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A Log-Linear \((2 +5/6)\)-Approximation Algorithm for Parallel Machine Scheduling with a Single Orthogonal Resource

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Euro-Par 2021: Parallel Processing (Euro-Par 2021)

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Abstract

As the gap between compute and I/O performance tends to grow, modern High-Performance Computing (HPC) architectures include a new resource type: an intermediate persistent fast memory layer, called burst buffers. This is just one of many kinds of renewable resources which are orthogonal to the processors themselves, such as network bandwidth or software licenses. Ignoring orthogonal resources while making scheduling decisions just for processors may lead to unplanned delays of jobs of which resource requirements cannot be immediately satisfied. We focus on a classic problem of makespan minimization for parallel-machine scheduling of independent sequential jobs with additional requirements on the amount of a single renewable orthogonal resource. We present an easily-implementable log-linear algorithm that we prove is \(2\frac{5}{6}\)-approximation. In simulation experiments, we compare our algorithm to standard greedy list-scheduling heuristics and show that, compared to LPT, resource-based algorithms generate significantly shorter schedules.

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References

  1. Blazewicz, J.: Complexity of computer scheduling algorithms under resource constraints. In: Proceedings of the First Meeting AFCET-SMF on Applied Mathematics, pp. 169–178 (1978)

    Google Scholar 

  2. Blazewicz, J., Cellary, W., Slowinski, R., Weglarz, J.: Scheduling under resource constraints-deterministic models. JC Baltzer AG (1986)

    Google Scholar 

  3. Blazewicz, J., Lenstra, J., Kan, A.R.: Scheduling subject to resource constraints: classification and complexity. Discret. Appl. Math. 5(1), 11–24 (1983). https://doi.org/10.1016/0166-218X(83)90012-4

    Article  MathSciNet  MATH  Google Scholar 

  4. Edis, E.B., Oguz, C., Ozkarahan, I.: Parallel machine scheduling with additional resources: notation, classification, models and solution methods. Eur. J. Oper. Res. 230(3), 449–463 (2013). https://doi.org/10.1016/j.ejor.2013.02.042

    Article  MathSciNet  MATH  Google Scholar 

  5. Feitelson, D.G.: Job scheduling in multiprogrammed parallel systems (1997)

    Google Scholar 

  6. Garey, M., Graham, R.: Bounds for multiprocessor scheduling with resource constraints. SIAM J. Comput. 4, 187–200 (1975). https://doi.org/10.1137/0204015

    Article  MathSciNet  MATH  Google Scholar 

  7. Garey, M., Johnson, D.: Strong NP-completeness results: motivation, examples, and implications. J. Assoc. Comput. Mach. 25(3), 499–508 (1978). https://doi.org/10.1145/322077.322090

    Article  MathSciNet  MATH  Google Scholar 

  8. Graham, R.: Bounds for certain multiprocessing anomalies. Bell Syst. Tech. J. 45(9), 1563–1581 (1966). https://doi.org/10.1002/j.1538-7305.1966.tb01709.x

    Article  MATH  Google Scholar 

  9. Graham, R.: Bounds on multiprocessing timing anomalies. SIAM J. Appl. Math. 17(2), 416–429 (1969)

    Article  MathSciNet  Google Scholar 

  10. Graham, R., Lawler, E., Lenstra, J., Kan, A.R.: Optimization and approximation in deterministic sequencing and scheduling: a survey. In: Hammer, P., Johnson, E., Korte, B. (eds.) Discrete Optimization II, Annals of Discrete Mathematics, vol. 5, pp. 287–326. Elsevier (1979). https://doi.org/10.1016/S0167-5060(08)70356-X

  11. Hochbaum, D.S., Shmoys, D.B.: Using dual approximation algorithms for scheduling problems theoretical and practical results. J. ACM 34(1), 144–162 (1987). https://doi.org/10.1145/7531.7535

    Article  MathSciNet  Google Scholar 

  12. Jansen, K.: An EPTAS for scheduling jobs on uniform processors: using an MILP relaxation with a constant number of integral variables. SIAM J. Discrete Math. 24(2), 457–485 (2010). https://doi.org/10.1137/090749451

