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Approximating Nash social welfare by matching and local search

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

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Identification Number: 10.1145/3564246.3585255

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
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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