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Algorithmica

, Volume 80, Issue 4, pp 1357–1382 | Cite as

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).

Keywords

Unrelated scheduling Restricted assignment Configuration LP Integrality gap Estimation algorithm 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Institute of Computer ScienceUniversity of KielKielGermany

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