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.

## 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 |
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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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