  We consider the problem of assigning items to platforms in the presence of
group fairness constraints. In the input, each item belongs to certain
categories, called classes in this paper. Each platform specifies the group
fairness constraints through an upper bound on the number of items it can serve
from each class. Additionally, each platform also has an upper bound on the
total number of items it can serve. The goal is to assign items to platforms so
as to maximize the number of items assigned while satisfying the upper bounds
of each class. In some cases, there is a revenue associated with matching an
item 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 interesting
connection to computing a generalized maximum independent set on hypergraphs
and ranking items under group fairness constraints.
  We show that if the classes are arbitrary, then the problem is NP-hard and
has a strong inapproximability. We consider the problem in both online and
offline settings under natural restrictions on the classes. Under these
restrictions, the problem continues to remain NP-hard but admits approximation
algorithms with small approximation factors. We also implement some of the
algorithms. Our experiments show that the algorithms work well in practice both
in terms of efficiency and the number of items that get assigned to some
platform.
