (PTAS) for P |set j |C max has been presented in [10]. However, if m is part of the instance, there is no polynomial time approximation algorithm with ratio smaller that n δ , for any δ > 0, as shown in [11]. Although this negative result for the more general P |set j |C max , a 6-approximation algorithm has been presented in [3] for scheduling rigid jobs under contiguity and locality constraints.…”

Section: B Related Workmentioning

confidence: 99%

Scheduling Malleable Jobs Under Topological Constraints

Bampis¹,

Dogeas²,

Kononov

et al. 2020

2020 IEEE International Parallel and Distributed Processing Symposium (IPDPS)

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Bleuse et al. (EuroPar 2018) introduced a general model for interference-aware scheduling in large scale parallel platforms. They considered two different types of communications: the flows induced by data exchanges during computations and the flows related to Input/Output operations. Rather than taking into account these communications explicitly, they restrict the possible allocations of a job by external topological constraints. In their work, jobs are considered to be rigid: a job requires a specific number of machines in order to be executed. Here, we first adopt the same framework for the platform and the aforementioned topological constraints. We show that there is no polynomial time approximation algorithm under the rigid setting with ratio smaller than 3/2, unless P = NP. Then, we focus on the malleable setting. We show that in the proportional-malleable setting, where the work of every job remains constant independently of the number of machines on which it is executed, the scheduling problem remains NPhard even in the uniform case, where the maximum number of machines is the same for all the jobs. Then, we propose a 2-approximation algorithm for this case. Furthermore, we present an approximation algorithm solving the more general case where the maximum number of machines is job-dependent and the work of the jobs is increasing with respect to the number of used machines, due to the communication overhead.

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Section: B Related Workmentioning

confidence: 99%

Scheduling Malleable Jobs Under Topological Constraints

Bampis¹,

Dogeas²,

Kononov

et al. 2020

2020 IEEE International Parallel and Distributed Processing Symposium (IPDPS)

View full text Add to dashboard Cite

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Distance‐adaptive routing and spectrum assignment in rings

2016

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Distance adaptive spectrum allocation exploits the tradeoff between spectrum width and reach to improve resource utilisation by tailoring the modulation format to the level of impairments along the path. The authors first show that the distance-adaptive routing and spectrum assignment (DA-RSA) problem is a special case of a multiprocessor scheduling problem. The authors then develop a suite of efficient and effective DA-RSA algorithms for ring networks, that build upon list scheduling concepts. This work explores the tradeoffs involved in DA-RSA algorithm design, and opens up new research directions that may leverage the vast literature in scheduling theory. † Spectrum contiguity constraint: Each demand is assigned contiguous spectrum on all the edges of each route. † Spectrum continuity constraint: Each demand is assigned the same spectrum along all the edges of its route. † Non-overlapping spectrum constraint: Demands that share an edge are assigned non-overlapping parts of the available spectrum.

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