A PTAS for Scheduling Unrelated Machines of Few Different Types

Gehrke, Jan Clemens, Jansen, Klaus, Kraft, Stefan E. J. and Schikowski, Jakob (2018) A PTAS for Scheduling Unrelated Machines of Few Different Types International Journal of Foundations of Computer Science, 29 (04). pp. 591-621. DOI 10.1142/S0129054118410071.

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Abstract

Scheduling on Unrelated Machines is a classical optimization problem where n jobs have to be distributed to m machines. Each of the jobs j ∈ {1,...,n} has on machine i ∈ {1,...,m} a processing time pij ≥ 0. The goal is to minimize the makespan, i.e., the maximum completion time of the longest-running machine. Unless P = NP, this problem does not allow for a polynomial-time approximation algorithm with a ratio better than 3 2. A natural scenario is however that many machines are of the same type, like a CPU and GPU cluster: for each of the K machine types, the machines i 6= i0 of the same type k satisfy pij = pi0j for all jobs j. For the case where the number K of machine types is constant, this paper presents an approximation scheme, i.e., an algorithm of approximation ratio 1 + ε for ε > 0, with an improved running time only single exponential in 1 ε.

Document Type: Article
Keywords: Scheduling on Unrelated Machines; Scheduling on Unrelated Machines of few different types; Polynomial Time Approximation Scheme; PTAS; Approximation algorithm; single exponential in approximation ratio.
Research affiliation: Kiel University > Kiel Marine Science
OceanRep > The Future Ocean - Cluster of Excellence
Kiel University
Refereed: Yes
DOI etc.: 10.1142/S0129054118410071
ISSN: 0129-0541
Projects: Future Ocean
Date Deposited: 01 Aug 2018 09:09
Last Modified: 13 Mar 2019 09:32
URI: http://eprints.uni-kiel.de/id/eprint/43884

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