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Online bottleneck matching on a line

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Abstract

We study the online bottleneck matching problem on a line, which is to match a sequence of m requests arriving one-by-one in an online fashion to a given set of m servers, such that each server is matched exactly once and the maximum distance between any request and its server is minimized. When the distances between any two adjacent servers are the same, we present an optimal online algorithm with a competitive ratio of \(m+1\). When \(m=3\), we present an optimal online algorithm whose competitive ratio is determined by the relative distance between adjacent servers and no more than \(3+\sqrt{2}\), which matches the previous best lower bound proposed thirty years ago.

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No datasets were generated or analyzed during the current study.

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Acknowledgements

We thank the anonymous reviewers for their valuable comments and constructive suggestions, which helped us significantly improve the quality of our work.

Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 12071417) and Postgraduate Research and Innovation Foundation of Yunnan University (KC-22223092).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Yunnan University, Kunming, 650504, China

    Man Xiao, Shu Zhao & Weidong Li

  2. Dianchi College, Kunming, 650228, China

    Jinhua Yang

Authors
  1. Man Xiao
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  2. Shu Zhao
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  3. Weidong Li
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  4. Jinhua Yang
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Contributions

MX proposed the methods, and wrote the manuscript; SZ proposed some ideas and proved some theorems. WL proposed the problem, checked the proofs and modified the manuscript. JY provided suggestions for the methods and reviewed the manuscript; All authors have read and agreed to the published version of the manuscript.

Corresponding author

Correspondence to Weidong Li.

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The preliminary result of this paper has been published in the proceedings of the 15th Annual International Conference on Combinatorial Optimization and Applications.

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Xiao, M., Zhao, S., Li, W. et al. Online bottleneck matching on a line. J Comb Optim 45, 108 (2023). https://doi.org/10.1007/s10878-023-01036-3

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  • DOI: https://doi.org/10.1007/s10878-023-01036-3

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