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A note on \({\mathbb {NP}}\)-hardness of preemptive mean flow-time scheduling for parallel machines

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Abstract

In the paper “The complexity of mean flow time scheduling problems with release times”, by Baptiste, Brucker, Chrobak, Dürr, Kravchenko and Sourd, the authors claimed to prove strong \({\mathbb {NP}}\)-hardness of the scheduling problem \(P|{\textit{pmtn}},r_j|\sum C_j\), namely multiprocessor preemptive scheduling where the objective is to minimize the mean flow time. We point out a serious error in their proof and give a new proof of strong \({\mathbb {NP}}\)-hardness for this problem.

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References

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Acknowledgments

M. Chrobak was partially supported by National Science Foundation Grant CCF-1217314. The authors would like to thank anonymous reviewers for many useful comments and suggestions.

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Authors and Affiliations

  1. École des Mines de Nantes, IRCCyN UMR CNRS 6597 (Institut de Recherche en Communication et en Cybernétique de Nantes), LUNAM Université, 4 rue Alfred Kastler, La Chantrerie, BP 20722, 44307 , Nantes Cedex 3, France

    Odile Bellenguez-Morineau & Damien Prot

  2. Computer Science Department, University of California, Riverside, CA , 92521, USA

    Marek Chrobak

  3. CNRS, LIP6, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 , Paris Cedex 05, France

    Christoph Dürr

Authors
  1. Odile Bellenguez-Morineau
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  2. Marek Chrobak
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  3. Christoph Dürr
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  4. Damien Prot
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Corresponding author

Correspondence to Damien Prot.

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Bellenguez-Morineau, O., Chrobak, M., Dürr, C. et al. A note on \({\mathbb {NP}}\)-hardness of preemptive mean flow-time scheduling for parallel machines. J Sched 18, 299–304 (2015). https://doi.org/10.1007/s10951-014-0380-2

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  • DOI: https://doi.org/10.1007/s10951-014-0380-2

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