EFX: a simpler approach and an (almost) optimal guarantee via rainbow cycle number

H Akrami, N Alon, BR Chaudhury, J Garg… - Operations …, 2024 - pubsonline.informs.org
The existence of envy-freeness up to any good (EFX) allocations is a fundamental open
problem in discrete fair division. The goal is to determine the existence of an allocation of a …

Breaking the 3/4 barrier for approximate maximin share

H Akrami, J Garg - Proceedings of the 2024 Annual ACM-SIAM …, 2024 - SIAM
We study the fundamental problem of fairly allocating a set of indivisible goods among n
agents with additive valuations using the desirable fairness notion of maximin share (MMS) …

Fair-share allocations for agents with arbitrary entitlements

M Babaioff, T Ezra, U Feige - Mathematics of Operations …, 2024 - pubsonline.informs.org
We consider the problem of fair allocation of indivisible goods to n agents with no transfers.
When agents have equal entitlements, the well-established notion of the maximin share …

Improving approximation guarantees for maximin share

H Akrami, J Garg, E Sharma, S Taki - arXiv preprint arXiv:2307.12916, 2023 - arxiv.org
We consider fair division of a set of indivisible goods among $ n $ agents with additive
valuations using the fairness notion of maximin share (MMS). MMS is the most popular …

Randomized and deterministic maximin-share approximations for fractionally subadditive valuations

H Akrami, K Mehlhorn, M Seddighin… - Advances in Neural …, 2024 - proceedings.neurips.cc
We consider the problem of guaranteeing maximin-share ($\MMS $) when allocating a set of
indivisible items to a set of agents with fractionally subadditive ($\XOS $) valuations. For …

Fair Shares: Feasibility, Domination, and Incentives

M Babaioff, U Feige - Mathematics of Operations Research, 2024 - pubsonline.informs.org
We consider fair allocation of indivisible goods to n equally entitled agents. Every agent i
has a valuation function vi from some given class of valuation functions. A share s is a …

Fair division with subjective divisibility

X Bei, S Liu, X Lu - arXiv preprint arXiv:2310.00976, 2023 - arxiv.org
The classic fair division problems assume the resources to be allocated are either divisible
or indivisible, or contain a mixture of both, but the agents always have a predetermined and …

Achieving Maximin Share and EFX/EF1 Guarantees Simultaneously

H Akrami, N Rathi - arXiv preprint arXiv:2409.01963, 2024 - arxiv.org
We study the problem of computing\emph {fair} divisions of a set of indivisible goods among
agents with\emph {additive} valuations. For the past many decades, the literature has …

Multi-agent online scheduling: MMS allocations for indivisible items

S Zhou, R Bai, X Wu - International Conference on Machine …, 2023 - proceedings.mlr.press
We consider the problem of fairly allocating a sequence of indivisible items that arrive online
in an arbitrary order to a group of $ n $ agents with additive normalized valuation functions …

The budgeted maximin share allocation problem

B Deng, W Li - Optimization Letters, 2024 - Springer
We are given a set of indivisible goods and a set of m agents where each good has a size
and each agent has an additive valuation function and a budget. The budgeted maximin …