TY - GEN

T1 - Reforming an Envy-Free Matching

AU - Ito, Takehiro

AU - Iwamasa, Yuni

AU - Kakimura, Naonori

AU - Kamiyama, Naoyuki

AU - Kobayashi, Yusuke

AU - Nozaki, Yuta

AU - Okamoto, Yoshio

AU - Ozeki, Kenta

N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant Numbers JP18H04091, JP19K11814, JP20H05793, JP20H05795, JP20K11670, JP20K23323, JP18H05291, JP19H05485, and JP21H03397, Japan. We thank the reviewers and the meta-reviewers for their helpful comments.
Publisher Copyright:
© 2022, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.

PY - 2022/6/30

Y1 - 2022/6/30

N2 - We consider the problem of reforming an envy-free matching when each agent is assigned a single item. Given an envy-free matching, we consider an operation to exchange the item of an agent with an unassigned item preferred by the agent that results in another envy-free matching. We repeat this operation as long as we can. We prove that the resulting envy-free matching is uniquely determined up to the choice of an initial envy-free matching, and can be found in polynomial time. We call the resulting matching a reformist envy-free matching, and then we study a shortest sequence to obtain the reformist envy-free matching from an initial envy-free matching. We prove that a shortest sequence is computationally hard to obtain even when each agent accepts at most four items and each item is accepted by at most three agents. On the other hand, we give polynomial-time algorithms when each agent accepts at most three items or each item is accepted by at most two agents. Inapproximability and fixed-parameter (in)tractability are also discussed.

AB - We consider the problem of reforming an envy-free matching when each agent is assigned a single item. Given an envy-free matching, we consider an operation to exchange the item of an agent with an unassigned item preferred by the agent that results in another envy-free matching. We repeat this operation as long as we can. We prove that the resulting envy-free matching is uniquely determined up to the choice of an initial envy-free matching, and can be found in polynomial time. We call the resulting matching a reformist envy-free matching, and then we study a shortest sequence to obtain the reformist envy-free matching from an initial envy-free matching. We prove that a shortest sequence is computationally hard to obtain even when each agent accepts at most four items and each item is accepted by at most three agents. On the other hand, we give polynomial-time algorithms when each agent accepts at most three items or each item is accepted by at most two agents. Inapproximability and fixed-parameter (in)tractability are also discussed.

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M3 - Conference contribution

AN - SCOPUS:85146328697

T3 - Proceedings of the 36th AAAI Conference on Artificial Intelligence, AAAI 2022

SP - 5084

EP - 5091

BT - AAAI-22 Technical Tracks 5

PB - Association for the Advancement of Artificial Intelligence

T2 - 36th AAAI Conference on Artificial Intelligence, AAAI 2022

Y2 - 22 February 2022 through 1 March 2022

ER -