Fairly Allocating Many Goods with Few Queries

We investigate the query complexity of fair allocation indivisible goods. For two agents with arbitrary monotonic utilities, we design an algorithm that computes satisfying envy-freeness up to one good (EF1), a relaxation envy-freeness, using logarithmic number queries. show bound also holds for three additive and polylogarithmic utilities. These results suggest it is possible fairly allocate goods in practice even when extremely large. By contrast, prove computing another its relaxations, any (EFX), requires linear queries there are only identical