Skip to main content
SpringerLink
Log in

Online Makespan Minimization with Budgeted Uncertainty

  • Conference paper
  • First Online:
Algorithms and Data Structures (WADS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12808))

Included in the following conference series:

Abstract

We study Online Makespan Minimization with uncertain job processing times. Jobs are assigned to m parallel and identical machines. Preemption is not allowed. Each job has a regular processing time while up to \(\varGamma \) jobs fail and require additional processing time. The goal is to minimize the makespan, the time it takes to process all jobs if these \(\varGamma \) failing jobs are chosen worst possible. This models real-world applications where acts of nature beyond control have to be accounted for.

So far Makespan Minimization With Budgeted Uncertainty has only been studied as an offline problem. We are first to provide a comprehensive analysis of the corresponding online problem.

We provide a lower bound of 2 for general deterministic algorithms showing that the problem is more difficult than its special case, classical Online Makespan Minimization. We further analyze Graham’s Greedy strategy and show that it is precisely \(\left( 3-\frac{2}{m}\right) \)-competitive. This bound is tight. We finally provide a more sophisticated deterministic algorithm whose competitive ratio approaches 2.9052.

Work supported by the European Research Council, Grant Agreement No. 691672, project APEG.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The term ‘critically flat’ is not a misnomer, by Remark 2 such a schedule is, in particular, flat.

References

  1. Albers, S.: Better bounds for online scheduling. SIAM J. Comput. 29(2), 459–473 (1999)

    Article  MathSciNet  Google Scholar 

  2. Albers, S., Janke, M.: Scheduling in the random-order model. In: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Schloss Dagstuhl-Leibniz-Zentrum für Informatik (2020)

    Google Scholar 

  3. Aloulou, M.A., Croce, F.D.: Complexity of single machine scheduling problems under scenario-based uncertainty. Oper. Res. Lett. 36(3), 338–342 (2008)

    Article  MathSciNet  Google Scholar 

  4. Bartal, Y., Fiat, A., Karloff, H., Vohra, R.: New algorithms for an ancient scheduling problem. In: Proceedings of the Twenty-Fourth Annual ACM Symposium on Theory of Computing, pp. 51–58 (1992)

    Google Scholar 

  5. Bartal, Y., Karloff, H.J., Rabani, Y.: A better lower bound for on-line scheduling. Inf. Process. Lett. 50(3), 113–116 (1994)

    Article  MathSciNet  Google Scholar 

  6. Bertsimas, D., Sim, M.: Robust discrete optimization and network flows. Math. Program. Ser. B 98(1–3), 49–71 (2003). https://doi.org/10.1007/s10107-003-0396-4

  7. Bertsimas, D., Sim, M.: The price of robustness. Oper. Res. 52(1), 35–53 (2004)

    Article  MathSciNet  Google Scholar 

  8. Bougeret, M., Jansen, K., Poss, M., Rohwedder, L.: Approximation results for makespan minimization with budgeted uncertainty. In: Bampis, E., Megow, N. (eds.) WAOA 2019. LNCS, vol. 11926, pp. 60–71. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-39479-0_5

    Chapter  MATH  Google Scholar 

  9. Bougeret, M., Pessoa, A.A., Poss, M.: Robust scheduling with budgeted uncertainty. Discrete Appl. Math. 261, 93–107 (2019)

    Article  MathSciNet  Google Scholar 

  10. Chen, L., Ye, D., Zhang, G.: Approximating the optimal algorithm for online scheduling problems via dynamic programming. Asia-Pac. J. Oper. Res. 32(01), 1540011 (2015)

    Article  MathSciNet  Google Scholar 

  11. Cheng, T.E., Kellerer, H., Kotov, V.: Semi-on-line multiprocessor scheduling with given total processing time. Theor. Comput. Scie. 337(1–3), 134–146 (2005)

    Google Scholar 

  12. Cohen, I., Im, S., Panigrahi, D.: Online two-dimensional load balancing. In: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Schloss Dagstuhl-Leibniz-Zentrum für Informatik (2020)

    Google Scholar 

  13. Dantzig, G.B.: Linear programming under uncertainty. Manage. Sci. 1(3–4), 197–206 (1955)

    Google Scholar 

  14. Dürr, C., Erlebach, T., Megow, N., Meißner, J.: Scheduling with explorable uncertainty. In: 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Schloss Dagstuhl-Leibniz-Zentrum für Informatik (2018)

    Google Scholar 

  15. Dürr, C., Erlebach, T., Megow, N., Meißner, J.: An adversarial model for scheduling with testing. Algorithmica 82(12), 3630–3675 (2020). https://doi.org/10.1007/s00453-020-00742-2

    Article  MathSciNet  MATH  Google Scholar 

  16. Englert, M., Özmen, D., Westermann, M.: The power of reordering for online minimum makespan scheduling. In: 2008 49th Annual IEEE Symposium on Foundations of Computer Science, pp. 603–612. IEEE (2008)

    Google Scholar 

  17. Erlebach, T., Hoffmann, M., Kammer, F.: Query-competitive algorithms for cheapest set problems under uncertainty. Theor. Comput. Sci. 613, 51–64 (2016)

    Article  MathSciNet  Google Scholar 

  18. Faigle, U., Kern, W., Turán, G.: On the performance of on-line algorithms for partition problems. Acta Cybernetica 9(2), 107–119 (1989)

