IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v1y1998i4d10.1023_a1009794729459.html
   My bibliography  Save this article

Optimal On-Line Scheduling of Parallel Jobs with Dependencies

Author

Listed:
  • Anja Feldmann

    (Carnegie Mellon University)

  • Ming-Yang Kao

    (Duke University)

  • Jiří Sgall

    (Mathematical Institute)

  • Shang-Hua Teng

    (University of Minnesota)

Abstract

We study the following general on-line scheduling problem. Paralleljobs arrive on a parallel machine dynamically according to thedependencies between them. Each job requests a certain number ofprocessors in a specific communication configuration, but its runningtime is not known until it is completed. We present optimal on-linealgorithms for PRAMs and one-dimensional meshes, and efficientalgorithms for hypercubes and general meshes. For PRAMs we obtainoptimal tradeoffs between the competitive ratio and the largestnumber of processors requested by any job. Our results demonstrate that on-line scheduling with dependenciesdiffers from scheduling without dependencies in several crucialaspects. First, it is essential to use virtualization, i.e., toschedule parallel jobs on fewer processors than requested. Second,the maximal number of processors requested by a job has significantinfluence on the performance. Third, the geometric structure of thenetwork topology is an even more important factor than in the absenceof dependencies.

Suggested Citation

  • Anja Feldmann & Ming-Yang Kao & Jiří Sgall & Shang-Hua Teng, 1998. "Optimal On-Line Scheduling of Parallel Jobs with Dependencies," Journal of Combinatorial Optimization, Springer, vol. 1(4), pages 393-411, December.
    • Handle: RePEc:spr:jcomop:v:1:y:1998:i:4:d:10.1023_a:1009794729459
    DOI: 10.1023/A:1009794729459
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1009794729459
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1009794729459?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. J. K. Lenstra & A. H. G. Rinnooy Kan, 1978. "Complexity of Scheduling under Precedence Constraints," Operations Research, INFORMS, vol. 26(1), pages 22-35, February.
    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. Vredeveld, T., 2009. "Stochastic Online Scheduling," Research Memorandum 052, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    2. Havill, Jessen T. & Mao, Weizhen, 2008. "Competitive online scheduling of perfectly malleable jobs with setup times," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1126-1142, 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. Nodari Vakhania, 2001. "Tight Performance Bounds of CP-Scheduling on Out-Trees," Journal of Combinatorial Optimization, Springer, vol. 5(4), pages 445-464, December.
    2. C N Potts & V A Strusevich, 2009. "Fifty years of scheduling: a survey of milestones," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 41-68, May.
    3. Lenstra, J. K. & Rinnooy Kan, A. H. G., 1979. "Complexity Results For Scheduling Chains On A Single Machine," Econometric Institute Archives 272176, Erasmus University Rotterdam.
    4. Ravindran Vijayalakshmi, Vipin & Schröder, Marc & Tamir, Tami, 2024. "Minimizing total completion time with machine-dependent priority lists," European Journal of Operational Research, Elsevier, vol. 315(3), pages 844-854.
    5. Han Hoogeveen & Petra Schuurman & Gerhard J. Woeginger, 2001. "Non-Approximability Results for Scheduling Problems with Minsum Criteria," INFORMS Journal on Computing, INFORMS, vol. 13(2), pages 157-168, May.
    6. Bampis, Evripidis & Giannakos, Aristotelis & Konig, Jean-Claude, 1996. "On the complexity of scheduling with large communication delays," European Journal of Operational Research, Elsevier, vol. 94(2), pages 252-260, October.
    7. Yan Zhao & Liping Chen & Gang Xie & Jianjun Zhao & Jianwan Ding, 2018. "GPU implementation of a cellular genetic algorithm for scheduling dependent tasks of physical system simulation programs," Journal of Combinatorial Optimization, Springer, vol. 35(1), pages 293-317, January.
    8. Jiang, Xiaojuan & Lee, Kangbok & Pinedo, Michael L., 2021. "Ideal schedules in parallel machine settings," European Journal of Operational Research, Elsevier, vol. 290(2), pages 422-434.
    9. Zhang, An & Qi, Xiangtong & Li, Guanhua, 2020. "Machine scheduling with soft precedence constraints," European Journal of Operational Research, Elsevier, vol. 282(2), pages 491-505.
    10. 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.
    11. Gómez Sánchez, Mariam & Lalla-Ruiz, Eduardo & Fernández Gil, Alejandro & Castro, Carlos & Voß, Stefan, 2023. "Resource-constrained multi-project scheduling problem: A survey," European Journal of Operational Research, Elsevier, vol. 309(3), pages 958-976.
    12. Lenstra, J. K. & Rinnooy Kan, A. H. G., 1980. "An Introduction To Multiprocessor Scheduling," Econometric Institute Archives 272258, Erasmus University Rotterdam.
    13. José R. Correa & Andreas S. Schulz, 2005. "Single-Machine Scheduling with Precedence Constraints," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 1005-1021, November.
    14. Keqin Li, 1999. "Analysis of the List Scheduling Algorithm for Precedence Constrained Parallel Tasks," Journal of Combinatorial Optimization, Springer, vol. 3(1), pages 73-88, July.
    15. Katarina Cechlarova & Bettina Klaus & David F.Manlove, 2018. "Pareto optimal matchings of students to courses in the presence of prerequisites," Cahiers de Recherches Economiques du Département d'économie 16.04, Université de Lausanne, Faculté des HEC, Département d’économie.
    16. Yuan, J.J. & Lin, Y.X. & Ng, C.T. & Cheng, T.C.E., 2007. "Approximability of single machine scheduling with fixed jobs to minimize total completion time," European Journal of Operational Research, Elsevier, vol. 178(1), pages 46-56, April.
    17. Ahadi, Khatereh & Sullivan, Kelly M. & Mitchell, Kenneth Ned, 2018. "Budgeting maintenance dredging projects under uncertainty to improve the inland waterway network performance," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 119(C), pages 63-87.
    18. José R. Correa & Martin Skutella & José Verschae, 2012. "The Power of Preemption on Unrelated Machines and Applications to Scheduling Orders," Mathematics of Operations Research, INFORMS, vol. 37(2), pages 379-398, May.
    19. D. Prot & O. Bellenguez-Morineau, 2018. "A survey on how the structure of precedence constraints may change the complexity class of scheduling problems," Journal of Scheduling, Springer, vol. 21(1), pages 3-16, February.
    20. Felix Happach, 2021. "Makespan minimization with OR-precedence constraints," Journal of Scheduling, Springer, vol. 24(3), pages 319-328, 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:jcomop:v:1:y:1998:i:4:d:10.1023_a:1009794729459. 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.