Skip to main content
SpringerLink
Log in

Parallel solutions for preemptive makespan scheduling on two identical machines

  • Published:
Journal of Scheduling Aims and scope Submit manuscript

Abstract

We consider online preemptive scheduling of jobs arriving one by one, to be assigned to two identical machines, with the goal of makespan minimization. We study the effect of selecting the best solution out of two independent solutions constructed in parallel in an online fashion. Two cases are analyzed, where one case is purely online, and in the other one jobs are presented sorted by non-increasing sizes. We show that using two solutions rather than one improves the performance significantly, but that an optimal solution cannot be obtained for any constant number of solutions constructed in parallel. Our algorithms have the best possible competitive ratios out of algorithms for each one of the classes.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Albers, S. (1999). Better bounds for online scheduling. SIAM Journal on Computing, 29(2), 459–473.

    Article  Google Scholar 

  • Albers, S., & Hellwig, M. (2012). Semi-online scheduling revisited. Theoretical Computer Science, 443, 1–9.

    Article  Google Scholar 

  • Albers, S., & Hellwig, M. (2017). On the value of job migration in online makespan minimization. Algorithmica, 79(2), 598–623.

    Article  Google Scholar 

  • Albers, S., & Hellwig, M. (2017). Online makespan minimization with parallel schedules. Algorithmica, 78(2), 492–520.

    Article  Google Scholar 

  • Aspnes, J., Azar, Y., Fiat, A., Plotkin, S. A., & Waarts, O. (1997). On-line routing of virtual circuits with applications to load balancing and machine scheduling. Journal of the ACM, 44(3), 486–504.

    Article  Google Scholar 

  • Azar, Y., & Regev, O. (2001). On-line bin-stretching. Theoretical Computer Science, 268(1), 17–41.

    Article  Google Scholar 

  • Berman, P., Charikar, M., & Karpinski, M. (2000). On-line load balancing for related machines. Journal of Algorithms, 35(1), 108–121.

    Article  Google Scholar 

  • Böckenhauer, H., Komm, D., Královic, R., Královic, R., & Mömke, T. (2017). Online algorithms with advice: The tape model. Information and Computation, 254, 59–83.

    Article  Google Scholar 

  • Boyar, J., Favrholdt, L. M., Kudahl, C., Larsen, K. S., & Mikkelsen, J. W. (2017). Online algorithms with advice: A survey. ACM Computing Surveys, 50(2), 19:1-19:34.

    Google Scholar 

  • Boyar, J., Favrholdt, L. M., Kudahl, C., & Mikkelsen, J. W. (2018). Weighted online problems with advice. Theory of Computing Systems, 62(6), 1443–1469.

    Article  Google Scholar 

  • Chen, B., van Vliet, A., & Woeginger, G. J. (1995). An optimal algorithm for preemptive on-line scheduling. Operations Research Letters, 18(3), 127–131.

    Article  Google Scholar 

  • Chen, X., Lan, Y., Benko, A., Dósa, G., & Han, X. (2011). Optimal algorithms for online scheduling with bounded rearrangement at the end. Theoretical Computer Science, 412(45), 6269–6278.

    Article  Google Scholar 

  • Cheng, T. C. E., Kellerer, H., & Kotov, V. (2012). Algorithms better than LPT for semi-online scheduling with decreasing processing times. Operations Research Letters, 40(5), 349–352.

    Article  Google Scholar 

  • Dohrau, J. (2015). Online makespan scheduling with sublinear advice. In Proceedings of the 41st international conference on current trends in theory and practice of computer science (SOFSEM’15), pp. 177–188.

  • Ebenlendr, T., Jawor, W., & Sgall, J. (2009). Preemptive online scheduling: Optimal algorithms for all speeds. Algorithmica, 53(4), 504–522.

    Article  Google Scholar 

  • Ebenlendr, T., & Sgall, J. (2009). Optimal and online preemptive scheduling on uniformly related machines. Journal of Scheduling, 12(5), 517–527.

    Article  Google Scholar 

  • Ebenlendr, T., & Sgall, J. (2011). Semi-online preemptive scheduling: One algorithm for all variants. Theory of Computing Systems, 48(3), 577–613.

    Article  Google Scholar 

  • Epstein, L. (2001). Optimal preemptive on-line scheduling on uniform processors with non-decreasing speed ratios. Operations Research Letters, 29(2), 93–98.

    Article  Google Scholar 

  • Epstein, L. (2003). Bin stretching revisited. Acta Informatica, 39(2), 97–117.

