Approximating the Nash Social Welfare with Budget-Additive Valuations

@article{Garg2018ApproximatingTN,
  title={Approximating the Nash Social Welfare with Budget-Additive Valuations},
  author={Jugal Garg and Martin Hoefer and Kurt Mehlhorn},
  journal={ArXiv},
  year={2018},
  volume={abs/1707.04428}
}
We present the first constant-factor approximation algorithm for maximizing the Nash social welfare when allocating indivisible items to agents with budget-additive valuation functions. Budget-additive valuations represent an important class of submodular functions. They have attracted a lot of research interest in recent years due to many interesting applications. For every $\varepsilon > 0$, our algorithm obtains a $(2.404 + \varepsilon)$-approximation in time polynomial in the input size and… 
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