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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
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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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Conference Information
Committee COMP  
Conference Date 2007-06-29 - 2007-06-29 
Place (in Japanese) (See Japanese page) 
Place (in English) Hokkaido University 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2007-06-COMP 
Language English (Japanese title is available) 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Weighted Random Popular Matchings 
Sub Title (in English)  
Keyword(1) popular matchings  
Keyword(2) random popular matchings  
Keyword(3) weighted popular matchings  
Keyword(4) 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.)
2nd Author's Name Osamu Watanabe  
2nd Author's Affiliation Tokyo Institute of Technology (Tokyo Inst. of Tech.)
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Speaker
Date Time 2007-06-29 11:20:00 
Presentation Time 25 
Registration for COMP 
Paper # IEICE-COMP2007-23 
Volume (vol) IEICE-107 
Number (no) no.127 
Page pp.41-48 
#Pages IEICE-8 
Date of Issue IEICE-COMP-2007-06-22 


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