Skip to main content
Springer Nature Link
Log in

Online algorithms for the mixed ring loading problem with two nodes

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

In this paper, we introduce the mixed ring loading problem, where the ring contains undirected and bidirected links. When the ring consists of two nodes, we consider the online mixed ring loading problem under three different scenarios including splittable, integer splittable and unsplittable. When the demands are (integer) splittable, we present an (asymptotically) optimal online algorithm. When the demands are unsplittable, we present an online algorithm which generalizes the previous result.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Becchetti, L., Di Ianni, M., Marchetti-Spaccamela, A.: Approximation algorithms for routing and call scheduling in all-optical chains and rings. Theoret. Comput. Sci. 287(2), 429–448 (2002)

    Article  MathSciNet  Google Scholar 

  2. Bernardino, A.M., Bernardino, E.M., Sanchez-Perez, J.M., Gomez-Pulido, J.A., Vega-Rodriguez, M.A.: Solving ring loading problems using bio-inspired algorithms. J. Netw. Comput. Appl. 34(2), 668–685 (2011)

    Article  Google Scholar 

  3. Cosares, S., Saniee, I.: An optimization problem related to balancing loads on sonet rings. Telecommun. Syst. 3(2), 165–181 (1994)

    Article  Google Scholar 

  4. Dell’Amico, M., Labbé, M., Maffioli, F.: Exact solution of the sonet ring loading problem. Oper. Res. Lett. 25(3), 119–129 (1999)

    Article  Google Scholar 

  5. Havill, J.T., Hutson, K.R.: Optimal online ring routing. Networks 57(2), 187–197 (2011)

    Article  MathSciNet  Google Scholar 

  6. Karhi, S., Shabtay, D.: Online scheduling of two job types on a set of multipurpose machines. Int. J. Prod. Econ. 150, 155–162 (2014)

    Article  Google Scholar 

  7. Khanna, S.: A polynomial time approximation scheme for the sonet ring loading problem. Bell Labs Tech. J. 2(2), 36–41 (1997)

    Article  Google Scholar 

  8. Li, W., Li, J., Guan, L.: Approximation algorithms for the ring loading problem with penalty cost. Inf. Process. Lett. 114(1–2), 56–59 (2014)

    Article  MathSciNet  Google Scholar 

  9. Myung, Y.S., Kim, H.G.: On the ring loading problem with demand splitting. Oper. Res. Lett. 32(2), 167–173 (2004)

    Article  MathSciNet  Google Scholar 

  10. Myung, Y.S., Kim, H.G., Tcha, D.W.: Optimal load balancing on sonet bidirectional rings. Oper. Res. 45(1), 148–152 (1997)

    Article  Google Scholar 

  11. Nong, Q., Yuan, J., Lin, Y.: The weighted link ring loading problem. J. Comb. Optim. 18(1), 38–50 (2009)

    Article  MathSciNet  Google Scholar 

  12. Schrijver, A., Seymour, P., Winkler, P.: The ring loading problem. SIAM Rev. 41(4), 777–791 (1999)

    Article  MathSciNet  Google Scholar 

  13. Schrijver, A., Seymour, P.D., Winkler, P.: The ring loading problem. SIAM J. Discrete Math. 11(1), 1–14 (1998)

    Article  MathSciNet  Google Scholar 

  14. Skutella, M.: A note on the ring loading problem. SIAM J. Discrete Math. 30(1), 327–342 (2016)

    Article  MathSciNet  Google Scholar 

  15. Wang, B.F.: Linear time algorithms for the ring loading problem with demand splitting. J. Algorithms 54(1), 45–57 (2005)

    Article  MathSciNet  Google Scholar 

  16. Wilfong, G.T., Winkler, P.: Ring routing and wavelength translation. In: Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 333–341 (1998)

Download references

Acknowledgements

The work is supported in part by the National Natural Science Foundation of China [Nos. 61662088, 11761078], Program for Excellent Young Talents of Yunnan University, Training Program of National Science Fund for Distinguished Young Scholars, IRTSTYN, and Key Joint Project of the Science and Technology Department of Yunnan Province and Yunnan University [No. 2018FY001(-014)].

Author information

Authors and Affiliations

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

    Li Guan, Weidong Li & Man Xiao

Authors
  1. Li Guan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Weidong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Man Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Weidong Li.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Guan, L., Li, W. & Xiao, M. Online algorithms for the mixed ring loading problem with two nodes. Optim Lett 15, 1229–1239 (2021). https://doi.org/10.1007/s11590-020-01632-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-020-01632-w

Keywords

Search

Navigation