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Fair allocation of indivisible goods studies allocating $m$ goods among $n$ agents in a fair manner. While fairness is a fundamental requirement in many real-world applications, it often conflicts with (economic) efficiency. This raises a…

Computer Science and Game Theory · Computer Science 2025-06-03 Xiaolin Bu , Zihao Li , Shengxin Liu , Jiaxin Song , Biaoshuai Tao

The marginal maximum a posteriori probability (MAP) estimation problem, which calculates the mode of the marginal posterior distribution of a subset of variables with the remaining variables marginalized, is an important inference problem…

Machine Learning · Statistics 2013-07-19 Qiang Liu , Alexander Ihler

We analyze the performance of the greedy algorithm, and also a discrete semi-gradient based algorithm, for maximizing the sum of a suBmodular and suPermodular (BP) function (both of which are non-negative monotone non-decreasing) under two…

Discrete Mathematics · Computer Science 2018-01-24 Wenruo Bai , Jeffrey A. Bilmes

We study fair allocation of indivisible goods among strategic agents with additive valuations. Motivated by impossibility results for deterministic truthful mechanisms, we focus on randomized mechanisms that are…

Computer Science and Game Theory · Computer Science 2026-05-01 Moshe Babaioff , Uriel Feige , Noam Manaker Morag

We consider the problem of fairly allocating a set of indivisible goods among agents with additive valuations. Ex-ante fairness (proportionality) can trivially be obtained by giving all goods to a random agent. Yet, such an allocation is…

Computer Science and Game Theory · Computer Science 2026-01-26 Moshe Babaioff , Yuval Grofman

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…

In this paper we consider a generalization of the well-known budgeted maximum coverage problem. We are given a ground set of elements and a set of bins. The goal is to find a subset of elements along with an associated set of bins, such…

Data Structures and Algorithms · Computer Science 2018-08-10 Francesco Cellinese , Gianlorenzo D'Angelo , Gianpiero Monaco , Yllka Velaj

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 consider discrete allocation problem where $m$ indivisible goods are to be divided among $n$ agents. When agents' valuations are additive, the well-known cycle cancelling lemma by Lenstra, Shmoys, and Tardos plays a key role in design…

Computer Science and Game Theory · Computer Science 2025-11-27 Chandra Chekuri , Pooja Kulkarni , Ruta Mehta , Jan Vondrak

Discrimination in machine learning often arises along multiple dimensions (a.k.a. protected attributes); it is then desirable to ensure \emph{intersectional fairness} -- i.e., that no subgroup is discriminated against. It is known that…

Machine Learning · Statistics 2023-06-27 Mathieu Molina , Patrick Loiseau

We consider the fair division of indivisible items using the maximin shares measure. Recent work on the topic has focused on extending results beyond the class of additive valuation functions. In this spirit, we study the case where the…

Discrete Mathematics · Computer Science 2023-10-20 Zhentao Li , Adrian Vetta

Submodular function minimization is well studied, and existing algorithms solve it exactly or up to arbitrary accuracy. However, in many applications, such as structured sparse learning or batch Bayesian optimization, the objective function…

Machine Learning · Computer Science 2022-03-10 Marwa El Halabi , Stefanie Jegelka

A set function is called XOS if it can be represented by the maximum of additive functions. When such a representation is fixed, the number of additive functions required to define the XOS function is called the width. In this paper, we…

Data Structures and Algorithms · Computer Science 2020-07-09 Yuval Filmus , Yasushi Kawase , Yusuke Kobayashi , Yutaro Yamaguchi

In this work, we consider the maximization of submodular functions constrained by independence systems. Because of the wide applicability of submodular functions, this problem has been extensively studied in the literature, on specialized…

Data Structures and Algorithms · Computer Science 2019-06-11 Alan Kuhnle

We investigate the problem of fairly allocating indivisible goods among interested agents using the concept of maximin share. Procaccia and Wang showed that while an allocation that gives every agent at least her maximin share does not…

Computer Science and Game Theory · Computer Science 2018-04-19 Warut Suksompong

Boolean Matrix Factorization (BMF) aims to find an approximation of a given binary matrix as the Boolean product of two low-rank binary matrices. Binary data is ubiquitous in many fields, and representing data by binary matrices is common…

Machine Learning · Computer Science 2022-07-26 Fedor Fomin , Fahad Panolan , Anurag Patil , Adil Tanveer

If a two-player social welfare maximization problem does not admit a PTAS, we prove that any maximal-in-range truthful mechanism that runs in polynomial time cannot achieve an approximation factor better than 1/2. Moreover, for the k-player…

Computer Science and Game Theory · Computer Science 2009-12-18 Shaddin Dughmi , Hu Fu , Robert Kleinberg

A set of $m$ indivisible goods is to be allocated to a set of $n$ agents. Each agent $i$ has an additive valuation function $v_i$ over goods. The value of a good $g$ for agent $i$ is either $1$ or $s$, where $s$ is a fixed rational number…

Computer Science and Game Theory · Computer Science 2026-02-23 Kurt Mehlhorn

Greedy algorithms are widely used for problems in machine learning such as feature selection and set function optimization. Unfortunately, for large datasets, the running time of even greedy algorithms can be quite high. This is because for…

Machine Learning · Statistics 2017-03-09 Rajiv Khanna , Ethan Elenberg , Alexandros G. Dimakis , Sahand Negahban , Joydeep Ghosh

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…

Computer Science and Game Theory · Computer Science 2025-05-19 Salil Gokhale , Harshul Sagar , Rohit Vaish , Vignesh Viswanathan , Jatin Yadav