@inproceedings{cbcf8c97301e4ac7b6bc142315a2631a,

title = "Approximating Nash Social Welfare by Matching and Local Search",

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.",

keywords = "Approximation Algorithms, Combinatorial Optimization, Envy-freeness, Fairness, Local Search, Nash Social Welfare",

author = "Jugal Garg and Edin Husi{\'c} and Wenzheng Li and V{\'e}gh, {L{\'a}szl{\'o} A.} and Jan Vondr{\'a}k",

note = "Publisher Copyright: {\textcopyright} 2023 ACM.; 55th Annual ACM Symposium on Theory of Computing, STOC 2023 ; Conference date: 20-06-2023 Through 23-06-2023",

year = "2023",

month = jun,

day = "2",

doi = "10.1145/3564246.3585255",

language = "English (US)",

series = "Proceedings of the Annual ACM Symposium on Theory of Computing",

publisher = "Association for Computing Machinery",

pages = "1298--1310",

editor = "Barna Saha and Servedio, {Rocco A.}",

booktitle = "STOC 2023 - Proceedings of the 55th Annual ACM Symposium on Theory of Computing",

address = "United States",

}