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An EPTAS for Scheduling on Unrelated Machines of Few Different Types

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Algorithms and Data Structures (WADS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10389))

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Abstract

In the classical problem of scheduling on unrelated parallel machines, a set of jobs has to be assigned to a set of machines. The jobs have a processing time depending on the machine and the goal is to minimize the makespan, that is, the maximum machine load. It is well known that this problem is NP-hard and does not allow polynomial time approximation algorithms with approximation guarantees smaller than 1.5, unless P\(=\)NP. We consider the case that there is only a constant number K of machine types. Two machines have the same type, if all jobs have the same processing time for them. We present an efficient polynomial time approximation scheme (EPTAS) for this problem, that is, for any \(\varepsilon > 0\) an assignment with makespan of length at most \((1+\varepsilon )\) times the optimum can be found in polynomial time in the input length and the exponent is independent of \(1/\varepsilon \). In particular we achieve a running time of , where |I| denotes the input length. Furthermore, we study the case where the minimum machine load has to be maximized and achieve a similar result.

This work was partially supported by the German Research Foundation (DFG) project JA 612/16-1.

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Authors and Affiliations

  1. Christian-Albrechts-Universität zu Kiel, 24118, Kiel, Germany

    Klaus Jansen & Marten Maack

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  1. Klaus Jansen
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  2. Marten Maack
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Correspondence to Marten Maack .

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Editors and Affiliations

  1. Computer Science, University of Toronto , Toronto, Ontario, Canada

    Faith Ellen

  2. Computer Science, Memorial University of Newfoundland , St. John’s, Newfoundland and Labrador, Canada

    Antonina Kolokolova

  3. Carleton University, Ottawa, Ontario, Canada

    Jörg-Rüdiger Sack

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Jansen, K., Maack, M. (2017). An EPTAS for Scheduling on Unrelated Machines of Few Different Types. In: Ellen, F., Kolokolova, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2017. Lecture Notes in Computer Science(), vol 10389. Springer, Cham. https://doi.org/10.1007/978-3-319-62127-2_42

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  • DOI: https://doi.org/10.1007/978-3-319-62127-2_42

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  • Print ISBN: 978-3-319-62126-5

  • Online ISBN: 978-3-319-62127-2

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