IDEAS home Printed from https://ideas.repec.org/a/spr/jsched/v20y2017i3d10.1007_s10951-016-0478-9.html
   My bibliography  Save this article

A parameterized complexity view on non-preemptively scheduling interval-constrained jobs: few machines, small looseness, and small slack

Author

Listed:
  • René Bevern

    (Novosibirsk State University)

  • Rolf Niedermeier

    (TU Berlin)

  • Ondřej Suchý

    (Czech Technical University in Prague)

Abstract

We study the problem of non-preemptively scheduling n jobs, each job j with a release time $$t_j$$ t j , a deadline $$d_j$$ d j , and a processing time $$p_j$$ p j , on m parallel identical machines. Cieliebak et al. (2004) considered the two constraints $$|d_j-t_j|\le \lambda {}p_j$$ | d j - t j | ≤ λ p j and $$|d_j-t_j|\le p_j +\sigma $$ | d j - t j | ≤ p j + σ and showed the problem to be NP-hard for any $$\lambda >1$$ λ > 1 and for any $$\sigma \ge 2$$ σ ≥ 2 . We complement their results by parameterized complexity studies: we show that, for any $$\lambda >1$$ λ > 1 , the problem remains weakly NP-hard even for $$m=2$$ m = 2 and strongly W[1]-hard parameterized by m. We present a pseudo-polynomial-time algorithm for constant m and $$\lambda $$ λ and a fixed-parameter tractability result for the parameter m combined with $$\sigma $$ σ .

Suggested Citation

  • René Bevern & Rolf Niedermeier & Ondřej Suchý, 2017. "A parameterized complexity view on non-preemptively scheduling interval-constrained jobs: few machines, small looseness, and small slack," Journal of Scheduling, Springer, vol. 20(3), pages 255-265, June.
    • Handle: RePEc:spr:jsched:v:20:y:2017:i:3:d:10.1007_s10951-016-0478-9
    DOI: 10.1007/s10951-016-0478-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10951-016-0478-9
    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/s10951-016-0478-9?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. Sevastianov, S. V., 2005. "An introduction to multi-parameter complexity analysis of discrete problems," European Journal of Operational Research, Elsevier, vol. 165(2), pages 387-397, September.
    2. Federico Malucelli & Sara Nicoloso, 2007. "Shiftable intervals," Annals of Operations Research, Springer, vol. 150(1), pages 137-157, March.
    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. Matthias Bentert & Robert Bredereck & Péter Györgyi & Andrzej Kaczmarczyk & Rolf Niedermeier, 2023. "A multivariate complexity analysis of the material consumption scheduling problem," Journal of Scheduling, Springer, vol. 26(4), pages 369-382, August.
    2. Danny Hermelin & Matthias Mnich & Simon Omlor, 2024. "Serial batching to minimize the weighted number of tardy jobs," Journal of Scheduling, Springer, vol. 27(6), pages 545-556, December.
    3. Danny Hermelin & Shlomo Karhi & Michael Pinedo & Dvir Shabtay, 2021. "New algorithms for minimizing the weighted number of tardy jobs on a single machine," Annals of Operations Research, Springer, vol. 298(1), pages 271-287, March.
    4. de Weerdt, Mathijs & Baart, Robert & He, Lei, 2021. "Single-machine scheduling with release times, deadlines, setup times, and rejection," European Journal of Operational Research, Elsevier, vol. 291(2), pages 629-639.
    5. Hermelin, Danny & Kubitza, Judith-Madeleine & Shabtay, Dvir & Talmon, Nimrod & Woeginger, Gerhard J., 2019. "Scheduling two agents on a single machine: A parameterized analysis of NP-hard problems," Omega, Elsevier, vol. 83(C), pages 275-286.
    6. Danny Hermelin & Dvir Shabtay & Chen Zelig & Michael Pinedo, 2022. "A general scheme for solving a large set of scheduling problems with rejection in FPT time," Journal of Scheduling, Springer, vol. 25(2), pages 229-255, April.
    7. Klaus Heeger & Danny Hermelin & George B. Mertzios & Hendrik Molter & Rolf Niedermeier & Dvir Shabtay, 2023. "Equitable scheduling on a single machine," Journal of Scheduling, Springer, vol. 26(2), pages 209-225, April.
    8. Hermelin, Danny & Pinedo, Michael & Shabtay, Dvir & Talmon, Nimrod, 2019. "On the parameterized tractability of single machine scheduling with rejection," European Journal of Operational Research, Elsevier, vol. 273(1), pages 67-73.
    9. S. Bessy & R. Giroudeau, 2019. "Parameterized complexity of a coupled-task scheduling problem," Journal of Scheduling, Springer, vol. 22(3), pages 305-313, June.

    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. Cheng, T.C.E. & Shafransky, Y. & Ng, C.T., 2016. "An alternative approach for proving the NP-hardness of optimization problems," European Journal of Operational Research, Elsevier, vol. 248(1), pages 52-58.
    2. Ahmadian, Mohammad Mahdi & Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2021. "Four decades of research on the open-shop scheduling problem to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 295(2), pages 399-426.

    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:20:y:2017:i:3:d:10.1007_s10951-016-0478-9. 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.