Nash Social Welfare for 2-value Instances

06/28/2021 ∙ by Hannaneh Akrami, et al. ∙ 0

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.

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