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Online bottleneck matching on a line

Author

Listed:
  • Man Xiao

    (Yunnan University)

  • Shu Zhao

    (Yunnan University)

  • Weidong Li

    (Yunnan University)

  • Jinhua Yang

    (Dianchi College)

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 $$m+1$$ m + 1 . When $$m=3$$ m = 3 , we present an optimal online algorithm whose competitive ratio is determined by the relative distance between adjacent servers and no more than $$3+\sqrt{2}$$ 3 + 2 , which matches the previous best lower bound proposed thirty years ago.

Suggested Citation

  • Man Xiao & Shu Zhao & Weidong Li & Jinhua Yang, 2023. "Online bottleneck matching on a line," Journal of Combinatorial Optimization, Springer, vol. 45(4), pages 1-17, May.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:4:d:10.1007_s10878-023-01036-3
    DOI: 10.1007/s10878-023-01036-3
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    References listed on IDEAS

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    1. Barbara M. Anthony & Christine Chung, 2016. "Serve or skip: the power of rejection in online bottleneck matching," Journal of Combinatorial Optimization, Springer, vol. 32(4), pages 1232-1253, November.
    2. Barbara M. Anthony & Christine Chung, 2014. "Online bottleneck matching," Journal of Combinatorial Optimization, Springer, vol. 27(1), pages 100-114, January.
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