TY - GEN
T1 - Ordinal Maximin Share Approximation for Chores
AU - Hosseini, Hadi
AU - Searns, Andrew
AU - Segal-Halevi, Erel
N1 - Publisher Copyright:
© 2022 International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - Fair Division
KW - Maximin Share Guarantee
KW - Resource Allocation
UR - http://www.scopus.com/inward/record.url?scp=85130308485&partnerID=8YFLogxK
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AN - SCOPUS:85130308485
T3 - Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS
SP - 597
EP - 605
BT - International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2022
T2 - 21st International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2022
Y2 - 9 May 2022 through 13 May 2022
ER -