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Non-Clairvoyant Makespan Minimization Scheduling with Predictions

Authors Evripidis Bampis , Alexander Kononov , Giorgio Lucarelli , Fanny Pascual

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Author Details

Evripidis Bampis
  • Sorbonne Université, CNRS, LIP6, F-75005 Paris, France
Alexander Kononov
  • Sobolev Institute of Mathematics, Novosibirsk, Russia
  • Novosibirsk State University, Russia
Giorgio Lucarelli
  • LCOMS, University of Lorraine, Metz, France
Fanny Pascual
  • Sorbonne Université, CNRS, LIP6, F-75005 Paris, France

Funding

  • Bampis, Evripidis: This work was partially supported by the French National Research Agency (Algoridam ANR-19-CE48-0016).
  • Kononov, Alexander: This research was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project FWNF-2022-0019).

Cite AsGet BibTex

Evripidis Bampis, Alexander Kononov, Giorgio Lucarelli, and Fanny Pascual. Non-Clairvoyant Makespan Minimization Scheduling with Predictions. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 9:1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ISAAC.2023.9

Abstract

We revisit the classical non-clairvoyant problem of scheduling a set of n jobs on a set of m parallel identical machines where the processing time of a job is not known until the job finishes. Our objective is the minimization of the makespan, i.e., the date at which the last job terminates its execution. We adopt the framework of learning-augmented algorithms and we study the question of whether (possibly erroneous) predictions may help design algorithms with a competitive ratio which is good when the prediction is accurate (consistency), deteriorates gradually with respect to the prediction error (smoothness), and not too bad and bounded when the prediction is arbitrarily bad (robustness). We first consider the non-preemptive case and we devise lower bounds, as a function of the error of the prediction, for any deterministic learning-augmented algorithm. Then we analyze a variant of Longest Processing Time first (LPT) algorithm (with and without release dates) and we prove that it is consistent, smooth, and robust. Furthermore, we study the preemptive case and we provide lower bounds for any deterministic algorithm with predictions as a function of the prediction error. Finally, we introduce a variant of the classical Round Robin algorithm (RR), the Predicted Proportional Round Robin algorithm (PPRR), which we prove to be consistent, smooth and robust.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • scheduling
  • online
  • learning-augmented algorithm

