Approximating nash social welfare under rado valuations

The Nash social welfare problem asks for an allocation of indivisible items to agents in order maximize the geometric mean agents' valuations. We give overview constant-factor approximation algorithm when have Rado valuations [Garg et al. 2021]. are a common generalization assignment (OXS) and weighted matroid rank functions. Our approach also gives first asymmetric under same valuations, provided that maximum ratio between weights is bounded by constant.