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Paper Abstract and Keywords
Presentation 2024-03-14 14:45
Reforming an Envy-Free Matching with Ties
Yuni Iwamasa, Jun Kawahara, Yuito Ueda (Kyoto Univ.) COMP2023-32
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
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)
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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  
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 
Date of Issue 2024-03-07 (COMP) 

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