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References

  1. URL: https://algorithms-with-predictions.github.io.
  2. Maryam Amiri and Leili Mohammad Khanli. Survey on prediction models of applications for resources provisioning in cloud. J. Netw. Comput. Appl., 82:93-113, 2017. Google Scholar
  3. Spyros Angelopoulos, Christoph Dürr, Shendan Jin, Shahin Kamali, and Marc P. Renault. Online computation with untrusted advice. In ITCS, 2020. Google Scholar
  4. Antonios Antoniadis, Christian Coester, Marek Eliás, Adam Polak, and Bertrand Simon. Online metric algorithms with untrusted predictions. In ICML, 2020. Google Scholar
  5. Antonios Antoniadis, Peyman Jabbarzade Ganje, and Golnoosh Shahkarami. A novel prediction setup for online speed-scaling. In Artur Czumaj and Qin Xin, editors, 18th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2022, June 27-29, 2022, Tórshavn, Faroe Islands, volume 227 of LIPIcs, pages 9:1-9:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. Google Scholar
  6. Étienne Bamas, Andreas Maggiori, Lars Rohwedder, and Ola Svensson. Learning augmented energy minimization via speed scaling. In NeurIPS, 2020. Google Scholar
  7. Evripidis Bampis, Konstantinos Dogeas, Alexander V. Kononov, Giorgio Lucarelli, and Fanny Pascual. Scheduling with untrusted predictions. In Luc De Raedt, editor, Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence, IJCAI 2022, Vienna, Austria, 23-29 July 2022, pages 4581-4587. ijcai.org, 2022. Google Scholar
  8. Evripidis Bampis, Bruno Escoffier, Themis Gouleakis, Niklas Hahn, Kostas Lakis, Golnoosh Shahkarami, and Michalis Xefteris. Learning-augmented online TSP on rings, trees, flowers and (almost) everywhere else. In Inge Li Gørtz, Martin Farach-Colton, Simon J. Puglisi, and Grzegorz Herman, editors, 31st Annual European Symposium on Algorithms, ESA 2023, September 4-6, 2023, Amsterdam, The Netherlands, volume 274 of LIPIcs, pages 12:1-12:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. URL: https://doi.org/10.4230/LIPIcs.ESA.2023.12.
  9. Evripidis Bampis, Bruno Escoffier, and Michalis Xefteris. Canadian traveller problem with predictions. In Parinya Chalermsook and Bundit Laekhanukit, editors, Approximation and Online Algorithms, pages 116-133. Springer International Publishing, 2022. Google Scholar
  10. Allan Borodin and Ran El-Yaniv. Online computation and competitive analysis. Cambridge University Press, 1998. Google Scholar
  11. Bo Chen and Arjen P.A. Vestjens. Scheduling on identical machines: How good is lpt in an on-line setting? Operations Research Letters, 21(4):165-169, 1997. Google Scholar
  12. Franziska Eberle, Alexander Lindermayr, Nicole Megow, Lukas Nölke, and Jens Schlöter. Robustification of online graph exploration methods. Proceedings of the AAAI Conference on Artificial Intelligence, 36(9):9732-9740, June 2022. Google Scholar
  13. Donald K. Friesen. Tighter bounds for the multifit processor scheduling algorithm. SIAM J. Comput., 13(1):170-181, 1984. Google Scholar
  14. Donald K. Friesen and Michael A. Langston. Evaluation of a multifit-based scheduling algorithm. J. Algorithms, 7(1):35-59, 1986. Google Scholar
  15. Sreenivas Gollapudi and Debmalya Panigrahi. Online algorithms for rent-or-buy with expert advice. In ICML, 2019. Google Scholar
  16. Themis Gouleakis, Konstantinos Lakis, and Golnoosh Shahkarami. Learning-Augmented Algorithms for Online TSP on the Line. To appear in AAAI, 2023. CoRR abs/2206.00655. Google Scholar
  17. Ronald L. Graham. Bounds for certain multiprocessing anomalies. Bell System Technical J., 45(9):1563-1581, 1966. Google Scholar
  18. Ronald L. Graham. Bounds on multiprocessing timing anomalies. SIAM Journal of Applied Mathematics, 17(2):416-429, 1969. Google Scholar
  19. Dorit S. Hochbaum. Approximation Algorithms for NP-hard Problems. PWS Publishing, 1997. Google Scholar
  20. Dorit S. Hochbaum and David B. Shmoys. A polynomial approximation scheme for scheduling on uniform processors: Using the dual approximation approach. SIAM J. Comput., 17(3):539-551, 1988. Google Scholar
  21. Sungjin Im, Ravi Kumar, Mahshid Montazer Qaem, and Manish Purohit. Non-clairvoyant scheduling with predictions. In SPAA, pages 285-294. ACM, 2021. Google Scholar
  22. Edward G. Coffman Jr., M. R. Garey, and David S. Johnson. An application of bin-packing to multiprocessor scheduling. SIAM J. Comput., 7(1):1-17, 1978. Google Scholar
