• Corpus ID: 238259113

# Sublinear Approximation Algorithm for Nash Social Welfare with XOS Valuations

@article{Barman2021SublinearAA,
title={Sublinear Approximation Algorithm for Nash Social Welfare with XOS Valuations},
author={Siddharth Barman and Anand Krishna and Pooja Kulkarni and Shivika Narang},
journal={ArXiv},
year={2021},
volume={abs/2110.00767}
}
• Published 2 October 2021
• Economics, Computer Science
• ArXiv
We study the problem of allocating indivisible goods among n agents with the objective of maximizing Nash social welfare (NSW). This welfare function is defined as the geometric mean of the agents’ valuations and, hence, it strikes a balance between the extremes of social welfare (arithmetic mean) and egalitarian welfare (max-min value). Nash social welfare has been extensively studied in recent years for various valuation classes. In particular, a notable negative result is known when the…
2 Citations

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## References

SHOWING 1-10 OF 26 REFERENCES
Approximating Nash Social Welfare under Binary XOS and Binary Subadditive Valuations
• Economics, Computer Science
WINE
• 2021
It is proved that an exponential number of value queries are necessarily required to obtain even a sub-linear approximation for Nash social welfare under binary subadditive valuations, which implies that—in the case of binary XOS valuations—there necessarily exists an allocation that simultaneously satisfies multiple fairness and efficiency criteria.
Approximating Nash Social Welfare under Submodular Valuations through (Un)Matchings
• Computer Science
SODA
• 2020
The problem of approximating maximum Nash social welfare when allocating m indivisible items among n asymmetric agents with submodular valuations is extended to far more general settings and is shown to be strictly harder than all currently known settings with an e/(e-1) factor of the hardness of approximation.
Approximating Nash social welfare under rado valuations
• Computer Science
STOC
• 2021
The approach gives the first constant-factor approximation algorithm for the asymmetric case under Rado valuations, provided that the maximum ratio between the weights is bounded by a constant.
Tight Approximation Algorithms for p-Mean Welfare Under Subadditive Valuations
• Computer Science
ESA
• 2020
Polynomial-time algorithms for the fair and efficient allocation of indivisible goods among agents that have subadditive valuations over the goods and approximation guarantees are essentially tight for XOS and, hence, subadditives valuations are developed.
Approximating the Nash Social Welfare with Budget-Additive Valuations
• Economics
SODA
• 2018
It is shown that the market instances arising from the Nash social welfare problem always have an equilibrium, and the set of equilibria is not convex, answering a question of [Cole et al, EC 2017].
Greedy Algorithms for Maximizing Nash Social Welfare
• Economics
AAMAS
• 2018
The effectiveness of simple, greedy algorithms in solving the problem of fairly allocating a set of indivisible goods among agents with additive valuations is studied, showing that when agents have binary valuations over the goods, an exact solution can be found in polynomial time via a greedy algorithm.
Approximating the Nash Social Welfare with Indivisible Items
• Economics
SIAM J. Comput.
• 2018
We study the problem of allocating a set of indivisible items among agents with additive valuations, with the goal of maximizing the geometric mean of the agents' valuations, i.e., the Nash social
Fair and Efficient Allocations under Subadditive Valuations
• Economics
AAAI
• 2021
A polynomial-time algorithm is designed that outputs an allocation that satisfies either of the two approximations of EFX as well as achieves an $\mathcal{O}(n)$ approximation to the Nash welfare.
On maximizing welfare when utility functions are subadditive
• U. Feige
• Economics, Mathematics
STOC '06
• 2006
A way of rounding any fractional solution to a linear programming relaxation to solve the problem of maximizing welfare so as to give a feasible solution of welfare at least half that of the value of the fractional Solution.