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Thek-partitioning problem

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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.

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References

  1. Chen B (1993) A note on LPT scheduling. Op. Res. Letters 14:139–142

    Google Scholar 

  2. Coffman EG Jr, Garey MR, Johnson DS(1978) An application of bin-packing to multiprocessor scheduling. SIAM J. Comput. 7:1–17

    Google Scholar 

  3. Garey MR, Johnson DS (1979) Computers and intractability: A guide to the theory of NP-completeness. Freeman, San Francisco

    Google Scholar 

  4. Graham RL (1966) Bounds for certain multiprocessing anomalies. Bell System Tech. 45:1563–1581

    Google Scholar 

  5. Graham RL (1969) Bounds on multiprocessing timing anomalies. SIAM J. Appl. Math. 17:263–269

    Google Scholar 

  6. Kellerer H, Kotov V, A 7/6 approximation algorithm for 3-partitioning and its application to multiprocessor scheduling. Submitted for publication

  7. Kellerer H, Woeginger G (1993) A tight bound for 3-partitioning. Discr. Appl. Math. 45:249–259

    Google Scholar 

  8. EL Lawler EL Lenstra JK, Rinnoy Kan AHG, Shmoys DB (1993) Sequencing and scheduling: Algorithms and complexity. In: Handbook of Operations Research, volume 4, North-Holland, Amsterdam, pp. 445–552

    Google Scholar 

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Authors and Affiliations

  1. Institut für Mathematik, Technische Universität München, Arcisstraße 21, D-80290, München, Germany

    Luitpold Babel

  2. Institut für Statistik, Ökonometrie und Operations Research, Universität Graz, Universitätsstraße 15, A-8010, Graz, Austria

    Hans Kellerer

  3. Faculty of Applied Mathematics and Computer Science, University of Minsk, 220080, Minsk, Byelarussia

    Vladimir Kotov

Authors
  1. Luitpold Babel
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  2. Hans Kellerer
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  3. Vladimir Kotov
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Babel, L., Kellerer, H. & Kotov, V. Thek-partitioning problem. Mathematical Methods of Operations Research 47, 59–82 (1998). https://doi.org/10.1007/BF01193837

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  • DOI: https://doi.org/10.1007/BF01193837

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