Fine Grained Complexity of Fair and Efficient Allocations

Fair Division is a flourishing field that has garnered a lot of attention in recent times. Allocating a set of valuable resources fairly among interested agents along with guaranteeing everyone's satisfaction is a crucial task with a wide range of applications, both routine and high-stakes. This paper presents our existing and ongoing work in the following directions - a) minimizing envy when absolute envy-freeness is unachievable b) identifying the structured instances where fair and efficient allocation problems admit fast algorithms c) quantifying the trade-off between fairness (EF1/EQ1) and efficiency notions (social welfare functions) of an allocation.