Diverse Fair Allocations: Complexity and Algorithms

In this work, we initiate the study of diversity of solutions in the context of fair division of indivisible goods. In particular, we explore the notions of disjoint, distinct and symmetric allocations and study their complexity in terms of the fairness notions of envy-freeness and equitability upto one item. We show that for binary valuations, the above problems are polynomial time solvable. In contrast we show NP-hardness of disjoint and symmetric case, when the valuations are additive.