IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v47y1998i1p59-82.html
   My bibliography  Save this article

Thek-partitioning problem

Author

Listed:
  • Luitpold Babel
  • Hans Kellerer
  • Vladimir Kotov

Abstract

Thek-partitioning problem is defined as follows: Given a set of items {I 1 ,I 2 ,...,I n } where itemIj is of weightwj ≥ 0, find a partitionS 1 ,S 2 ,...,S m of this set with ¦S i ¦ =k such that the maximum weight of all subsetsS i is minimal,k-partitioning is strongly related to the classical multiprocessor scheduling problem of minimizing the makespan on identical machines. This paper provides suitable tools for the construction of algorithms which solve exactly the problem. Several approximation algorithms are presented for this NP-hard problem. The worst-case behavior of the algorithms is analyzed. The best of these algorithms achieves a performance bound of 4/3. Copyright Physica-Verlag 1998

Suggested Citation

  • Luitpold Babel & Hans Kellerer & Vladimir Kotov, 1998. "Thek-partitioning problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(1), pages 59-82, February.
    • Handle: RePEc:spr:mathme:v:47:y:1998:i:1:p:59-82
    DOI: 10.1007/BF01193837
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/BF01193837
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/BF01193837?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.

    Citations

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


    Cited by:

    1. Alexander Lawrinenko & Stefan Schwerdfeger & Rico Walter, 2018. "Reduction criteria, upper bounds, and a dynamic programming based heuristic for the max–min $$k_i$$ k i -partitioning problem," Journal of Heuristics, Springer, vol. 24(2), pages 173-203, April.
    2. Guajardo, Mario & Rönnqvist, Mikael, 2015. "Operations research models for coalition structure in collaborative logistics," European Journal of Operational Research, Elsevier, vol. 240(1), pages 147-159.
    3. Shi Ping Chen & Yong He & Guohui Lin, 2002. "3-Partitioning Problems for Maximizing the Minimum Load," Journal of Combinatorial Optimization, Springer, vol. 6(1), pages 67-80, March.
    4. Elif Akçalı & Alper Üngör & Reha Uzsoy, 2005. "Short‐term capacity allocation problem with tool and setup constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(8), pages 754-764, December.
    5. Dell'Amico, Mauro & Iori, Manuel & Martello, Silvano & Monaci, Michele, 2006. "Lower bounds and heuristic algorithms for the ki-partitioning problem," European Journal of Operational Research, Elsevier, vol. 171(3), pages 725-742, 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:mathme:v:47:y:1998:i:1:p:59-82. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.