Ordinal Maximin Share Approximation for Chores

Hadi Hosseini, Andrew Searns, Erel Segal-Halevi

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

4 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 languageEnglish
Title of host publicationInternational Conference on Autonomous Agents and Multiagent Systems, AAMAS 2022
PublisherInternational Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)
Pages597-605
Number of pages9
ISBN (Electronic)9781713854333
StatePublished - 2022
Externally publishedYes
Event21st International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2022 - Auckland, Virtual, New Zealand
Duration: 9 May 202213 May 2022

Publication series

NameProceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS
Volume1
ISSN (Print)1548-8403
ISSN (Electronic)1558-2914

Conference

Conference21st International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2022
Country/TerritoryNew Zealand
CityAuckland, Virtual
Period9/05/2213/05/22

Bibliographical note

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

Keywords

  • Fair Division
  • Maximin Share Guarantee
  • Resource Allocation

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