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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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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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