An EPTAS for Scheduling on Unrelated Machines of Few Different Types

Jansen, Klaus and Maack, Marten (2017) An EPTAS for Scheduling on Unrelated Machines of Few Different Types Cornell University Library .

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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 are only a constant number K of machine types. Two machines have the same type if all jobs have the same processing time for them. This variant of the problem is strongly NP-hard already for K=1. We present an efficient polynomial time approximation scheme (EPTAS) for the problem, that is, for any ε>0 an assignment with makespan of length at most (1+ε) times the optimum can be found in polynomial time in the input length and the exponent is independent of 1/ε. In particular we achieve a running time of 2(Klog(K)1εlog41ε)+poly(|I|), where |I| denotes the input length. Furthermore, we study three other problem variants and present an EPTAS for each of them: The Santa Claus problem, where the minimum machine load has to be maximized; the case of scheduling on unrelated parallel machines with a constant number of uniform types, where machines of the same type behave like uniformly related machines; and the multidimensional vector scheduling variant of the problem where both the dimension and the number of machine types are constant. For the Santa Claus problem we achieve the same running time. The results are achieved, using mixed integer linear programming and rounding techniques.

Document Type: Article
Research affiliation: Kiel University > Kiel Marine Science
OceanRep > The Future Ocean - Cluster of Excellence
Kiel University
Refereed: Yes
Date Deposited: 19 Dec 2017 10:28
Last Modified: 19 Dec 2017 12:50

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