Bipartite matching, where agents on one side of a market are matched to agents or items on the other, is a classical problem in computer science and economics, with widespread application in healthcare, education, advertising, and general resource allocation. A practitioner’s goal is typically to maximize a matching market’s economic efficiency, possibly subject to some fairness requirements that promote equal access to resources. A natural balancing act exists between fairness and efficiency in matching markets, and has been the subject of much research. In this paper, we study a complementary goal—balancing diversity and efficiency—in a generalization of bipartite matching where agents on one side of the market can be matched to sets of agents on the other. Adapting a classical definition of the diversity of a set, we propose a quadratic programming-based approach to solving a super-modular minimization problem that balances diversity and total weight of the solution. We also provide a scalable greedy algorithm with theoretical performance bounds. We then define the price of diversity, a measure of the efficiency loss due to enforcing diversity, and give a worst-case theoretical bound. Finally, we demonstrate the efficacy of our methods on three real-world datasets, and show that the price of diversity is not bad in practice. Our code is publicly accessible for further research.


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  author    = {Faez Ahmed, John P. Dickerson, Mark Fuge},
  title     = {Diverse Weighted Bipartite b-Matching},
  booktitle = {Proceedings of the Twenty-Sixth International Joint Conference on
               Artificial Intelligence, {IJCAI-17}},
  pages     = {35--41},
  year      = {2017},
  doi       = {10.24963/ijcai.2017/6},
  url       = {https://doi.org/10.24963/ijcai.2017/6},