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This paper is merged with arXiv:2107.08965v2. We refer the reader to the fulland updated version.  We study the problem of allocating a set of indivisible goods among agentswith 2-value additive valuations. Our goal is to find an allocation withmaximum Nash social welfare, i.e., the geometric mean of the valuations of theagents. We give a polynomial-time algorithm to find a Nash social welfaremaximizing 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 positiveinteger $p$. We then extend our algorithm to find a better approximation factorfor general 2-value instances.

Nash Social Welfare for 2-value Instances