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Better permutations for the single-processor scheduling with time restrictions

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Abstract

In this paper, we consider single-processor scheduling with time restrictions. Given a fixed integer \(B\ge 2\) and a set of jobs, we need to schedule the jobs sequentially on a single processor subject to the following B-constraint. For any real x, no unit time interval \([x, x+1)\) is allowed to intersect more than B jobs. We show that there exists a permutation of the jobs which can be processed within a factor of \(\frac{5}{4}\) of the optimum (plus an additional small constant) when \(B\ge 5\) and this factor is best possible. When \(B=3, 4\), the corresponding factor equals \(\frac{B}{B-1}\). Furthermore, we present an asymptotically optimal permutation for \(B=2\). The results for \(B\ge 4\) improve the previous work on this problem.

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Acknowledgments

The authors would like to acknowledge the anonymous referees for their careful reading of our paper and their valuable comments.

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Authors and Affiliations

  1. Department of Mathematics, Hangzhou Dianzi University, Hangzhou, 310018, People’s Republic of China

    An Zhang, Feilang Ye & Yong Chen

  2. Taizhou University, Linhai, 317000, Zhejiang, People’s Republic of China

    Guangting Chen

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  1. An Zhang
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  2. Feilang Ye
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  3. Yong Chen
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  4. Guangting Chen
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Corresponding authors

Correspondence to An Zhang or Guangting Chen.

Additional information

Supported by the National Natural Science Foundation of China (11201105) and the Zhejiang Provincial Natural Science Foundation of China (LY16A010015). Supported by the National Natural Science Foundation of China (11401149). Supported by the National Natural Science Foundation of China (11571252).

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Zhang, A., Ye, F., Chen, Y. et al. Better permutations for the single-processor scheduling with time restrictions. Optim Lett 11, 715–724 (2017). https://doi.org/10.1007/s11590-016-1038-0

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  • DOI: https://doi.org/10.1007/s11590-016-1038-0

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