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On-line Single Machine Scheduling with Release Dates and Submodular Rejection Penalties

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Algorithmic Aspects in Information and Management (AAIM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13513))

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Abstract

In this paper, we consider the on-line single machine scheduling problem with release dates and submodular rejection penalties. We are given a single machine and a sequence of jobs that arrive on-line and must be immediately and irrevocably either assigned on the machine or rejected. The objective is to minimize the sum of the makespan of the accepted jobs and the penalty of the rejected jobs which is determined by a submodular function. We prove that there is no on-line algorithm with a constant competitive ratio if the penalty submodular function is nonmonotone. When the penalty submodular function is monotone, we present an on-line algorithm with a competitive ratio 3.

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Acknowledgements

The work is supported in part by the National Natural Science Foundation of China [No. 12071417], and National Key R &D Program of China [No. 2020AAA 0105200].

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Authors and Affiliations

  1. School of Information Science and Engineering, Yunnan University, Kunming, People’s Republic of China

    Xiaofei Liu

  2. School of Electronic Engineering and Computer Science, Peking University, Beijing, People’s Republic of China

    Yaoyu Zhu

  3. School of Mathematics and Statistics, Yunnan University, Kunming, People’s Republic of China

    Weidong Li

  4. Beijing Academy of Artificial Intelligence, Beijing, People’s Republic of China

    Lei Ma

  5. National Biomedical Imaging Center, Peking University, Beijing, People’s Republic of China

    Lei Ma

Authors
  1. Xiaofei Liu
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  2. Yaoyu Zhu
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  3. Weidong Li
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  4. Lei Ma
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Corresponding author

Correspondence to Lei Ma .

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Editors and Affiliations

  1. Guangdong University of Technology, Guangzhou, China

    Qiufen Ni

  2. University of Texas at Dallas, Richardson, TX, USA

    Weili Wu

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Liu, X., Zhu, Y., Li, W., Ma, L. (2022). On-line Single Machine Scheduling with Release Dates and Submodular Rejection Penalties. In: Ni, Q., Wu, W. (eds) Algorithmic Aspects in Information and Management. AAIM 2022. Lecture Notes in Computer Science, vol 13513. Springer, Cham. https://doi.org/10.1007/978-3-031-16081-3_6

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  • DOI: https://doi.org/10.1007/978-3-031-16081-3_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-16080-6

  • Online ISBN: 978-3-031-16081-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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