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We study the problem of approximating maximum Nash social welfare (NSW) when allocating m indivisible items among n asymmetric agents with submodular valuations. The NSW is a well-established notion of fairness and efficiency, defined as…

We consider the problem of approximating maximum Nash social welfare (NSW) while allocating a set of indivisible items to $n$ agents. The NSW is a popular objective that provides a balanced tradeoff between the often conflicting…

We study the problem of maximizing Nash social welfare, which is the geometric mean of agents' utilities, in two well-known models. The first model involves one-sided preferences, where a set of indivisible items is allocated among a group…

We establish a compatibility between fairness and efficiency, captured via Nash Social Welfare (NSW), under the broad class of subadditive valuations. We prove that, for subadditive valuations, there always exists a partial allocation that…

The Nash social welfare (NSW) is a well-known social welfare measurement that balances individual utilities and the overall efficiency. In the context of fair allocation of indivisible goods, it has been shown by Caragiannis et al. (EC 2016…

We study the Nash Social Welfare problem: Given $n$ agents with valuation functions $v_i:2^{[m]} \rightarrow {\mathbb R}$, partition $[m]$ into $S_1,\ldots,S_n$ so as to maximize $(\prod_{i=1}^{n} v_i(S_i))^{1/n}$. The problem has been…

We give the first $O(1)$-approximation for the weighted Nash Social Welfare problem with additive valuations. The approximation ratio we obtain is $e^{1/e} + \epsilon \approx 1.445 + \epsilon$, which matches the best known approximation…

The maximum Nash social welfare (NSW) -- which maximizes the geometric mean of agents' utilities -- is a fundamental solution concept with remarkable fairness and efficiency guarantees. The computational aspects of NSW have been extensively…

We study the problem of allocating items to agents with submodular valuations with the goal of maximizing the weighted Nash social welfare (NSW). The best-known results for unweighted and weighted objectives are the $(4+\epsilon)$…

We present a constant-factor approximation algorithm for the Nash social welfare maximization problem with subadditive valuations accessible via demand queries. More generally, we propose a template for NSW optimization by solving a…

We study the problem of fairly allocating a set of indivisible goods among agents with additive valuations. The extent of fairness of an allocation is measured by its Nash social welfare, which is the geometric mean of the valuations of the…

Envy-free up to one good (EF1) and envy-free up to any good (EFX) are two well-known extensions of envy-freeness for the case of indivisible items. It is shown that EF1 can always be guaranteed for agents with subadditive valuations. In…

We study the problem of allocating a set of indivisible goods among agents with subadditive valuations in a fair and efficient manner. Envy-Freeness up to any good (EFX) is the most compelling notion of fairness in the context of…

We study the problem of allocating a set of indivisible items to agents with supermodular utilities to maximize the Nash social welfare. We show that the problem is NP-hard for any approximation factor.

We study coverage problems in which, for a set of agents and a given threshold $T$, the goal is to select $T$ subsets (of the agents) that, while satisfying combinatorial constraints, achieve fair and efficient coverage among the agents. In…

We study the problem of allocating $m$ items to $n$ agents subject to maximizing the Nash social welfare (NSW) objective. We write a novel convex programming relaxation for this problem, and we show that a simple randomized rounding…

This paper is merged with arXiv:2107.08965v2. We refer the reader to the full and updated version. We study the problem of allocating a set of indivisible goods among agents with 2-value additive valuations. Our goal is to find an…

We study the problem of allocating indivisible goods among agents in a fair and economically efficient manner. In this context, the Nash social welfare-defined as the geometric mean of agents' valuations for their assigned bundles-stands as…

We study the problem of allocating a set of indivisible goods among a set of agents with \emph{2-value additive valuations}. In this setting, each good is valued either $1$ or $p/q$, for some fixed co-prime numbers $p,q\in \mathbb{N}$ such…

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…