Online Bipartite Matching via Smoothness

TL;DR

This paper analyzes online bipartite matching using a smoothness framework, revealing new insights into its revenue covering properties and connecting it with value covering concepts.

Contribution

It provides a novel interpretation of online bipartite matching as a revenue covering problem, extending the smoothness analysis framework.

Findings

Online bipartite matching is shown to be 1-revenue covered.

The analysis connects value covering with the feasibility setting.

New observations follow from the smoothness perspective.

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.