Ordinal Maximin Share Approximation for Chores

Hadi Hosseini; Andrew Searns; Erel Segal-Halevi

Ordinal Maximin Share Approximation for Chores

Hadi Hosseini
, Andrew Searns
, Erel Segal-Halevi

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

12 Scopus citations

Abstract

We study the problem of fairly allocating a set of m indivisible chores (items with non-positive value) to n agents. We consider the desirable fairness notion of 1-out-of-d maximin share (MMS)-the minimum value that an agent can guarantee by partitioning items into d bundles and receiving the least valued bundle-and focus on ordinal approximation of MMS that aims at finding the largest d ≤ n for which 1-out-of-d MMS allocation exists. Our main contribution is a polynomial-time algorithm for 1-out-of-⌊2n/3⌋ MMS allocation, and a proof of existence of 1-out-of-⌊3n/4⌋ MMS allocation of chores. Furthermore, we show how to use recently-developed algorithms for bin-packing to approximate the latter bound up to a logarithmic factor in polynomial time.

Original language	English
Title of host publication	International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2022
Publisher	International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)
Pages	597-605
Number of pages	9
ISBN (Electronic)	9781713854333
State	Published - 2022
Externally published	Yes
Event	21st International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2022 - Auckland, Virtual, New Zealand Duration: 9 May 2022 → 13 May 2022

Publication series

Name	Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS
Volume	1
ISSN (Print)	1548-8403
ISSN (Electronic)	1558-2914

Conference

Conference	21st International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2022
Country/Territory	New Zealand
City	Auckland, Virtual
Period	9/05/22 → 13/05/22

Bibliographical note

Publisher Copyright:
© 2022 International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved

Funding

Hadi Hosseini acknowledges support from NSF IIS grants #2052488 and #2107173. Erel Segal-Halevi is supported by the ISF grant 712/20. We are grateful to anonymous referees of EC 2021 and AAMAS 2022 for their valuable feedback.

Funders	Funder number
NSF IIS	2107173, 2052488
Iowa Science Foundation	712/20

Keywords

Fair Division
Maximin Share Guarantee
Resource Allocation

Cite this

Hosseini, H., Searns, A., & Segal-Halevi, E. (2022). Ordinal Maximin Share Approximation for Chores. In International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2022 (pp. 597-605). (Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS; Vol. 1). International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS).

Hosseini, Hadi ; Searns, Andrew ; Segal-Halevi, Erel. / Ordinal Maximin Share Approximation for Chores. International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2022. International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS), 2022. pp. 597-605 (Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS).

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Hosseini, H, Searns, A & Segal-Halevi, E 2022, Ordinal Maximin Share Approximation for Chores. in International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2022. Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS, vol. 1, International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS), pp. 597-605, 21st International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2022, Auckland, Virtual, New Zealand, 9/05/22.

Ordinal Maximin Share Approximation for Chores. / Hosseini, Hadi; Searns, Andrew; Segal-Halevi, Erel.
International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2022. International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS), 2022. p. 597-605 (Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS; Vol. 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Hosseini H, Searns A, Segal-Halevi E. Ordinal Maximin Share Approximation for Chores. In International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2022. International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS). 2022. p. 597-605. (Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS).

Ordinal Maximin Share Approximation for Chores

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Bibliographical note

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Keywords

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