On Fair Division under Heterogeneous Matroid Constraints *

Amitay Dror, Michal Feldman, Erel Segal-Halevi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

11 Scopus citations

Abstract

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 heterogeneous agents, where the heterogeneity is both in the agents’ feasibility constraints and in their valuations. In this work, we make progress on this problem by providing positive and negative results for different matroid and valuation types. Among other results, we devise poly-time algorithms for finding EF1 allocations in the following settings: (i) n agents with heterogeneous partition matroids and heterogeneous binary valuations, (ii) 2 agents with heterogeneous partition matroids and heterogeneous valuations, and (iii) at most 3 agents with heterogeneous binary valuations and identical base-orderable matroids.

Original languageEnglish
Title of host publication35th AAAI Conference on Artificial Intelligence, AAAI 2021
PublisherAssociation for the Advancement of Artificial Intelligence
Pages5312-5320
Number of pages9
ISBN (Electronic)9781713835974
StatePublished - 2021
Externally publishedYes
Event35th AAAI Conference on Artificial Intelligence, AAAI 2021 - Virtual, Online
Duration: 2 Feb 20219 Feb 2021

Publication series

Name35th AAAI Conference on Artificial Intelligence, AAAI 2021
Volume6B

Conference

Conference35th AAAI Conference on Artificial Intelligence, AAAI 2021
CityVirtual, Online
Period2/02/219/02/21

Bibliographical note

Publisher Copyright:
Copyright © 2021, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.

Funding

A. Dror and M.Feldman received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 866132), and the Israel Science Foundation (grant number 317/17). E. Segal-Halevi is supported by the Israel Science Foundation (grant number 712/20). We are grateful to Jonathan Turner, Jan Vondrak, Chandra Chekuri, Tony Huynh, Siddharth Barman and Arpita Biswas for their helpful comments.

FundersFunder number
Horizon 2020 Framework Programme866132
European Research Council
Israel Science Foundation712/20, 317/17

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