This paper is merged with arXiv:2107.08965v2. We refer the reader to the full and updated version. We study the problem of allocating a set of indivisible goods among agents with 2-value additive valuations. Our goal is to find an allocation with maximum Nash social welfare, i.e., the geometric mean of the valuations of the agents. We give a polynomial-time algorithm to find a Nash social welfare maximizing allocation when the valuation functions are integrally 2-valued, i.e., each agent has a value either 1 or p for each good, for some positive integer p. We then extend our algorithm to find a better approximation factor for general 2-value instances.
@article{arxiv.2106.14816,
title = {Nash Social Welfare for 2-value Instances},
author = {Hannaneh Akrami and Bhaskar Ray Chaudhury and Kurt Mehlhorn and Golnoosh Shahkarami and Quentin Vermande},
journal= {arXiv preprint arXiv:2106.14816},
year = {2021}
}