NP-Hardness of Approximating Nash Social Welfare with Supermodular Valuations
Alon Bebchuk
TL;DR
This paper proves that approximating the Nash social welfare in allocations with supermodular utilities is NP-hard, indicating fundamental computational difficulty regardless of the approximation quality.
Contribution
It establishes the NP-hardness of approximating Nash social welfare for supermodular valuations, a significant complexity result in fair division.
Findings
NP-hardness for any approximation factor
Implication of computational difficulty in fair division with supermodular utilities
Advances understanding of complexity in social welfare optimization
Abstract
We study the problem of allocating a set of indivisible items to agents with supermodular utilities to maximize the Nash social welfare. We show that the problem is NP-hard for any approximation factor.
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