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| Presentation | 2008-03-10 09:30 Approximation Algorithms for the Sex-Equal Stable Marriage Problem Hiroki Yanagisawa (IBM), Shuichi Miyazaki, Kazuo Iwama (Kyoto Univ.)  COMP2007-55 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | The stable marriage problem is a classical matching problem introduced by Gale and Shapley. It is known that for any instance, there exists a solution, and there is a polynomial time algorithm to find one. However, the matching obtained by this algorithm is man-optimal, that is, the matching is preferable for men but unpreferable for women, (or, if we exchange the role of men and women, the resulting matching is woman-optimal). The sex-equal stable marriage problem, posed by Gusfield and Irving, asks to find a stable matching ``fair'' for both genders, namely it asks to find a stable matching with the property that the sum of the men's score is as close as possible to that of the women's. This problem is known to be strongly NP-hard. In this paper, we give a polynomial time algorithm for finding {\em a near optimal} solution in the sex-equal stable marriage problem. Furthermore, we consider the problem of optimizing additional criterion: among stable matchings that are near optimal in terms of the sex-equality, find a minimum egalitarian stable matching. We show that this problem is NP-hard, and give a polynomial time algorithm whose approximation ratio is less than two. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | the stable marriage problem / the sex-equal stable marriage problem / approximation algorithms / / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 107, no. 537, COMP2007-55, pp. 1-8, March 2008. | |
| Paper # | COMP2007-55 | |
| Date of Issue | 2008-03-03 (COMP) | |
| ISSN | Print edition: ISSN 0913-5685 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 | COMP2007-55 |
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| Conference Information | |
| Committee | COMP |
| Conference Date | 2008-03-10 - 2008-03-10 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | COMP |
| Conference Code | 2008-03-COMP |
| Language | English (Japanese title is available) |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Approximation Algorithms for the Sex-Equal Stable Marriage Problem |
| Sub Title (in English) | |
| Keyword(1) | the stable marriage problem |
| Keyword(2) | the sex-equal stable marriage problem |
| Keyword(3) | approximation algorithms |
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| 1st Author's Name | Hiroki Yanagisawa |
| 1st Author's Affiliation | IBM (IBM) |
| 2nd Author's Name | Shuichi Miyazaki |
| 2nd Author's Affiliation | Kyoto University (Kyoto Univ.) |
| 3rd Author's Name | Kazuo Iwama |
| 3rd Author's Affiliation | Kyoto University (Kyoto Univ.) |
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| Speaker | Author-1 |
| Date Time | 2008-03-10 09:30:00 |
| Presentation Time | 25 minutes |
| Registration for | COMP |
| Paper # | COMP2007-55 |
| Volume (vol) | vol.107 |
| Number (no) | no.537 |
| Page | pp.1-8 |
| #Pages | 8 |
| Date of Issue | 2008-03-03 (COMP) |
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