Skip to main content
SpringerLink
Log in

Online Early Work Maximization Problem on Two Hierarchical Machines with Buffer or Rearrangements

  • Conference paper
  • First Online:
Algorithmic Aspects in Information and Management (AAIM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13513))

Included in the following conference series:

Abstract

In this paper, we consider two semi-online models of online early work maximization problem on two hierarchical machines. When a buffer size of K is available, we propose an optimal online algorithm with a competitive ratio of \(\frac{4}{3}\). If we are allowed to reassign at most K jobs after all the jobs have been scheduled, we propose an optimal online algorithm with a competitive ratio of \(\frac{4}{3}\).

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

References

  1. Chassid, O., Epstein, L.: The hierarchical model for load balancing on two machines. J. Comb. Optim. 15(4), 305–314 (2008)

    Article  MathSciNet  Google Scholar 

  2. Chen, X., Ding, N., Dosa, G., Han, X., Jiang, H.: Online hierarchical scheduling on two machines with known total size of low-hierarchy jobs. Int. J. Comput. Math. 92(5–6), 873–881 (2015)

    Article  MathSciNet  Google Scholar 

  3. Chen, X., Sterna, M., Han, X., Blazewicz, J.: Scheduling on parallel identical machines with late work criterion: offline and online cases. J. Sched. 19(6), 729–736 (2016)

    Article  MathSciNet  Google Scholar 

  4. Chen, X., Xu, Z., Dosa, G., Han, X., Jiang, H.: Semi-online hierarchical scheduling problems with buffer or rearrangements. Inf. Process. Lett. 113, 127–131 (2013)

    Article  MathSciNet  Google Scholar 

  5. Dai, B., Li, J., Li, W.: Semi-online hierarchical scheduling for bag-of-tasks on two machines. In: Proceedings of the 2018 2nd International Conference on Computer Science and Artificial Intelligence, pp. 609–614 (2018)

    Google Scholar 

  6. Epstein, L., Levin, A., Stee, R.V.: Max-min online allocations with a reordering buffer. SIAM J. Discret. Math. 25(3–4), 1230–1250 (2011)

    Article  MathSciNet  Google Scholar 

  7. Jiang, Y., He, Y., Tang, C.: Optimal online algorithms for scheduling on two identical machines under a grade of service. J. Zhejiang Univ. Sci. A 7, 309–314 (2006)

    Article  Google Scholar 

  8. Li, W., Li, J., Zhang, T.: Two approximation schemes for scheduling on parallel machines under a grade of service provision. Asia-Pacific J. Oper. Res. 29(05), 1250029 (2012)

    Article  MathSciNet  Google Scholar 

  9. Li, W.: Improved approximation schemes for early work scheduling on identical parallel machines with a common due date. J. Oper. Res. Soc. Chin. (2022). https://doi.org/10.1007/s40305-022-00402-y

  10. Luo, T., Xu, Y.: Semi-online hierarchical load balancing problem with bounded processing times. Theoret. Comput. Sci. 607, 75–82 (2015)

    Article  MathSciNet  Google Scholar 

  11. Park, J., Chang, S.Y., Lee, K.: Online and semi-online scheduling of two machines under a grade of service provision. Oper. Res. Lett. 34(6), 692–696 (2006)

    Article  MathSciNet  Google Scholar 

  12. Wu, G., Li, W.: Semi-online machine covering on two hierarchical machines with discrete processing times. In: Li, L., Lu, P., He, K. (eds.) NCTCS 2018. CCIS, vol. 882, pp. 1–7. Springer, Singapore (2018). https://doi.org/10.1007/978-981-13-2712-4_1

    Chapter  Google Scholar 

  13. Wu, Y., Cheng, T.C.E., Ji, M.: Optimal algorithms for semi-online machine covering on two hierarchical machines. Theoret. Comput. Sci. 531(6), 37–46 (2014)

    Article  MathSciNet  Google Scholar 

  14. Wu, Y., Ji, M., Yang, Q.F.: Optimal semi-online scheduling algorithms on two parallel identical machines under a grade of service provision. Int. J. Prod. Econ. 135(1), 367–371 (2012)

    Article  Google Scholar 

  15. Xiao, M., Liu, X., Li, W.: Semi-online early work maximization problem on two hierarchical machines with partial information of processing time. In: Wu, W., Du, H. (eds.) AAIM 2021. LNCS, vol. 13153, pp. 146–156. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-93176-6_13

    Chapter  Google Scholar 

  16. Xiao, M., Ding, L., Zhao, S., Li, W.: Semi-online algorithms for hierarchical scheduling on three parallel machines with a buffer size of 1. In: He, K., Zhong, C., Cai, Z., Yin, Y. (eds.) NCTCS 2020. CCIS, vol. 1352, pp. 47–56. Springer, Singapore (2021). https://doi.org/10.1007/978-981-16-1877-2_4

    Chapter  Google Scholar 

  17. Xiao, M., Wu, G., Li, W.: Semi-online machine covering on two hierarchical machines with known total size of low-hierarchy jobs. In: Sun, X., He, K., Chen, X. (eds.) NCTCS 2019. CCIS, vol. 1069, pp. 95–108. Springer, Singapore (2019). https://doi.org/10.1007/978-981-15-0105-0_7

    Chapter  Google Scholar 

  18. Zhang, A., Jiang, Y., Fan, L., Hu, J.: Optimal online algorithms on two hierarchical machines with tightly-grouped processing times. J. Comb. Optim. 29(4), 781–795 (2013). https://doi.org/10.1007/s10878-013-9627-7

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgment

The work is supported in part by the National Natural Science Foundation of China [No. 12071417].

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Yunnan University, Kunming, 650504, People’s Republic of China

    Man Xiao, Xihua Bai & Weidong Li

Authors
  1. Man Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xihua Bai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Weidong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Weidong Li .

Editor information

Editors and Affiliations

  1. Guangdong University of Technology, Guangzhou, China

    Qiufen Ni

  2. University of Texas at Dallas, Richardson, TX, USA

    Weili Wu

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Xiao, M., Bai, X., Li, W. (2022). Online Early Work Maximization Problem on Two Hierarchical Machines with Buffer or Rearrangements. In: Ni, Q., Wu, W. (eds) Algorithmic Aspects in Information and Management. AAIM 2022. Lecture Notes in Computer Science, vol 13513. Springer, Cham. https://doi.org/10.1007/978-3-031-16081-3_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-16081-3_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-16080-6

  • Online ISBN: 978-3-031-16081-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation