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Approximation Algorithms for Two Parallel Dedicated Machine Scheduling with Conflict Constraints

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Combinatorial Optimization and Applications (COCOA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13135))

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Abstract

We investigate two parallel dedicated machine scheduling with conflict constraints. The problem of minimizing the makespan has been shown to be NP-hard in the strong sense under the assumption that the processing sequence of jobs on one machine is given and fixed a priori. The problem without any fixed sequence was previously recognized as weakly NP-hard. In this paper, we first present a \(\frac{9}{5}\)-approximation algorithm for the problem with a fixed sequence. Then we show that the tight approximation ratios of the algorithm are \(\frac{7}{4}\) and \(\frac{5}{3}\) for two subproblems which remain strongly NP-hard. We also send an improved algorithm with approximation ratio \(3-\sqrt{2} \approx 1.586\) for one subproblem. Finally, we prove that the problem without any fixed sequence is actually strongly NP-hard, and design a \(\frac{5}{3}\)-approximation algorithm to solve it.

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Acknowledgements

This research is supported by the Zhejiang Provincial NSF Grant LY21A010014 and the NSFC Grants 11771114, 11971139.

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Authors and Affiliations

  1. Department of Mathematics, Hangzhou Dianzi University, Hangzhou, 310018, China

    An Zhang, Liang Zhang, Yong Chen & Xing Wang

  2. Taizhou University, Linhai, 317000, China

    Guangting Chen

Authors
  1. An Zhang
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  2. Liang Zhang
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  3. Yong Chen
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  4. Guangting Chen
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  5. Xing Wang
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Corresponding authors

Correspondence to An Zhang or Guangting Chen .

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Editors and Affiliations

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

    Ding-Zhu Du

  2. University of New Brunswick, Fredericton, NB, Canada

    Donglei Du

  3. Tianjin University of Technology, Tianjin, China

    Chenchen Wu

  4. Beijing University of Technology, Beijing, China

    Dachuan Xu

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Zhang, A., Zhang, L., Chen, Y., Chen, G., Wang, X. (2021). Approximation Algorithms for Two Parallel Dedicated Machine Scheduling with Conflict Constraints. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Combinatorial Optimization and Applications. COCOA 2021. Lecture Notes in Computer Science(), vol 13135. Springer, Cham. https://doi.org/10.1007/978-3-030-92681-6_10

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  • DOI: https://doi.org/10.1007/978-3-030-92681-6_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-92680-9

  • Online ISBN: 978-3-030-92681-6

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