DeepAI AI Chat
Log In Sign Up

Estimating the Nash Social Welfare for coverage and other submodular valuations

by   Wenzheng Li, et al.

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.


page 1

page 2

page 3

page 4


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

We present a 380-approximation algorithm for the Nash Social Welfare pro...

Are Gross Substitutes a Substitute for Submodular Valuations?

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

Approximate F_2-Sketching of Valuation Functions

We study the problem of constructing a linear sketch of minimum dimensio...

Weighted Envy-Freeness for Submodular Valuations

We investigate the fair allocation of indivisible goods to agents with p...

Dividing Good and Better Items Among Agents with Submodular Valuations

We study the problem of fairly allocating a set of indivisible goods amo...

Computing Stable Coalitions: Approximation Algorithms for Reward Sharing

Consider a setting where selfish agents are to be assigned to coalitions...

Fair Multiwinner Elections with Allocation Constraints

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