DeepAI
Log In Sign Up

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

07/19/2021

Maximizing Nash Social Welfare in 2-Value Instances

We consider the problem of maximizing the Nash social welfare when alloc...
12/19/2021

Tractable Fragments of the Maximum Nash Welfare Problem

We study the problem of maximizing Nash welfare (MNW) while allocating i...
01/05/2022

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

We study the problem of efficiently and fairly allocating a set of indiv...
06/04/2021

Approximating Nash Social Welfare under Binary XOS and Binary Subadditive Valuations

We study the problem of allocating indivisible goods among agents in a f...
01/27/2018

Greedy Algorithms for Maximizing Nash Social Welfare

We study the problem of fairly allocating a set of indivisible goods amo...
05/15/2020

Tight Approximation Algorithms for p-Mean Welfare Under Subadditive Valuations

We develop polynomial-time algorithms for the fair and efficient allocat...
07/14/2020

Almost Envy-freeness, Envy-rank, and Nash Social Welfare Matchings

Envy-free up to one good (EF1) and envy-free up to any good (EFX) are tw...