Fair multi-cake cutting

Segal-Halevi, Erel

doi:10.1016/j.dam.2020.10.011

Cited by 9 publications

(2 citation statements)

References 25 publications

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“…Nyman, Su, and Zerbib (2020) proved that for k cakes, an EF allocation always exists when there are k(n − 1) + 1 agents and each cake is cut into k pieces. Besides that, there are also some works related to multi-cake cutting, such as multi-layered cake cutting and fair multi-cake cutting (Hosseini, Igarashi, and Searns 2020;Segal-Halevi 2021).…”

Section: Related Workmentioning

confidence: 99%

Fair Allocation of Items in Multiple Regions

Zhou,

Wei,

Tao

et al. 2024

AAAI

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We initiate the study of fair allocation with the set of divisible or indivisible items distributed in multiple regions. The key requirement is that each agent can only obtain items from one region. In this work, we consider two kinds of fairness concepts: envy-based notions including envy-freeness (EF) and envy-freeness up to one/any item (EF1/EFX), and share-based notions including proportionality (PROP) and proportionality up to one/any item (PROP1/PROPX). On the negative side, we show NP-hardness and inapproximability results about the aforementioned fairness notions. On the positive side, we propose several algorithms to compute the partial allocations that satisfy envy-based notions and allocations that approximate the above fairness notions.

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Section: Related Workmentioning

confidence: 99%

Fair Allocation of Items in Multiple Regions

Zhou,

Wei,

Tao

et al. 2024

AAAI

View full text Add to dashboard Cite

show abstract

“…They showed that the maximin share is not always attainable, but the minimax share (i.e., the worst-case share of an agent when the items are partitioned into n bundles and the agent gets the best bundle) can always be guaranteed. Segal-Halevi [50,Appendix B] showed that maximin share fairness can be attained when the cake is a collection of disconnected intervals and each agent should receive a connected piece. We are not aware of previous studies of maximin share fairness in pie cutting.…”

Section: Related Workmentioning

confidence: 99%