An Additive Approximation Scheme for the Nash Social Welfare Maximization with Identical Additive Valuations

  title={An Additive Approximation Scheme for the Nash Social Welfare Maximization with Identical Additive Valuations},
  author={Asei Inoue and Yusuke Kobayashi},
  booktitle={International Workshop on Combinatorial Algorithms},
We study the problem of efficiently and fairly allocating a set of indivisible goods among agents with identical and additive valuations for the goods. The objective is to maximize the Nash social welfare, which is the geometric mean of the agents’ valuations. While maximizing the Nash social welfare is NP-hard, a PTAS for this problem is presented by Nguyen and Rothe. The main contribution of this paper is to design a first additive PTAS for this problem, that is, we give a polynomial-time… 
2 Citations

Optimized Distortion and Proportional Fairness in Voting

The distortion of voting rules is studied, which is a worst-case measure comparing the utilitarian social welfare of the optimum outcome to the social welfare produced by the outcome selected by the voting rule, in the worst case over possible input profiles and utility functions that are consistent with the input.

Locally testable codes with constant rate, distance, and locality

This work constructs LTCs with constant rate, constant distance, and constant locality based on a new two-dimensional complex which they call a left-right Cayley complex, which is essentially a graph which, in addition to vertices and edges, also has squares.



Greedy Algorithms for Maximizing Nash Social Welfare

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.

Minimizing envy and maximizing average Nash social welfare in the allocation of indivisible goods

Approximating Nash social welfare under rado valuations

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.

Approximating the Nash Social Welfare with Budget-Additive Valuations

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].

Finding Fair and Efficient Allocations

A pseudopolynomial time algorithm for finding allocations that are EF1 and Pareto efficient; in particular, when the valuations are bounded, the algorithm finds such an allocation in polynomial time.

Estimating the Nash Social Welfare for coverage and other submodular valuations

This work provides a 1 e (1 − 1 e )-approximation of the optimal value for several classes of submodular valuations: coverage, sums of matroid rank functions, and certain matching-based valuations.

Additive Approximation Schemes for Load Balancing Problems

A local-search based algorithm is proposed which rounds a solution to the slot-MILP introducing an additive error on the target load intervals of at most $\epsilon\cdot p_{\max}$.

The Unreasonable Fairness of Maximum Nash Welfare

It is proved that the maximum Nash welfare solution selects allocations that are envy free up to one good --- a compelling notion that is quite elusive when coupled with economic efficiency.

On Fair Division of Indivisible Items

A polynomial time approximation algorithm is given that maximizes Nash social welfare up to a factor of e^{1/e} \approx 1.445$.

Nash Social Welfare for Indivisible Items under Separable, Piecewise-Linear Concave Utilities

Two constant factor algorithms for a substantial generalization of the problem of allocating indivisible items to agents - to the case of separable, piecewise-linear concave utility functions.