    Article  MathSciNet  MATH  Google Scholar 

  13. Jansen, K., Klein, K.M., Verschae, J.: Closing the gap for makespan scheduling via sparsification techniques. Math. Oper. Res. 45(4), 1371–1392 (2020). https://doi.org/10.1287/moor.2019.1036

    Article  MathSciNet  MATH  Google Scholar 

  14. Jansen, K., Maack, M., Rau, M.: Approximation schemes for machine scheduling with resource (in-)dependent processing times 15(3) (2019). https://doi.org/10.1145/3302250

  15. Kellerer, H.: An approximation algorithm for identical parallel machine scheduling with resource dependent processing times. Oper. Res. Lett. 36(2), 157–159 (2008). https://doi.org/10.1016/j.orl.2007.08.001

    Article  MathSciNet  MATH  Google Scholar 

  16. Klusáček, D., Tóth, Š, Podolníková, G.: Real-life experience with major reconfiguration of job scheduling system. In: Desai, N., Cirne, W. (eds.) JSSPP 2015-2016. LNCS, vol. 10353, pp. 83–101. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-61756-5_5

    Chapter  Google Scholar 

  17. Kovalyov, M.Y., Shafransky, Y.M.: Uniform machine scheduling of unit-time jobs subject to resource constraints. Discrete Appl. Math. 84(1), 253–257 (1998). https://doi.org/10.1016/S0166-218X(97)00138-8

    Article  MathSciNet  MATH  Google Scholar 

  18. Krause, K.L., Shen, V.Y., Schwetman, H.D.: A task-scheduling algorithm for a multiprogramming computer system. SIGOPS Oper. Syst. Rev. 7(4), 112–118 (1973). https://doi.org/10.1145/957195.808058

    Article  Google Scholar 

  19. MetaCentrum Czech National Grid: MetaCentrum workload logs (2015). https://www.cs.huji.ac.il/labs/parallel/workload/l_metacentrum2/index.html

  20. Naruszko, A., Przybylski, B., Rzadca, K.: Artifact and instructions to generate experimental results for the Euro-Par 2021 paper: A log-linear \((2+5/6)\)-approximation algorithm for parallel machine scheduling with a single orthogonal resource, August 2021. https://doi.org/10.6084/m9.figshare.14748267

  21. Niemeier, M., Wiese, A.: Scheduling with an orthogonal resource constraint. In: Erlebach, T., Persiano, G. (eds.) WAOA 2012. LNCS, vol. 7846, pp. 242–256. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38016-7_20

    Chapter  Google Scholar 

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Acknowledgements and Data Availability Statement

This research is supported by a Polish National Science Center grant Opus (UMO-2017/25/B/ST6/00116). The authors would like to thank anonymous reviewers for their in-depth comments that helped to significantly improve the quality of the paper.

The datasets and code generated during and/or analyzed during the current study are available in the Figshare repository: https://doi.org/10.6084/m9.figshare.14748267 [20].

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Authors and Affiliations

  1. Institute of Informatics, University of Warsaw, Warsaw, Poland

    Adrian Naruszko, Bartłomiej Przybylski & Krzysztof Rządca

Authors
  1. Adrian Naruszko
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  2. Bartłomiej Przybylski
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  3. Krzysztof Rządca
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Corresponding author

Correspondence to Bartłomiej Przybylski .

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Editors and Affiliations

  1. Universidade de Lisboa, Lisbon, Portugal

    Leonel Sousa

  2. Universidade de Lisboa, Lisbon, Portugal

    Nuno Roma

  3. Universidade de Lisboa, Lisbon, Portugal

    Pedro Tomás

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Naruszko, A., Przybylski, B., Rządca, K. (2021). A Log-Linear \((2 +5/6)\)-Approximation Algorithm for Parallel Machine Scheduling with a Single Orthogonal Resource. In: Sousa, L., Roma, N., Tomás, P. (eds) Euro-Par 2021: Parallel Processing. Euro-Par 2021. Lecture Notes in Computer Science(), vol 12820. Springer, Cham. https://doi.org/10.1007/978-3-030-85665-6_10

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  • DOI: https://doi.org/10.1007/978-3-030-85665-6_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-85664-9

  • Online ISBN: 978-3-030-85665-6

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