A Note on Approximating Weighted Nash Social Welfare with Additive Valuations

We give the first $O(1)$-approximation for the weighted Nash Social Welfare problem with additive valuations. The approximation ratio we obtain is $e^{1/e} + \epsilon \approx 1.445 + \epsilon$, which matches the best known approximation ratio for the unweighted case \cite{BKV18}.