Skip to main content
SpringerLink
Log in

Optimal online algorithms on two hierarchical machines with tightly-grouped processing times

  • Published:
Journal of Combinatorial Optimization Aims and scope Submit manuscript

Abstract

This paper considers an online hierarchical scheduling problem on two parallel identical machines. The objective is to minimize the makspan. It is assumed that all jobs have bounded processing times in between \(p\) and \(rp\), where \(p>0\) and \(r\ge 1\). We first improve a previous result by giving an optimal online algorithm for the non-preemptive version. For the preemptive version, we present an optimal preemptive algorithm without introducing idle time for all \(r\ge 1\). If the algorithm is allowed to use idle time, we show that the semi-online information that jobs are tightly-grouped cannot help improve the bound of the pure online problem.

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

  • Bar-Noy A, Freund A, Naor J (2001) On-line load balancing in a hierarchical server topology. SIAM Journal on Computing. 31:527–549

    Article  MATH  MathSciNet  Google Scholar 

  • Chassid O, Epstein L (2008) The hierarchical model for load balancing on two machines. Journal of Combinatorial Optimization. 15(4):305–314

    Article  MATH  MathSciNet  Google Scholar 

  • Crescenzi P, Gambosi G, Penna P (2004) On-line algorithms for the channel assignment problem in cellular networks. Discrete Applied Mathematics. 137:237–266

    Article  MATH  MathSciNet  Google Scholar 

  • Dósa G, Epstein L (2008) Preemptive scheduling on a small number of hierarchical machines. Information and Computation. 206(5):602–619

    Article  MATH  MathSciNet  Google Scholar 

  • He Y, Zhang G (1999) Semi on-line scheduling on two identical machines. Computing. 62:179–187

    Article  MATH  MathSciNet  Google Scholar 

  • Jiang Y (2008) Online scheduling on parallel machines with two GoS levels. Journal of Combinatorial Optimization. 16:28–38

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  • Liu M, Chu C, Xu Y, Zheng F (2011) Semi-online scheduling on 2 machines under a grade of service provision with bounded processing times. Journal of Combinatorial Optimization. 21:138–149

    Article  MATH  MathSciNet  Google Scholar 

  • Park J, Chang S, Lee K (2006) Online and semi-online scheduling of two machines under a grade of service provision. Operations Research Letters. 34:692–696

    Article  MATH  MathSciNet  Google Scholar 

  • Tan Z, Zhang A (2010) A note on hierarchical scheduling on two uniform machines. Journal of Combinatorial Optimization. 20:85–95

    Article  MATH  MathSciNet  Google Scholar 

  • Tan Z, Zhang A (2011) Online hierarchical scheduling: An approach using mathematical programming. Theoretical Computer Science. 412:246–256

    Article  MATH  MathSciNet  Google Scholar 

  • Wu Y, Ji M, Yang Q (2012) Optimal semi-online scheduling algorithms on two parallel identical machines under a grade of service provision. International Journal of Production Economics. 135:367–371

    Article  Google Scholar 

  • Zhang A, Jiang Y, Tan Z (2009) Online parallel machines scheduling with two hierarchies. Theoretical Computer Science. 410:3597–3605

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

An Zhang, Yiwei Jiang, and Jueliang Hu were supported by the National Natural Science Foundation of China through Grant Nos. 11201105, 11001242, and 11071220 respectively. Yiwei Jiang is also supported by Zhejiang Province Natural Science Foundation of China (Y6090175).

Author information

Authors and Affiliations

  1. Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou,  310018, People’s Republic of China

    An Zhang

  2. Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou,  310018, People’s Republic of China

    Yiwei Jiang

  3. Department of Computer Science, The University of Texas at Dallas, Dallas, TX, 75080, USA

    Lidan Fan

  4. School of Science, Zhejiang Sci-Tech University, Hangzhou, 310018, People’s Republic of China

    Jueliang Hu

Authors
  1. An Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yiwei Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lidan Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jueliang Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yiwei Jiang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, A., Jiang, Y., Fan, L. et al. Optimal online algorithms on two hierarchical machines with tightly-grouped processing times. J Comb Optim 29, 781–795 (2015). https://doi.org/10.1007/s10878-013-9627-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10878-013-9627-7

Keywords

Search

Navigation