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Related papers: A Note on EFX Inapproximability for Chores

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We study the fair division of indivisible items and provide new insights into the EFX problem, which is widely regarded as the central open question in fair division, and the PMMS problem, a strictly stronger variant of EFX. Our first…

Computer Science and Game Theory · Computer Science 2025-07-31 Jarosław Byrka , Franciszek Malinka , Tomasz Ponitka

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…

Computer Science and Game Theory · Computer Science 2020-08-18 Bhaskar Ray Chaudhury , Jugal Garg , Ruta Mehta

The existence of EFX allocations is a central open problem in discrete fair division. An allocation is EFX (envy-free up to any good) if no agent envies another agent after the removal of any single good from the other agent's bundle. We…

Computer Science and Game Theory · Computer Science 2026-05-15 Hannaneh Akrami , Alexander Mayorov , Kurt Mehlhorn , Shreyas Srinivas , Christoph Weidenbach

Envy-freeness up to any good (EFX) is a popular and important fairness property in the fair allocation of indivisible goods, of which its existence in general is still an open question. In this work, we investigate the problem of…

Computer Science and Game Theory · Computer Science 2025-04-08 Tzeh Yuan Neoh , Nicholas Teh

We study the problem of fair allocation of a set of indivisible goods among $n$ agents with $k$ distinct additive valuations, with the goal of achieving approximate envy-freeness up to any good ($\alpha-\mathrm{EFX}$). It is known that EFX…

Computer Science and Game Theory · Computer Science 2025-08-22 Vishwa Prakash HV , Ruta Mehta , Prajakta Nimbhorkar

We study the problem of allocating indivisible chores among agents with binary supermodular cost functions. In other words, each chore has a marginal cost of $0$ or $1$ and chores exhibit increasing marginal costs (or decreasing marginal…

Computer Science and Game Theory · Computer Science 2023-03-14 Vignesh Viswanathan , Yair Zick

We study the fair division problem and the existence of allocations satisfying the fairness criterion envy-freeness up to any item (EFX). The existence of EFX allocations is a major open problem in the fair division literature. We consider…

Computational Engineering, Finance, and Science · Computer Science 2023-08-11 Xiaolin Bu , Jiaxin Song , Ziqi Yu

Envy-freeness up to any good (EFX) is a central fairness notion for allocating indivisible goods, yet its existence is unresolved in general. In the setting with few surplus items, where the number of goods exceeds the number of agents by a…

Computer Science and Game Theory · Computer Science 2026-01-21 Eugene Lim , Tzeh Yuan Neoh , Nicholas Teh

The existence of EFX allocations is a major open problem in fair division, even for additive valuations. The current state of the art is that no setting where EFX allocations are impossible is known, and EFX is known to exist for ($i$)…

Computer Science and Game Theory · Computer Science 2021-03-02 Ben Berger , Avi Cohen , Michal Feldman , Amos Fiat

This paper addresses the problem of finding fair orientations of graphs of chores, in which each vertex corresponds to an agent, each edge corresponds to a chore, and a chore has zero marginal utility to an agent if its corresponding edge…

Computer Science and Game Theory · Computer Science 2025-10-17 Kevin Hsu , Valerie King

We initiate the study of indivisible chore allocation for agents with asymmetric shares. The fairness concept we focus on is the weighted natural generalization of maxmin share: WMMS fairness and OWMMS fairness. We first highlight the fact…

Computer Science and Game Theory · Computer Science 2019-06-19 Haris Aziz , Hau Chan , Bo Li

We consider Max-min Share (MmS) allocations of items both in the case where items are goods (positive utility) and when they are chores (negative utility). We show that fair allocations of goods and chores have some fundamental connections…

Computer Science and Game Theory · Computer Science 2016-04-07 Haris Aziz , Gerhard Rauchecker , Guido Schryen , Toby Walsh

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

Ensuring fairness while limiting costs, such as transportation or storage, is an important challenge in resource allocation, yet most work has focused on cost minimization without fairness or fairness without explicit cost considerations.…

Computer Science and Game Theory · Computer Science 2026-01-19 Eva Deltl

We study the fair allocation of indivisible goods under cardinality constraints, where each agent must receive a bundle of fixed size. This models practical scenarios, such as assigning shifts or forming equally sized teams. Recently,…

Computer Science and Game Theory · Computer Science 2025-07-29 Alviona Mancho , Evangelos Markakis , Nicos Protopapas

Equitable allocation of indivisible items involves partitioning the items among agents such that everyone derives (almost) equal utility. We consider the approximate notion of \textit{equitability up to one item} (EQ1) and focus on the…

Computer Science and Game Theory · Computer Science 2025-08-22 Hadi Hosseini , Aditi Sethia

Submodular continuous functions are a category of (generally) non-convex/non-concave functions with a wide spectrum of applications. We characterize these functions and demonstrate that they can be maximized efficiently with approximation…

Machine Learning · Computer Science 2019-05-07 Andrew An Bian , Baharan Mirzasoleiman , Joachim M. Buhmann , Andreas Krause

We consider the problem of assigning indivisible chores to agents with different entitlements in the maximin share value (\MMS) context. While constant-\MMS\ allocations/assignments are guaranteed to exist for both goods and chores in the…

Computer Science and Game Theory · Computer Science 2025-10-14 Masoud Seddighin , Saeed Seddighin

Submodularity is a fundamental phenomenon in combinatorial optimization. Submodular functions occur in a variety of combinatorial settings such as coverage problems, cut problems, welfare maximization, and many more. Therefore, a lot of…

Data Structures and Algorithms · Computer Science 2011-11-08 Shaddin Dughmi

We study a discrete fair division problem where $n$ agents have additive valuation functions over a set of $m$ goods. We focus on the well-known $\alpha$-EFX fairness criterion, according to which the envy of an agent for another agent is…

Computer Science and Game Theory · Computer Science 2026-02-10 Aris Filos-Ratsikas , Georgios Kalantzis , Alexandros A. Voudouris