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Comments on “Competitive analysis of a better on-line algorithm to minimize total completion time on a single-machine”

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Abstract

For the single machine scheduling problem of minimizing the total completion time, Montoya Torres (J Glob Opt 27:97–103, 2003) presented a semi-online algorithm under the assumption that release dates are known in advance, and showed that it was \({\sqrt{3}}\)-competitive. However, there are flaws in the proof, and the conclusion about the competitive ratio is not correct. In this note, we show that the semi-online algorithm cannot perform better than the best non-clairvoyant online algorithm with a competitive ratio of 2.

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References

  1. Montoya Torres J.R.: Competitive analysis of a better on-line algorithm to minimize total completion time on a single-machine. J. Glob. Opt. 27(1), 97–103 (2003)

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Authors and Affiliations

  1. Department of Automation, Shanghai Jiao Tong University, Shanghai, China

    Jiping Tao, Zhijun Chao & Yugeng Xi

Authors
  1. Jiping Tao
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  2. Zhijun Chao
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  3. Yugeng Xi
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Corresponding author

Correspondence to Yugeng Xi.

Additional information

This work is supported by National Science Foundation of China (Grant No. 60934007) and Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20070248004).

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Tao, J., Chao, Z. & Xi, Y. Comments on “Competitive analysis of a better on-line algorithm to minimize total completion time on a single-machine”. J Glob Optim 49, 359–362 (2011). https://doi.org/10.1007/s10898-010-9549-1

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  • DOI: https://doi.org/10.1007/s10898-010-9549-1

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