DeepAI AI Chat
Log In Sign Up

Estimating the Nash Social Welfare for coverage and other submodular valuations

01/06/2021
by   Wenzheng Li, et al.
0

We study the Nash Social Welfare problem: Given n agents with valuation functions v_i:2^[m]→ℝ, partition [m] into S_1,…,S_n so as to maximize (∏_i=1^n v_i(S_i))^1/n. The problem has been shown to admit a constant-factor approximation for additive, budget-additive, and piecewise linear concave separable valuations; the case of submodular valuations is open. We provide a 1/e (1-1/e)^2-approximation of the optimal value for several classes of submodular valuations: coverage, sums of matroid rank functions, and certain matching-based valuations.

READ FULL TEXT

page 1

page 2

page 3

page 4

03/18/2021

A constant-factor approximation algorithm for Nash Social Welfare with submodular valuations

We present a 380-approximation algorithm for the Nash Social Welfare pro...
02/26/2021

Are Gross Substitutes a Substitute for Submodular Valuations?

The class of gross substitutes (GS) set functions plays a central role i...
07/01/2019

Approximate F_2-Sketching of Valuation Functions

We study the problem of constructing a linear sketch of minimum dimensio...
09/14/2022

Weighted Envy-Freeness for Submodular Valuations

We investigate the fair allocation of indivisible goods to agents with p...
02/06/2023

Dividing Good and Better Items Among Agents with Submodular Valuations

We study the problem of fairly allocating a set of indivisible goods amo...
08/27/2015

Computing Stable Coalitions: Approximation Algorithms for Reward Sharing

Consider a setting where selfish agents are to be assigned to coalitions...
05/04/2023

Fair Multiwinner Elections with Allocation Constraints

We consider the multiwinner election problem where the goal is to choose...