相关论文: A constant-factor approximation algorithm for Nash…
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 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 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.
For any $\varepsilon>0$, we give a simple, deterministic $(4+\varepsilon)$-approximation algorithm for the Nash social welfare (NSW) problem under submodular valuations. We also consider the asymmetric variant of the problem, where the…
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 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 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 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 study the problem of assigning items to agents so as to maximize the \emph{weighted} Nash Social Welfare (NSW) under submodular valuations. The best-known result for the problem is an $O(nw_{\max})$-approximation due to Garg, Husic, Li,…
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…
We develop polynomial-time algorithms for the fair and efficient allocation of indivisible goods among $n$ agents that have subadditive valuations over the goods. We first consider the Nash social welfare as our objective and design a…
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…
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 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…
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…
Recently Cole and Gkatzelis gave the first constant factor approximation algorithm for the problem of allocating indivisible items to agents, under additive valuations, so as to maximize the Nash Social Welfare. We give constant factor…
We consider the problem of maximizing the Nash social welfare when allocating a set $\mathcal{G}$ of indivisible goods to a set $\mathcal{N}$ of agents. We study instances, in which all agents have 2-value additive valuations: The value of…
We study the problem of allocating indivisible goods among $n$ agents with the objective of maximizing Nash social welfare (NSW). This welfare function is defined as the geometric mean of the agents' valuations and, hence, it strikes a…
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…