Splitting Necklaces, with Constraints

Jojić, Duško; Panina, Gaiane; Živaljević, Rade T.

doi:10.1137/20m1331949

Cited by 4 publications

(2 citation statements)

References 21 publications

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“…Recent research on fair division extensively investigates the setting where agents may have both positive and negative values for the items (Aziz et al 2019;Meunier and Zerbib 2019;Segal-Halevi 2018;Bérczi et al 2020;Jojić, Panina, and Živaljević 2021). In particular, Aziz et al (2019) proposed an extension of EF1 to this more general setting, requiring agents' envy to disappear after removal of one chore from an envious bundle or that of one good from an envied bundle.…”

Section: Discussionmentioning

confidence: 99%

How to Cut a Discrete Cake Fairly

Igarashi

2023

AAAI

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Cake-cutting is a fundamental model of dividing a heterogeneous resource, such as land, broadcast time, and advertisement space. In this study, we consider the problem of dividing indivisible goods fairly under the connectivity constraints of a path. We prove that a connected division of indivisible items satisfying a discrete counterpart of envy-freeness, called envy-freeness up to one good (EF1), always exists for any number of agents n with monotone valuations. Our result settles an open question raised by Bilò et al. (2019), who proved that an EF1 connected division always exists for four agents with monotone valuations. Moreover, the proof can be extended to show the following (1) ``secretive" and (2) ``extra" versions: (1) for n agents with monotone valuations, the path can be divided into n connected bundles such that an EF1 assignment of the remaining bundles can be made to the other agents for any selection made by the “secretive agent”; (2) for n+1 agents with monotone valuations, the path can be divided into n connected bundles such that when any ``extra agent” leaves, an EF1 assignment of the bundles can be made to the remaining agents.

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Section: Discussionmentioning

confidence: 99%

How to Cut a Discrete Cake Fairly

Igarashi

2023

AAAI

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“…It is open whether this result extends to three or more agents. Jojic, Panina, and Zivaljevic (2021) prove the existence of a balanced allocation in which all agents assign approximately the same value to all bundles (an "almost consensus" allocation). Note that constraints imposing a lower bound on the number of items allocated to an agent, such as balancedness constraints, are not matroid constraints, since they are not downward-closed.…”

Section: Related Workmentioning

confidence: 96%

On Fair Division under Heterogeneous Matroid Constraints

Dror

Feldman

Segal-Halevi

2023

jair

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We study fair allocation of indivisible goods among additive agents with feasibility constraints. In these settings, every agent is restricted to get a bundle among a specified set of feasible bundles. Such scenarios have been of great interest to the AI community due to their applicability to real-world problems. Following some impossibility results, we restrict attention to matroid feasibility constraints that capture natural scenarios, such as the allocation of shifts to medical doctors and the allocation of conference papers to referees. We focus on the common fairness notion of envy-freeness up to one good (EF1). Previous algorithms for finding EF1 allocations are either restricted to agents with identical feasibility constraints or allow free disposal of items. An open problem is the existence of EF1 complete allocations among agents who differ both in their valuations and in their feasibility constraints. In this work, we make progress on this problem by providing positive and negative results for several matroid and valuation types. Among other results, we devise polynomial-time algorithms for finding EF1 allocations in the following settings: (i) n agents with heterogeneous (non-identical) binary valuations and partition matroids with heterogeneous capacities; (ii) two agents with heterogeneous additive valuations and partition matroids with heterogeneous capacities; and (iii) three agents with heterogeneous binary valuations and identical base-orderable matroid constraints.

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Envy-free Division of Multi-layered Cakes

Igarashi

Meunier

2022

Web and Internet Economics

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Splitting Necklaces, with Constraints

Cited by 4 publications

References 21 publications

How to Cut a Discrete Cake Fairly

How to Cut a Discrete Cake Fairly

On Fair Division under Heterogeneous Matroid Constraints

Envy-free Division of Multi-layered Cakes

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