A constant factor approximation for Nash social welfare with subadditive valuations

TL;DR

This paper introduces a constant-factor approximation algorithm for maximizing Nash social welfare with subadditive valuations, utilizing a novel LP-based template and rounding technique applicable to various problem variants.

Contribution

It provides the first constant-factor approximation for NSW with subadditive valuations and offers a versatile LP-based framework for related welfare maximization problems.

Findings

Achieved a constant-factor approximation for NSW with subadditive valuations

Developed a general LP-based template for welfare optimization

Applicable to multiple variants of the problem

Abstract

We present a constant-factor approximation algorithm for the Nash social welfare maximization problem with subadditive valuations accessible via demand queries. More generally, we propose a template for NSW optimization by solving a configuration-type LP and using a rounding procedure for (utilitarian) social welfare as a blackbox, which could be applicable to other variants of the problem.