    Article  Google Scholar 

  • Epstein, L., & Favrholdt, L. M. (2002). Optimal preemptive semi-online scheduling to minimize makespan on two related machines. Operetions Research Letters, 30(4), 269–275.

    Article  Google Scholar 

  • Epstein, L., & Favrholdt, L. M. (2005). Optimal non-preemptive semi-online scheduling on two related machines. Journal of Algorithms, 57(1), 49–73.

    Article  Google Scholar 

  • Epstein, L., & Levin, A. (2014). Robust algorithms for preemptive scheduling. Algorithmica, 69(1), 26–57.

    Article  Google Scholar 

  • Epstein, L., Noga, J., Seiden, S. S., Sgall, J., & Woeginger, G. J. (2001). Randomized online scheduling on two uniform machines. Journal of Scheduling, 4(2), 71–92.

    Article  Google Scholar 

  • Faigle, U., Kern, W., & Turán, G. (1989). On the performance of online algorithms for partition problems. Acta Cybernetica, 9(2), 107–119.

    Google Scholar 

  • Fekete, S.P., Grosse-Holz, J., Keldenich, P., & Schmidt, A. (2019). Parallel online algorithms for the bin packing problem. In Proceedings of the 17th workshop on approximation and online algorithms (WAOA’19), pp. 106–119.

  • Fleischer, R., & Wahl, M. (2000). Online scheduling revisited. Journal of Scheduling, 3(6), 343–353.

    Article  Google Scholar 

  • Graham, R. L. (1966). Bounds for certain multiprocessing anomalies. Bell System Technical Journal, 45(9), 1563–1581.

    Article  Google Scholar 

  • Graham, R. L. (1969). Bounds on multiprocessing timing anomalies. SIAM Journal of Applied Mathematics, 17(2), 416–429.

    Article  Google Scholar 

  • Jeż, Ł, Schwartz, J., Sgall, J., & Békési, J. (2013). Lower bounds for online makespan minimization on a small number of related machines. Journal of Scheduling, 16(5), 539–547.

  • Kellerer, H., & Kotov, V. (2013). An efficient algorithm for bin stretching. Operations Research Letters, 41(4), 343–346.

  • Kellerer, H., Kotov, V., & Gabay, M. (2015). An efficient algorithm for semi-online multiprocessor scheduling with given total processing time. Journal of Scheduling, 18(6), 623–630.

  • Kellerer, H., Kotov, V., Speranza, M. G., & Tuza, Z. (1997). Semi on-line algorithms for the partition problem. Operations Research Letters, 21(5), 235–242.

    Article  Google Scholar 

  • Kovács, A. (2010). New approximation bounds for LPT scheduling. Algorithmica, 57(2), 413–433.

    Article  Google Scholar 

  • Levin, A. (2022). Robust algorithms for preemptive scheduling on uniform machines of non-increasing job sizes. Information Processing Letters, 174, 106211.

    Article  Google Scholar 

  • McNaughton, R. (1959). Scheduling with deadlines and loss functions. Management Science, 6(1), 1–12.

    Article  Google Scholar 

  • Renault, M. P., Rosén, A., & van Stee, R. (2015). Online algorithms with advice for bin packing and scheduling problems. Theoretical Computer Science, 600, 155–170.

    Article  Google Scholar 

  • Rudin, J. F., III., & Chandrasekaran, R. (2003). Improved bounds for the online scheduling problem. SIAM Journal on Computing, 32(3), 717–735.

    Article  Google Scholar 

  • Sanders, P., Sivadasan, N., & Skutella, M. (2009). Online scheduling with bounded migration. Mathematics of Operations Research, 34(2), 481–498.

    Article  Google Scholar 

  • Seiden, S. S., Sgall, J., & Woeginger, G. J. (2000). Semi-online scheduling with decreasing job sizes. Operations Research Letters, 27(5), 215–221.

    Article  Google Scholar 

  • Sgall, J. (1997). A lower bound for randomized on-line multiprocessor scheduling. Information Processing Letters, 63(1), 51–55.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Haifa, Haifa, Israel

    Leah Epstein

Authors
  1. Leah Epstein
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Leah Epstein.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Epstein, L. Parallel solutions for preemptive makespan scheduling on two identical machines. J Sched 26, 61–76 (2023). https://doi.org/10.1007/s10951-022-00764-4

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10951-022-00764-4

Keywords

Search

Navigation