Appendix A More related works

Besides proportionality, in another parallel line of research, envy-freeness and its relaxations, namely envy-free up to one item (EF1) and envy-free up to any item (EFX), are also widely studied. It was shown in [35] and [11] for goods and chores, respectively, that an EF1 allocation exists for the monotone combinatorial functions. However, the existence of EFX allocations is still unknown even with additive functions. Therefore, approximation algorithms were proposed in [2, 42] for additive functions and in [39, 16] for subadditive functions. We refer the readers to [3] for a detailed survey on fair allocation of indivisible items.