  23. Murali Kodialam and T. V. Lakshman. Prediction augmented segment routing. In 2021 IEEE 22nd International Conference on High Performance Switching and Routing (HPSR), pages 1-6, 2021. Google Scholar
  24. M.A. Langston. A. Processors cheduling with improved heuristic algorithms. Doctoral dissertation,. PhD thesis, Texas A&M Univ., College Station, Tex., 1981. Google Scholar
  25. Silvio Lattanzi, Thomas Lavastida, Benjamin Moseley, and Sergei Vassilvitskii. Online scheduling via learned weights. In SODA, pages 1859-1877. SIAM, 2020. Google Scholar
  26. Thomas Lavastida, Benjamin Moseley, R. Ravi, and Chenyang Xu. Learnable and instance-robust predictions for online matching, flows and load balancing. In Petra Mutzel, Rasmus Pagh, and Grzegorz Herman, editors, 29th Annual European Symposium on Algorithms, ESA 2021, September 6-8, 2021, Lisbon, Portugal (Virtual Conference), volume 204 of LIPIcs, pages 59:1-59:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. Google Scholar
  27. Joseph Leung, Laurie Kelly, and James H. Anderson. Handbook of Scheduling: Algorithms, Models, and Performance Analysis. CRC Press, Inc., USA, 2004. Google Scholar
  28. Alexander Lindermayr and Nicole Megow. Permutation predictions for non-clairvoyant scheduling. In Kunal Agrawal and I-Ting Angelina Lee, editors, SPAA '22: 34th ACM Symposium on Parallelism in Algorithms and Architectures, Philadelphia, PA, USA, July 11 - 14, 2022, pages 357-368. ACM, 2022. Google Scholar
  29. Thodoris Lykouris and Sergei Vassilvitskii. Competitive caching with machine learned advice. In ICML, volume 80 of Proceedings of Machine Learning Research, pages 3302-3311. PMLR, 2018. Google Scholar
  30. Robert McNaughton. Scheduling with deadlines and loss functions. Management Science, 6(1):1-12, 1959. Google Scholar
  31. Michael Mitzenmacher and Sergei Vassilvitskii. Algorithms with predictions. In Beyond Worst Case Analysis, pages 646-662. Cambridge University Press, 2021. Google Scholar
  32. Michael Mitzenmacher and Sergei Vassilvitskii. Algorithms with predictions. Communications of the ACM, 65(7):33-35, 2022. Google Scholar
  33. Narges Peyravi and Ali Moeini. Estimating runtime of a job in hadoop mapreduce. Journal of Big Data, 7(: 44), 2020. Google Scholar
  34. Kirk Pruhs, Jirí Sgall, and Eric Torng. Online scheduling. In Joseph Y.-T. Leung, editor, Handbook of Scheduling - Algorithms, Models, and Performance Analysis. Chapman and Hall/CRC, 2004. Google Scholar
  35. Manish Purohit, Zoya Svitkina, and Ravi Kumar. Improving online algorithms via ml predictions. In NeurIPS, 2018. Google Scholar
  36. Dhruv Rohatgi. Near-optimal bounds for online caching with machine learned advice. In SODA, 2020. Google Scholar
  37. Sartaj Sahni. Algorithms for scheduling independent tasks. J. ACM, 23(1):116-127, 1976. Google Scholar
  38. Jirí Sgall. On-line scheduling. In A. Fiat and G. J. Woeginger, editors, Online Algorithms: The State of the Art, pages 196-231. Springer, 1998. Google Scholar
  39. David B. Shmoys, Joel Wein, and David P. Williamson. Scheduling parallel machines on-line. SIAM J. Comput., 24(6):1313-1331, 1995. Google Scholar
  40. Daniel Dominic Sleator and Robert Endre Tarjan. Amortized efficiency of list update and paging rules. Commun. ACM, 28(2):202-208, 1985. Google Scholar
  41. Shufan Wang and Jian Li. Online algorithms for multi-shop ski rental with machine learned predictions. In AAMAS, 2020. Google Scholar
  42. Alexander Wei. Better and simpler learning-augmented online caching. In APPROX/RANDOM, 2020. Google Scholar
  43. Alexander Wei and Fred Zhang. Optimal robustness-consistency trade-offs for learning-augmented online algorithms. In NeurIPS, 2020. Google Scholar
  44. Hirochika Yamashiro and Hirofumi Nonaka. Estimation of processing time using machine learning and real factory data for optimization of parallel machine scheduling problem. Operations Research Perspectives, 8(: 100196), 2021. Google Scholar
  45. Tianming Zhao, Wei Li, and Albert Y. Zomaya. Uniform machine scheduling with predictions. In Akshat Kumar, Sylvie Thiébaux, Pradeep Varakantham, and William Yeoh, editors, Proceedings of the Thirty-Second International Conference on Automated Planning and Scheduling, ICAPS 2022, Singapore (virtual), June 13-24, 2022, pages 413-422. AAAI Press, 2022. Google Scholar
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