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In bipartite matching problems, vertices on one side of a bipartite graph arepaired with those on the other. In its online variant, one side of the graph isavailable offline, while the vertices on the other side arrive online. When avertex arrives, an irrevocable and immediate decision should be made by thealgorithm; either match it to an available vertex or drop it. Examples of suchproblems include matching workers to firms, advertisers to keywords, organs topatients, and so on. Much of the literature focuses on maximizing the totalrelevance---modeled via total weight---of the matching. However, in manyreal-world problems, it is also important to consider contributions ofdiversity: hiring a diverse pool of candidates, displaying a relevant butdiverse set of ads, and so on. In this paper, we propose the Online SubmodularBipartite Matching (\osbm) problem, where the goal is to maximize a submodularfunction $f$ over the set of matched edges. This objective is general enough tocapture the notion of both diversity (\emph{e.g.,} a weighted coveragefunction) and relevance (\emph{e.g.,} the traditional linear function)---aswell as many other natural objective functions occurring in practice(\emph{e.g.,} limited total budget in advertising settings). We propose novelalgorithms that have provable guarantees and are essentially optimal whenrestricted to various special cases. We also run experiments on real-world andsynthetic datasets to validate our algorithms.

Balancing Relevance and Diversity in Online Bipartite Matching via Submodularity