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An EPTAS for Scheduling on Unrelated Machines of Few Different Types

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10389)

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 Open image in new window , 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.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Christian-Albrechts-Universität zu KielKielGermany

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