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Scheduling Parallel Jobs Online with Convex and Concave Parallelizability

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Abstract

Online scheduling of parallelizable jobs has received a significant amount of attention recently. Scalable algorithms are known—that is, algorithms that are (1 + ε)-speed O(1)-competitive for any fixed ε>0. Previous research has focused on the case where each job’s parallelizability can be expressed as a concave speedup curve. However, there are cases where a job’s speedup curve can be convex. Considering convex speedup curves has received attention in the offline setting, but, to date, there are no positive results in the online model. In this work, we consider scheduling jobs with convex or concave speedup curves for the first time in the online setting. We give a new algorithm that is (1 + ε)-speed O(1)-competitive. There are strong lower bounds on the competitive ratio if the algorithm is not given resource augmentation over the adversary, and thus this is essentially the best positive result one can show for this setting.

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Notes

  1. Specifically, [17] gives an \({\Omega }(\log n/m)\) lower bound.

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Acknowledgments

We would like to thank Michael Bender for helpful discussions, and Bertrand Simon for informing us of reference [2]. We would also like to thank the anonymous reviewers for their helpful comments.

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Authors and Affiliations

  1. Google Inc., 1600 Ampitheatre Parkway, Mountain View, CA, 94043, USA

    Roozbeh Ebrahimi

  2. Stony Brook University, Stony Brook, NY, 11794, USA

    Samuel McCauley

  3. Washington University in St. Louis, St. Louis, MO, 63130, USA

    Benjamin Moseley

Authors
  1. Roozbeh Ebrahimi
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  2. Samuel McCauley
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  3. Benjamin Moseley
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Corresponding author

Correspondence to Samuel McCauley.

Additional information

This research was supported in part by NSF grants CNS 1408695, CCF 1439084, IIS 1247726, IIS 1251137, and CCF 1217708. Samuel McCauley was also supported in part by Sandia National Laboratories.

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Ebrahimi, R., McCauley, S. & Moseley, B. Scheduling Parallel Jobs Online with Convex and Concave Parallelizability. Theory Comput Syst 62, 304–318 (2018). https://doi.org/10.1007/s00224-016-9722-0

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  • DOI: https://doi.org/10.1007/s00224-016-9722-0

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