Fair allocation of indivisible goods: Beyond additive valuations

We conduct a study on the problem of fair allocation indivisible goods when maximin share [1] is used as measure fairness. Most current studies this notion are limited to case that valuations additive. In paper, we go beyond additive and consider cases submodular, fractionally subadditive, subadditive. give constant approximation guarantees for agents with submodular XOS valuations, logarithmic bound subadditive valuations. Furthermore, complement our results by providing close upper bounds each class valuation functions. Finally, present algorithms find such allocations settings in polynomial time.