Document Open Access Logo

Online Makespan Scheduling Under Scenarios

Author Ekin Ergen

PDF

File

Thumbnail PDF
PDF
LIPIcs.ESA.2025.27.pdf
  • Filesize: 1.11 MB
  • 16 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
Keywords
  • online scheduling
  • scenario-based model
  • online algorithms

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

We consider a natural extension of online makespan scheduling on identical parallel machines by introducing scenarios. A scenario is a subset of jobs, and the task of our problem is to find a global assignment of the jobs to machines so that the maximum makespan under a scenario, i.e., the maximum makespan of any schedule restricted to a scenario, is minimized. 
For varying values of the number of scenarios and machines, we explore the competitiveness of online algorithms. We prove tight and near-tight bounds, several of which are achieved through novel constructions. In particular, we leverage the interplay between the unit processing time case of our problem and the hypergraph coloring problem both ways: We use hypergraph coloring techniques to steer an adversarial family of instances proving lower bounds for our problem, which in turn leads to lower bounds for several variants of online hypergraph coloring.

Cite As Get BibTex

Ekin Ergen. Online Makespan Scheduling Under Scenarios. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 27:1-27:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.27

Author Details

Ekin Ergen
  • Technical University of Berlin, Germany

Funding

The author was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - The Berlin Mathematics Research Center MATH+ (EXC-2046/1, project ID: 390685689).

Acknowledgements

I would like to thank Martin Skutella for inspiring me to consider this problem, for his invaluable suggestions and for the insightful discussions. I am also grateful to the anonymous reviewers for their careful reading and valuable feedback.

References

  1. Susanne Albers. Better bounds for online scheduling. SIAM Journal on Computing, 29(2):459-473, 1999. URL: https://doi.org/10.1137/S0097539797324874.
  2. Y. Bartal, A. Fiat, H. Karloff, and R. Vohra. New algorithms for an ancient scheduling problem. Journal of Computer and System Sciences, 51(3):359-366, 1995. URL: https://doi.org/10.1006/jcss.1995.1074.
  3. Dimitris Bertsimas, Patrick Jaillet, and Amedeo R. Odoni. A priori optimization. Operations Research, 38(6):1019-1033, 1990. URL: https://doi.org/10.1287/OPRE.38.6.1019.
  4. Danny Blom, Dylan Hyatt-Denesik, Afrouz Jabal Amelia, and Bart Smeulders. Approximation algorithms for k-scenario matching. In Marcin Bieńkowski and Matthias Englert, editors, Approximation and Online Algorithms, pages 89-103, Cham, 2025. Springer Nature Switzerland. Google Scholar
  5. Yulle Borges, Vinicius Loti de Lima, Flávio Miyazawa, Lehilton Pedrosa, Thiago Queiroz, and Rafael Schouery. Algorithms for the bin packing problem with scenarios. CoRR, May 2023. URL: https://doi.org/10.48550/arXiv.2305.15351.
  6. Thomas Bosman, Martijn van Ee, Ekin Ergen, Csanád Imreh, Alberto Marchetti-Spaccamela, Martin Skutella, and Leen Stougie. Total completion time scheduling under scenarios. In Proceedings of the 21st International Workshop on Approximation and Online Algorithms, pages 104-118. Springer, 2023. URL: https://doi.org/10.1007/978-3-031-49815-2_8.
  7. Attila Bódis and János Balogh. Bin packing problem with scenarios. Central European Journal of Operations Research, 27(2):377-395, June 2019. URL: https://doi.org/10.1007/s10100-018-0574-3.
  8. Moses Charikar, Alantha Newman, and Aleksandar Nikolov. Tight hardness results for minimizing discrepancy. In Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011, San Francisco, California, USA, January 23-25, 2011, pages 1607-1614, January 2011. URL: https://doi.org/10.1137/1.9781611973082.124.
  9. Ulrich Faigle, Walter Kern, and Gyorgy Turan. On the performance of on-line algorithms for partition problems. Acta Cybern., 9:107-119, January 1989. URL: https://cyber.bibl.u-szeged.hu/index.php/actcybern/article/view/3359.
  10. Esteban Feuerstein, Alberto Marchetti-Spaccamela, Frans Schalekamp, René Sitters, Suzanne van der Ster, Leen Stougie, and Anke van Zuylen. Minimizing worst-case and average-case makespan over scenarios. Journal of Scheduling, pages 1-11, 2016. Google Scholar
  11. Rudolf Fleischer and Michaela Wahl. Online scheduling revisited. In Mike S. Paterson, editor, Algorithms - ESA 2000, pages 202-210, Berlin, Heidelberg, 2000. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/3-540-45253-2_19.
  12. Gábor Galambos and Gerhard J. Woeginger. An on-line scheduling heuristic with better worst-case ratio than Graham’s list scheduling. SIAM Journal on Computing, 22(2):349-355, 1993. URL: https://doi.org/10.1137/0222026.
  13. R. L. Graham. Bounds for certain multiprocessing anomalies. The Bell System Technical Journal, 45(9):1563-1581, 1966. URL: https://doi.org/10.1002/j.1538-7305.1966.tb01709.x.
  14. Yaqiao Li and Denis Pankratov. Online vector bin packing and hypergraph coloring illuminated: Simpler proofs and new connections. CoRR, June 2023. URL: https://doi.org/10.48550/arXiv.2306.11241.
  15. J. Nagy-György and Cs. Imreh. Online hypergraph coloring. Information Processing Letters, 109(1):23-26, 2008. URL: https://doi.org/10.1016/j.ipl.2008.08.009.
  16. Christos H. Papadimitriou and Mihalis Yannakakis. The complexity of restricted spanning tree problems. J. ACM, 29(2):285-309, April 1982. URL: https://doi.org/10.1145/322307.322309.
  17. Karger D. R., Phillips S. J., and Torng E. A better algorithm for an ancient scheduling problem. Journal of Algorithms, 1996. Google Scholar
  18. John F. Rudin. Improved bounds for the on-line scheduling problem. PhD thesis, The University of Texas at Dallas, 2001. Google Scholar
  19. John F. Rudin and R. Chandrasekaran. Improved bounds for the online scheduling problem. SIAM Journal on Computing, 32(3):717-735, 2003. URL: https://doi.org/10.1137/S0097539702403438.
  20. Peter Sanders, Naveen Sivadasan, and Martin Skutella. Online scheduling with bounded migration. In Josep Díaz, Juhani Karhumäki, Arto Lepistö, and Donald Sannella, editors, Automata, Languages and Programming, pages 1111-1122, Berlin, Heidelberg, 2004. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/978-3-540-27836-8_92.
  21. Dvir Shabtay and Miri Gilenson. A state-of-the-art survey on multi-scenario scheduling. European Journal of Operational Research, 2022. Google Scholar
  22. Joel Spencer. Balancing games. Journal of Combinatorial Theory, Series B, 23(1):68-74, August 1977. URL: https://doi.org/10.1016/0095-8956(77)90057-0.
  23. Joel Spencer. Six standard deviations suffice. Transactions of the American Mathematical Society, 289(2):679-706, June 1985. Copyright: Copyright 2016 Elsevier B.V., All rights reserved. URL: https://doi.org/10.1090/S0002-9947-1985-0784009-0.
  24. Martijn van Ee, Leo van Iersel, Teun Janssen, and René Sitters. A priori TSP in the scenario model. Discrete Applied Mathematics, 250:331-341, 2018. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact