Garg, Jugal, Husić, Edin and Végh, László A. ORCID: 0000-0003-1152-200X
(2021)
*Approximating Nash social welfare under rado valuations.*
In: Khuller, Samir and Williams, Virginia Vassilevska, (eds.)
STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing.
Proceedings of the Annual ACM Symposium on Theory of Computing.
Association for Computing Machinery, ITA, 1412 - 1425.
ISBN 9781450380539

Text (Approximating Nash social welfare under rado valuations)
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## Abstract

We consider the problem of approximating maximum Nash social welfare (NSW) while allocating a set of indivisible items to n agents. The NSW is a popular objective that provides a balanced tradeoff between the often conflicting requirements of fairness and efficiency, defined as the weighted geometric mean of the agents' valuations. For the symmetric additive case of the problem, where agents have the same weight with additive valuations, the first constant-factor approximation algorithm was obtained in 2015. Subsequent work has obtained constant-factor approximation algorithms for the symmetric case under mild generalizations of additive, and O(n)-approximation algorithms for subadditive valuations and for the asymmetric case. In this paper, we make significant progress towards both symmetric and asymmetric NSW problems. We present the first constant-factor approximation algorithm for the symmetric case under Rado valuations. Rado valuations form a general class of valuation functions that arise from maximum cost independent matching problems, including as special cases assignment (OXS) valuations and weighted matroid rank functions. Furthermore, our approach also gives the first constant-factor approximation algorithm for the asymmetric case under Rado valuations, provided that the maximum ratio between the weights is bounded by a constant.

Item Type: | Book Section |
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Official URL: | https://dl.acm.org/doi/proceedings/10.1145/3406325 |

Additional Information: | © 2021 The Authors |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics |

Date Deposited: | 06 Jul 2021 09:21 |

Last Modified: | 20 Sep 2021 03:29 |

URI: | http://eprints.lse.ac.uk/id/eprint/110989 |

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