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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
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    Citations

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    Cited by:

    1. 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.
    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. 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.
    4. 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.
    5. 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.

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