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Edge-Weighted Online Windowed Matching

Author

Listed:
  • Itai Ashlagi

    (Management Science and Engineering Department, Stanford University, Stanford, California 94305)

  • Maximilien Burq

    (Verily Life Sciences LLC, South San Francisco, California 94080)

  • Chinmoy Dutta

    (Turing Research Inc., Mountain View, California 94040)

  • Patrick Jaillet

    (Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Amin Saberi

    (Management Science and Engineering Department, Stanford University, Stanford, California 94305)

  • Chris Sholley

    (Lyft, San Francisco, California 94107)

Abstract

Consider a matching problem, in which agents arrive to a marketplace over time and leave after some time periods. Agents can only be matched while present in the marketplace. Each pair of agents can yield a different match value, and a social planner seeks to maximize the total value from matches over a finite time horizon. First we study the case in which vertices arrive in an adversarial order. For the case when agents depart in the order of arrival, we provide a randomized 1 / 4 -competitive algorithm. When departure times are drawn independently from a distribution with nondecreasing hazard rate, we establish a 1 / 8 -competitive algorithm. When the arrival order is chosen uniformly at random and agents leave after a fixed number of time periods, a batching algorithm, which computes a maximum-weighted matching periodically, is shown to be 0.279-competitive.

Suggested Citation

  • Itai Ashlagi & Maximilien Burq & Chinmoy Dutta & Patrick Jaillet & Amin Saberi & Chris Sholley, 2023. "Edge-Weighted Online Windowed Matching," Mathematics of Operations Research, INFORMS, vol. 48(2), pages 999-1016, May.
    • Handle: RePEc:inm:ormoor:v:48:y:2023:i:2:p:999-1016
    DOI: 10.1287/moor.2022.1289
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