@incollection{BiswasPSVreview,
author="Biswas, Arpita
and Payan, Justin
and Sengupta, Rik
and Viswanathan, Vignesh",
editor="Mukherjee, Animesh
and Kulshrestha, Juhi
and Chakraborty, Abhijnan
and Kumar, Srijan",
title="The Theory of Fair Allocation Under Structured Set Constraints",
bookTitle="Ethics in Artificial Intelligence: Bias, Fairness and Beyond",
year="2023",
publisher="Springer Nature Singapore",
address="Singapore",
pages="115--129",
abstract="The topic of fair allocation of indivisible items has been receiving significant attention because of its applicability in real-world settings, such as budgeted course allocations, room allocations, reviewer assignments, inheritance partitioning, and many others. In this chapter, we present an introduction to the theory of fairly allocating indivisible items in the presence of structured constraints, a natural setting that captures real-world restrictions. This setting has led to several works focusing on questions such as: (1) what are mathematically robust descriptions of these constraints? (2) how do we define appropriate fairness notions under these constraints? (3) do fair allocations always exist for all such relevant instances? (4) can we provide efficient algorithms to compute optimal or approximately optimal allocations? Typically, these questions become even more challenging when there are additional constraints on the feasible allocations, which may occur due to connectivity requirements, or incompatibility between certain item pairs. A large body of recent work has focused on defining appropriate fairness notions, providing existence guarantees, and handling computational issues in obtaining fair allocations under structured restrictions. We summarize this literature briefly.",
isbn="978-981-99-7184-8"
}