    MathSciNet  MATH  Google Scholar 

  19. Feder, T., Motwani, R., Panigrahy, R., Olston, C., Widom, J.: Computing the median with uncertainty. In: Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing, pp. 602–607 (2000)

    Google Scholar 

  20. Fleischer, R., Wahl, M.: On-line scheduling revisited. J. Sched. 3(6), 343–353 (2000)

    Article  MathSciNet  Google Scholar 

  21. Galambos, G., Woeginger, G.J.: An on-line scheduling heuristic with better worst-case ratio than Graham’s list scheduling. SIAM J. Comput. 22(2), 349–355 (1993)

    Article  MathSciNet  Google Scholar 

  22. Graham, R.L.: Bounds for certain multiprocessing anomalies. Bell Syst. Tech. J. 45(9), 1563–1581 (1966)

    Article  Google Scholar 

  23. Gupta, M., Sabharwal, Y., Sen, S.: The update complexity of selection and related problems. arXiv preprint arXiv:1108.5525 (2011)

  24. Hochbaum, D.S., Shmoys, D.B.: Using dual approximation algorithms for scheduling problems theoretical and practical results. J. ACM (JACM) 34(1), 144–162 (1987)

    Article  MathSciNet  Google Scholar 

  25. Im, S., Kell, N., Kulkarni, J., Panigrahi, D.: Tight bounds for online vector scheduling. In: 2015 IEEE 56th Annual Symposium on Foundations of Computer Science, pp. 525–544. IEEE (2015)

    Google Scholar 

  26. Kahan, S.: A model for data in motion. In: Proceedings of the Twenty-Third Annual ACM Symposium on Theory of Computing, pp. 265–277 (1991)

    Google Scholar 

  27. Karger, D.R., Phillips, S.J., Torng, E.: A better algorithm for an ancient scheduling problem. J. Algor. 20(2), 400–430 (1996)

    Article  MathSciNet  Google Scholar 

  28. Kasperski, A., Kurpisz, A., Zieliński, P.: Approximating a two-machine flow shop scheduling under discrete scenario uncertainty. Eur. J. Oper. Res. 217(1), 36–43 (2012)

    Article  MathSciNet  Google Scholar 

  29. Kasperski, A., Kurpisz, A., Zieliński, P.: Parallel machine scheduling under uncertainty. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds.) IPMU 2012. CCIS, vol. 300, pp. 74–83. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31724-8_9

    Chapter  Google Scholar 

  30. Khanna, S., Tan, W.C.: On computing functions with uncertainty. In: Proceedings of the Twentieth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, pp. 171–182 (2001)

    Google Scholar 

  31. Lenstra, J.K., Shmoys, D.B., Tardos, E.: Approximation algorithms for scheduling unrelated parallel machines. Math. Program. 46(1–3), 259–271 (1990). https://doi.org/10.1007/BF01585745

  32. Mastrolilli, M., Mutsanas, N., Svensson, O.: Approximating single machine scheduling with scenarios. In: Goel, A., Jansen, K., Rolim, J.D.P., Rubinfeld, R. (eds.) APPROX/RANDOM-2008. LNCS, vol. 5171, pp. 153–164. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85363-3_13

    Chapter  Google Scholar 

  33. Olston, C., Widom, J.: Offering a Precision-Performance Tradeoff for Aggregation Queries Over Replicated Data. Tech. rep, Stanford (2000)

    Google Scholar 

  34. Basu Roy, A., Bougeret, M., Goldberg, N., Poss, M.: Approximating robust bin packing with budgeted uncertainty. In: Friggstad, Z., Sack, J.-R., Salavatipour, M.R. (eds.) WADS 2019. LNCS, vol. 11646, pp. 71–84. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-24766-9_6

    Chapter  Google Scholar 

  35. Rudin, J.F.: Improved bounds for the on-line scheduling problem (2001)

    Google Scholar 

  36. Sanders, P., Sivadasan, N., Skutella, M.: Online scheduling with bounded migration. Math. Oper. Res. 34(2), 481–498 (2009)

    Article  MathSciNet  Google Scholar 

  37. Singla, S.: The price of information in combinatorial optimization. In: Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 2523–2532. SIAM (2018)

    Google Scholar 

  38. Tadayon, B., Smith, J.C.: Algorithms and complexity analysis for robust single-machine scheduling problems. J. Sched. 18(6), 575–592 (2015). https://doi.org/10.1007/s10951-015-0418-0

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Technical University of Munich, Munich, Germany

    Susanne Albers & Maximilian Janke

Authors
  1. Susanne Albers
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Maximilian Janke
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Maximilian Janke .

Editor information

Editors and Affiliations

  1. University of Waterloo, Waterloo, ON, Canada

    Anna Lubiw

  2. University of Alberta, Edmonton, AB, Canada

    Mohammad Salavatipour

  3. Dalhousie University, Halifax, Canada

    Meng He

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Albers, S., Janke, M. (2021). Online Makespan Minimization with Budgeted Uncertainty. In: Lubiw, A., Salavatipour, M., He, M. (eds) Algorithms and Data Structures. WADS 2021. Lecture Notes in Computer Science(), vol 12808. Springer, Cham. https://doi.org/10.1007/978-3-030-83508-8_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-83508-8_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-83507-1

  • Online ISBN: 978-3-030-83508-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation