Minimizing Weighted Mean Completion Time for Malleable Tasks Scheduling

Beaumont, Olivier; Eyraud-Dubois, Lionel; Marchal, Loris

doi:10.1109/ipdps.2012.34

Cited by 9 publications

(7 citation statements)

References 16 publications

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“…Beaumont et el. [15] analyzed a natural extension of the WRR algorithm [34] to identical parallel machines and prove the same competitive ratio of 2 for non-clairvoyant P|𝑝𝑚𝑡𝑛| 𝑤 𝑗 𝐶 𝑗 . Like WRR, their algorithm Weighted Dynamic EQuipartition (WDEQ) assigns processing rates to jobs proportional to their weights making sure that no job receives a higher rate than executable on one machine simultaneously.…”

Section: Identical Parallel Machinesmentioning

confidence: 92%

“…Thus, [𝑟 𝑗 , 𝐶 𝑗 ] is not longer than [0, 𝐶 𝑗 ], giving 𝐶 𝑗 ≤ 𝑟 𝑗 + 𝐶 𝑗 . The facts that 𝑗 𝑤 𝑗 𝑟 𝑗 is a lower bound on the optimal objective value with release dates and 𝑗 𝑤 𝑗 𝐶 𝑗 is at most twice the optimal objective value without release dates [15] imply that WDEQ has a competitive ratio of at most 3 for 𝑃 |𝑟 𝑗 , 𝑝𝑚𝑡𝑛| 𝑤 𝑗 𝐶 𝐽 .…”

Section: Identical Parallel Machinesmentioning

confidence: 99%

“…Non-clairvoyant scheduling requires to schedule jobs without knowing their processing requirements a priori. This is a fundamental problem and has been studied extensively in many variations [46,34,15,29,28].…”

Section: Introductionmentioning

confidence: 99%

“…The most prominent strategy is the Round-Robin (RR) algorithm, which assigns equal rates to all alive jobs and is 2-competitive for 1|𝑝𝑚𝑡𝑛| 𝐶 𝑗 , which is best possible [46]. The same guarantee is possible using a natural generalization of RR to weighted jobs [34] and/or to identical machines [15,46]. Scheduling on unrelated machines is much Our contribution In this work, we contribute to non-clairvoyant scheduling with predictions in two ways: (i) we propose a new prediction model with a new error de nition, as an alternative to length predictions studied so far, and (ii) we revisit the classical idea of time sharing and develop a general framework for designing learning-augmented scheduling algorithms for more general settings, beyond the simple single-machine setting.…”

Section: Introductionmentioning

confidence: 99%

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Permutation Predictions for Non-Clairvoyant Scheduling

Alexander¹,

Megow²

2022

Preprint

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In non-clairvoyant scheduling, the task is to nd an online strategy for scheduling jobs with a priori unknown processing requirements with the objective to minimize the total (weighted) completion time. We revisit this well-studied problem in a recently popular learning-augmented setting that integrates (untrusted) predictions in online algorithm design. While previous works used predictions on processing requirements, we propose a new prediction model, which provides a relative order of jobs which could be seen as predicting algorithmic actions rather than parts of the unknown input. We show that these predictions have desired properties, admit a natural error measure as well as algorithms with strong performance guarantees and that they are learnable in both, theory and practice. We generalize the algorithmic framework proposed in the seminal paper by Kumar et al. (NeurIPS'18) and present the rst learning-augmented scheduling results for weighted jobs and unrelated machines. We demonstrate in empirical experiments the practicability and superior performance compared to the previously suggested single-machine algorithms.

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Section: Identical Parallel Machinesmentioning

confidence: 92%

Section: Identical Parallel Machinesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Permutation Predictions for Non-Clairvoyant Scheduling

Alexander¹,

Megow²

2022

Preprint

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“…This is for instance the case with the model studied by Prasanna and Musicus [21] where the processing time p i of task i is p i (k) = pi k α with α being a task-independent constant between 0 and 1 and k the number of allotted processors [21], [22]. Another instance is the simple single-threshold model, that is, the linear model [9], [10], [23], [24], [25]: p i (k) = pi k . Havill and Mao [26] added to that model an overhead affine in the number of processors used:…”

Section: Models Of Parallel Tasksmentioning

confidence: 99%

Malleable Task-Graph Scheduling with a Practical Speed-Up Model

Marchal

Simon

Sinnen

et al. 2018

IEEE Trans. Parallel Distrib. Syst.

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Scientific workloads are often described by Directed Acyclic task Graphs. Indeed, DAGs represent both a theoretical model and the structure employed by dynamic runtime schedulers to handle HPC applications. A natural problem is then to compute a makespan-minimizing schedule of a given graph. In this paper, we are motivated by task graphs arising from multifrontal factorizations of sparse matrices and therefore work under the following practical model. Tasks are malleable (i.e., a single task can be allotted a time-varying number of processors) and their speedup behaves perfectly up to a first threshold, then speedup increases linearly, but not perfectly, up to a second threshold where the speedup levels off and remains constant. After proving the NP-hardness of minimizing the makespan of DAGs under this model, we study several heuristics. We propose model-optimized variants for PROPSCHEDULING, widely used in linear algebra application scheduling, and FLOWFLEX. GREEDYFILLING is proposed, a novel heuristic designed for our speedup model, and we demonstrate that PROPSCHEDULING and GREEDYFILLING are 2-approximation algorithms. In the evaluation, employing synthetic data sets and task graphs arising from multifrontal factorization, the proposed optimized variants and GREEDYFILLING significantly outperform the traditional algorithms, whereby GREEDYFILLING demonstrates a particular strength for balanced graphs.

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