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Learn from history for online bipartite matching

Author

Listed:
  • Huili Zhang

    (Xi’an Jiaotong University)

  • Rui Du

    (Xi’an Jiaotong University)

  • Kelin Luo

    (University of Bonn)

  • Weitian Tong

    (Georgia Southern University)

Abstract

Motivated by various applications in the online platforms for ride-hailing and crowd-sourcing delivery, we study the edge-weighted online bipartite matching (EWOBM) problem. We assume a part of online vertices are released in advance to mimic historical information that the algorithm is able to access. Different from traditional approaches that usually learn informative distributions from large enough history sets, our algorithms enable to extra useful information for the history set of any size. When the online vertices arrive in a random order, we present an online algorithm, named as h -TP-OM, achieving a competitive ratio that increases as more historical information is considered. However, once enough historical information has been fed to the algorithm, additional historical information becomes useless. Based on h -TP-OM, we then propose a time-efficient greedy heuristic, named as h -TP-G, which even has better performances in applications, particularly on large-scale instances. When the arrival order of online vertices is determined by an adversary, we present another greedy heuristic algorithm, named as Greedy-RT. Experiments on both synthetic and real-world datasets are conducted to evaluate the practical performances of the proposed algorithms. The experiment results demonstrate the usefulness of historical information for both h -TP-OM and h -TP-G, and also show the time efficiency of h -TP-G and Greedy-RT.

Suggested Citation

  • Huili Zhang & Rui Du & Kelin Luo & Weitian Tong, 2022. "Learn from history for online bipartite matching," Journal of Combinatorial Optimization, Springer, vol. 44(5), pages 3611-3640, December.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:5:d:10.1007_s10878-022-00916-4
    DOI: 10.1007/s10878-022-00916-4
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    References listed on IDEAS

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    1. Patrick Jaillet & Xin Lu, 2014. "Online Stochastic Matching: New Algorithms with Better Bounds," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 624-646, August.
    2. H. W. Kuhn, 1955. "The Hungarian method for the assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 2(1‐2), pages 83-97, March.
    3. Vahideh H. Manshadi & Shayan Oveis Gharan & Amin Saberi, 2012. "Online Stochastic Matching: Online Actions Based on Offline Statistics," Mathematics of Operations Research, INFORMS, vol. 37(4), pages 559-573, November.
    4. Xiaoming Sun & Jia Zhang & Jialin Zhang, 2017. "Near optimal algorithms for online weighted bipartite matching in adversary model," Journal of Combinatorial Optimization, Springer, vol. 34(3), pages 689-705, October.
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