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We consider the problem of assigning items to platforms in the presence ofgroup fairness constraints. In the input, each item belongs to certaincategories, called classes in this paper. Each platform specifies the groupfairness constraints through an upper bound on the number of items it can servefrom each class. Additionally, each platform also has an upper bound on thetotal number of items it can serve. The goal is to assign items to platforms soas to maximize the number of items assigned while satisfying the upper boundsof each class. In some cases, there is a revenue associated with matching anitem to a platform, then the goal is to maximize the revenue generated.  This problem models several important real-world problems like ad-auctions,scheduling, resource allocations, school choice etc.We also show an interestingconnection to computing a generalized maximum independent set on hypergraphsand ranking items under group fairness constraints.  We show that if the classes are arbitrary, then the problem is NP-hard andhas a strong inapproximability. We consider the problem in both online andoffline settings under natural restrictions on the classes. Under theserestrictions, the problem continues to remain NP-hard but admits approximationalgorithms with small approximation factors. We also implement some of thealgorithms. Our experiments show that the algorithms work well in practice bothin terms of efficiency and the number of items that get assigned to someplatform.

Matchings with Group Fairness Constraints: Online and Offline Algorithms