IDEAS home Printed from https://ideas.repec.org/a/spr/jsched/v24y2021i5d10.1007_s10951-020-00676-1.html
   My bibliography  Save this article

A new LP rounding algorithm for the active time problem

Author

Listed:
  • Gruia Cǎlinescu

    (Illinois Institute of Technology)

  • Kai Wang

    (City University of Hong Kong
    HHL Leipzig Graduate School of Management)

Abstract

In this paper, we work on the scheduling problem with active time model. We have a set of preemptive jobs with integral release times, deadlines and required processing lengths, while the preemption of jobs is only allowed at integral time points. We have a single machine that can process at most g distinct job units at any given time unit when the machine is switched on. The objective is to find a schedule that completes all jobs within their timing constraints and minimizes the time when the machine is on, i.e., the active time. This problem has been studied by Chang et al. where they proposed an LP rounding approach which gives a 2-approximation solution. In this paper, we also give a 2-approximation algorithm based on LP rounding approach with a different rounding technique and analysis. Finally, we give a new linear programming formulation for which we conjecture that the integrality gap is 5/3, which might bring new hope for beating the barrier of 2 for the approximation ratio.

Suggested Citation

  • Gruia Cǎlinescu & Kai Wang, 2021. "A new LP rounding algorithm for the active time problem," Journal of Scheduling, Springer, vol. 24(5), pages 543-552, October.
    • Handle: RePEc:spr:jsched:v:24:y:2021:i:5:d:10.1007_s10951-020-00676-1
    DOI: 10.1007/s10951-020-00676-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10951-020-00676-1
    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/s10951-020-00676-1?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. Jessica Chang & Samir Khuller & Koyel Mukherjee, 2017. "LP rounding and combinatorial algorithms for minimizing active and busy time," Journal of Scheduling, Springer, vol. 20(6), pages 657-680, December.
    Full references (including those not matched with items on IDEAS)

    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.

      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:jsched:v:24:y:2021:i:5:d:10.1007_s10951-020-00676-1. 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.