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Estimating the Makespan of the Two-Valued Restricted Assignment Problem

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Abstract

We consider a special case of the scheduling problem on unrelated machines, namely the restricted assignment problem with two different processing times. We show that the configuration LP has an integrality gap of at most \(\frac{5}{3} \approx 1.667\) for this problem. This allows us to estimate the optimal makespan within a factor of \(\frac{5}{3}\), improving upon the previously best known estimation algorithm with ratio \(\frac{11}{6} \approx 1.833\) due to Chakrabarty et al. (in: Proceedings of the twenty-sixth annual ACM-SIAM symposium on discrete algorithms (SODA 2015), pp 1087–1101, 2015).

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Authors and Affiliations

  1. Institute of Computer Science, University of Kiel, 24118, Kiel, Germany

    Klaus Jansen, Kati Land & Marten Maack

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  1. Klaus Jansen
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  2. Kati Land
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  3. Marten Maack
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Corresponding author

Correspondence to Kati Land.

Additional information

Research was supported by German Research Foundation (DFG) Project JA 612/15-1.

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Jansen, K., Land, K. & Maack, M. Estimating the Makespan of the Two-Valued Restricted Assignment Problem. Algorithmica 80, 1357–1382 (2018). https://doi.org/10.1007/s00453-017-0314-4

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  • DOI: https://doi.org/10.1007/s00453-017-0314-4

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