Paper Abstract and Keywords |
Presentation |
2007-06-29 11:20
Weighted Random Popular Matchings Toshiya Itoh, Osamu Watanabe (Tokyo Inst. of Tech.) COMP2007-23 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
Let A be the set of n applicants and I be the set of m items. We assume that the set A is partitioned into A_{1},A_{2},\ldots,A_{k} and each A_{i} is assigned a weight w_{i} such that w_{1}>w_{2}>\cdots>w_{k}>0. Let us consider the problem of matching applicants to items, where each applicant x \in A provides a preference list defined on items. We say that an applicant x prefers an item p than an item q if p is located at higher position than q in the preference list. For any matchings M and M', we say that an applicant x prefers M over M' if x prefers M}(x) over M'(x). We say that M is more popular than M' if the total weight of applicants preferring M over M' is larger than that of applicants preferring M' over M, and define M to be a k-weighted popular matching if there are no other matchings that are more popular than M. For the case where k=1, Mahdian showed that if m > 1.42n, then
a random instance of the matching problem has a popular matching with high probability, but nothing is known for the k-weighted matching problems. In this paper, we analyze the k-weighted matching problems, and show that for any \beta such that m=\beta n, (lower bound) if \beta/n^{1/3}=o(1), then a random instance of the 2-weighted matching problems does not have a 2-weighted popular matching with probability 1-o(1); (upper bound) if n^{1/3}/\beta=o(1), then a random instance of the 2-weighted matching problems has a 2-weighted popular matching with probability 1-o(1). |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
popular matchings / random popular matchings / weighted popular matchings / well-formed matchings / / / / |
Reference Info. |
IEICE Tech. Rep., vol. 107, no. 127, COMP2007-23, pp. 41-48, June 2007. |
Paper # |
COMP2007-23 |
Date of Issue |
2007-06-22 (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) |
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COMP2007-23 |
Conference Information |
Committee |
COMP |
Conference Date |
2007-06-29 - 2007-06-29 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Hokkaido University |
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Registration To |
COMP |
Conference Code |
2007-06-COMP |
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English (Japanese title is available) |
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(See Japanese page) |
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(See Japanese page) |
Title (in English) |
Weighted Random Popular Matchings |
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popular matchings |
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random popular matchings |
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weighted popular matchings |
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well-formed matchings |
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1st Author's Name |
Toshiya Itoh |
1st Author's Affiliation |
Tokyo Institute of Technology (Tokyo Inst. of Tech.) |
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Osamu Watanabe |
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Tokyo Institute of Technology (Tokyo Inst. of Tech.) |
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Speaker |
Author-1 |
Date Time |
2007-06-29 11:20:00 |
Presentation Time |
25 minutes |
Registration for |
COMP |
Paper # |
COMP2007-23 |
Volume (vol) |
vol.107 |
Number (no) |
no.127 |
Page |
pp.41-48 |
#Pages |
8 |
Date of Issue |
2007-06-22 (COMP) |
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