Garg, Jugal, Husić, Edin ORCID: 0000-0002-6708-5112, Li, Wenzheng, Végh, László A. ORCID: 0000-0003-1152-200X and Vondrák, Jan
(2023)
*Approximating Nash social welfare by matching and local search.*
In: Saha, Barna and Servedio, Rocco A., (eds.)
STOC 2023 - Proceedings of the 55th Annual ACM Symposium on Theory of Computing.
Proceedings of the Annual ACM Symposium on Theory of Computing.
Association for Computing Machinery, pp. 1298-1310.
ISBN 9781450399135

## Abstract

For any >0, we give a simple, deterministic (4+)-approximation algorithm for the Nash social welfare (NSW) problem under submodular valuations. The previous best approximation factor was 380 via a randomized algorithm. We also consider the asymmetric variant of the problem, where the objective is to maximize the weighted geometric mean of agents' valuations, and give an (ω + 2 + )-approximation if the ratio between the largest weight and the average weight is at most ω. We also show that the 12-EFX envy-freeness property can be attained simultaneously with a constant-factor approximation. More precisely, we can find an allocation in polynomial time which is both 12-EFX and a (8+)-approximation to the symmetric NSW problem under submodular valuations. The previous best approximation factor under 12-EFX was linear in the number of agents.

Item Type: | Book Section |
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Additional Information: | © 2023 ACM. |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics H Social Sciences Q Science > QA Mathematics > QA75 Electronic computers. Computer science |

Date Deposited: | 12 Jul 2023 15:45 |

Last Modified: | 09 Jun 2024 16:45 |

URI: | http://eprints.lse.ac.uk/id/eprint/119720 |

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