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| Presentation | 2024-03-14 14:45 Reforming an Envy-Free Matching with Ties Yuni Iwamasa, Jun Kawahara, Yuito Ueda (Kyoto Univ.)  COMP2023-32 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | An envy-free matching is a type of matching between agents and items such that each agent have a preference order for the items they accept. For any agent, if no item more preferred to the item assigned to the agent is assigned to another agent, the assignment is called an envy-free matching. An envy-free matching that cannot be improved further by repeatedly exchanging an item assigned to an agent for an item not currently assigned to the agent, while maintaining envy-free, is called a reformist envy-free matching. It is known that the reformist envy-free matching obtained from a given envy-free matching is uniquely determined if the agent's preference order does not include ties. In this paper, we prove that reformist envy-free matching is uniquely determined under a certain equivalence relation when ties are included in the agent's preference order. We also prove that those matchings are transitive to each other by transitions in which the agent exchanges equally preferred items, using attribution to the combinational reconfiguration problem of bipartite matching. Finally, we formulate the problem of finding the optimal envy-free matching between reformist envy-free matchings obtained from an envy-free matching when the items are given a cost. We prove that the problem can be solved in polynomial time. | |
| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | envy-free matching / reformist envy-free matching / optimal reformist envy-free matching problem / / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 123, no. 444, COMP2023-32, pp. 23-30, March 2024. | |
| Paper # | COMP2023-32 | |
| Date of Issue | 2024-03-07 (COMP) | |
| ISSN | Online edition: ISSN 2432-6380 | |
| Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) | |
| Download PDF | COMP2023-32 |
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| Conference Information | |
| Committee | COMP |
| Conference Date | 2024-03-14 - 2024-03-14 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | The University of Electro-Communications |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | Theoretical Computer Science, etc |
| Paper Information | |
| Registration To | COMP |
| Conference Code | 2024-03-COMP |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Reforming an Envy-Free Matching with Ties |
| Sub Title (in English) | |
| Keyword(1) | envy-free matching |
| Keyword(2) | reformist envy-free matching |
| Keyword(3) | optimal reformist envy-free matching problem |
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| 1st Author's Name | Yuni Iwamasa |
| 1st Author's Affiliation | Kyoto University (Kyoto Univ.) |
| 2nd Author's Name | Jun Kawahara |
| 2nd Author's Affiliation | Kyoto University (Kyoto Univ.) |
| 3rd Author's Name | Yuito Ueda |
| 3rd Author's Affiliation | Kyoto University (Kyoto Univ.) |
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| Speaker | Author-3 |
| Date Time | 2024-03-14 14:45:00 |
| Presentation Time | 30 minutes |
| Registration for | COMP |
| Paper # | COMP2023-32 |
| Volume (vol) | vol.123 |
| Number (no) | no.444 |
| Page | pp.23-30 |
| #Pages | 8 |
| Date of Issue | 2024-03-07 (COMP) |
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