EFX: A Simpler Approach and an (Almost) Optimal Guarantee via Rainbow Cycle Number

Abstract

The existence of EFX allocations is a fundamental open problem in discrete fair division. Since the general problem has been elusive, progress is made on two fronts: (i) proving existence when the number of agents is small, and (ii) proving the existence of relaxations of EFX. In this paper, we improve and simplify the state-of-the-art results on both fronts with new techniques.