IDEAS home Printed from https://ideas.repec.org/a/spr/cejnor/v26y2018i1d10.1007_s10100-017-0481-z.html
   My bibliography  Save this article

Tight upper bounds for semi-online scheduling on two uniform machines with known optimum

Author

Listed:
  • György Dósa

    (University of Pannonia)

  • Armin Fügenschuh

    (Helmut Schmidt University/University of the Federal Armed Forces Hamburg)

  • Zhiyi Tan

    (Zhejiang University)

  • Zsolt Tuza

    (University of Pannonia
    Hungarian Academy of Sciences)

  • Krzysztof Węsek

    (Helmut Schmidt University/University of the Federal Armed Forces Hamburg
    Warsaw University of Technology)

Abstract

We consider a semi-online version of the problem of scheduling a sequence of jobs of different lengths on two uniform machines with given speeds 1 and s. Jobs are revealed one by one (the assignment of a job has to be done before the next job is revealed), and the objective is to minimize the makespan. In the considered variant the optimal offline makespan is known in advance. The most studied question for this online-type problem is to determine the optimal competitive ratio, that is, the worst-case ratio of the solution given by an algorithm in comparison to the optimal offline solution. In this paper, we make a further step towards completing the answer to this question by determining the optimal competitive ratio for s between $$\frac{5 + \sqrt{241}}{12} \approx 1.7103$$ 5 + 241 12 ≈ 1.7103 and $$\sqrt{3} \approx 1.7321$$ 3 ≈ 1.7321 , one of the intervals that were still open. Namely, we present and analyze a compound algorithm achieving the previously known lower bounds.

Suggested Citation

  • György Dósa & Armin Fügenschuh & Zhiyi Tan & Zsolt Tuza & Krzysztof Węsek, 2018. "Tight upper bounds for semi-online scheduling on two uniform machines with known optimum," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(1), pages 161-180, March.
    • Handle: RePEc:spr:cejnor:v:26:y:2018:i:1:d:10.1007_s10100-017-0481-z
    DOI: 10.1007/s10100-017-0481-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10100-017-0481-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10100-017-0481-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. György Dósa & M. Grazia Speranza & Zsolt Tuza, 2011. "Two uniform machines with nearly equal speeds: unified approach to known sum and known optimum in semi on-line scheduling," Journal of Combinatorial Optimization, Springer, vol. 21(4), pages 458-480, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Leah Epstein, 2018. "A survey on makespan minimization in semi-online environments," Journal of Scheduling, Springer, vol. 21(3), pages 269-284, June.
    2. György Dósa & Armin Fügenschuh & Zhiyi Tan & Zsolt Tuza & Krzysztof Węsek, 2019. "Tight lower bounds for semi-online scheduling on two uniform machines with known optimum," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(4), pages 1107-1130, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. György Dósa & Armin Fügenschuh & Zhiyi Tan & Zsolt Tuza & Krzysztof Węsek, 2019. "Tight lower bounds for semi-online scheduling on two uniform machines with known optimum," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(4), pages 1107-1130, December.
    2. Leah Epstein, 2018. "A survey on makespan minimization in semi-online environments," Journal of Scheduling, Springer, vol. 21(3), pages 269-284, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:cejnor:v:26:y:2018:i:1:d:10.1007_s10100-017-0481-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.