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Online Bipartite Matching via Smoothness

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  • Jason Hartline

Abstract

The online bipartite matching problem has offline buyers desiring to be matched to online items. The analysis of online bipartite matching of Eden et al. (2021) is a smoothness proof (Syrgkanis and Tardos, 2013). Moreover, it can be interpreted as combining a $\lambda = 1-1/e$ value covering (which holds for single-dimensional agents and randomized auctions) and $\mu = 1$ revenue covering (Hartline et al., 2014). Note that value covering is a fact about single-dimensional agents and has nothing to do with the underlying feasibility setting. Thus, the essential new result from Eden et al. (2021) is that online bipartite matching is $\mu=1$ revenue covered. A number of old and new observations follow from this perspective.

Suggested Citation

  • Jason Hartline, 2022. "Online Bipartite Matching via Smoothness," Papers 2203.13140, arXiv.org, revised Jul 2023.
    • Handle: RePEc:arx:papers:2203.13140
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