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Online bottleneck matching

Author

Listed:
  • Barbara M. Anthony

    (Southwestern University)

  • Christine Chung

    (Connecticut College)

Abstract

We consider the online bottleneck matching problem, where $$k$$ server-vertices lie in a metric space and $$k$$ request-vertices that arrive over time each must immediately be permanently assigned to a server-vertex. The goal is to minimize the maximum distance between any request and its server. Because no algorithm can have a competitive ratio better than $$O(k)$$ for this problem, we use resource augmentation analysis to examine the performance of three algorithms: the naive Greedy algorithm, Permutation, and Balance. We show that while the competitive ratio of Greedy improves from exponential (when each server-vertex has one server) to linear (when each server-vertex has two servers), the competitive ratio of Permutation remains linear when an extra server is introduced at each server-vertex. The competitive ratio of Balance is also linear with an extra server at each server-vertex, even though it has been shown that an extra server makes it constant-competitive for the min-weight matching problem.

Suggested Citation

  • Barbara M. Anthony & Christine Chung, 2014. "Online bottleneck matching," Journal of Combinatorial Optimization, Springer, vol. 27(1), pages 100-114, January.
    • Handle: RePEc:spr:jcomop:v:27:y:2014:i:1:d:10.1007_s10878-012-9581-9
    DOI: 10.1007/s10878-012-9581-9
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    Cited by:

    1. 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.
    2. David Bergman & Jason Imbrogno, 2017. "Surviving a National Football League Survivor Pool," Operations Research, INFORMS, vol. 65(5), pages 1343-1354, October.
    3. Li, Jianbin & Zheng, Yuting & Dai, Bin & Yu, Jiang, 2020. "Implications of matching and pricing strategies for multiple-delivery-points service in a freight O2O platform," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 136(C).
    4. 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.

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