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A primal–dual online algorithm for the k-server problem on weighted HSTs

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Abstract

In this paper, we show that there is a \(\frac{5}{2}\ell \cdot \ln (1+k)\)-competitive randomized algorithm for the k-sever problem on weighted Hierarchically Separated Trees (HSTs) with depth \(\ell \) when \(n=k+1\) where n is the number of points in the metric space, which improved previous best competitive ratio \(12 \ell \ln (1+4\ell (1+k))\) by Bansal et al. (FOCS, pp 267–276, 2011).

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Acknowledgements

We would like to thank the anonymous referees for their careful readings of the manuscripts and many useful suggestions. Wenbin Chen’s research has been partly supported by the National Natural Science Foundation of China (NSFC) under Grant No.11271097, Program for Innovative Research Team in Education Department of Guangdong Province Under Grant No.2015KCXTD014. and No. 2016KCXTD017 and the project KFKT2012B01 from State Key Laboratory for Novel Software Technology, Nanjing University. FuFang Li’s work had been co-financed by: Natural Science Foundation of China under Grant No.61472092; Guangdong Provincial Science and Technology Plan Project under Grant No. 2013B010401037; and GuangZhou Municipal High School Science Research Fund under Grant No.1201421317. Jianxiong Wang’s research was partially supported under Foundation for Distinguished Young Talents in Higher Education of Guangdong (2012WYM0105 and 2012LYM0105) and Funding Program for Research Development in Institutions of Higher Learning Under the Jurisdiction of Guangzhou Municipality (2012A143). Maobin Tang’s research has been supported under Guangdong Province’s Science and Technology Projects under Grant No. 2012A020602065 and the research project of Guangzhou education bureau under Grant No. 2012A075. Ke Qi’s research has been supported by the Guangzhou Science and Technology Plan Project under Grant No. 201605061403261 and 2014 State Scholarship Fund (201408440338). Xiuni Wang’s research has been supported by the National Natural Science Foundation of China (NSFC) under Grant No.61302061.

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Authors and Affiliations

  1. Department of Computer Science and Guangdong Provincial Engineering Technology Research Center for Mathematical Educational Software, Guangzhou University, Guangzhou, People’s Republic of China

    Wenbin Chen, Fufang Li, Jianxiong Wang, Ke Qi, Maobin Tang & Xiuni Wang

  2. State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, People’s Republic of China

    Wenbin Chen

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  1. Wenbin Chen
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Correspondence to Wenbin Chen.

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Chen, W., Li, F., Wang, J. et al. A primal–dual online algorithm for the k-server problem on weighted HSTs. J Comb Optim 34, 1133–1146 (2017). https://doi.org/10.1007/s10878-017-0135-z

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