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 Paper Abstract and Keywords Presentation 2007-06-29 11:20 Weighted Random Popular MatchingsToshiya 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 Copyrightandreproduction 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 COMP2007-23

 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 Keyword(5) Keyword(6) Keyword(7) Keyword(8) 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.) 3rd Author's Name 3rd Author's Affiliation () 4th Author's Name 4th Author's Affiliation () 5th Author's Name 5th Author's Affiliation () 6th Author's Name 6th Author's Affiliation () 7th Author's Name 7th Author's Affiliation () 8th Author's Name 8th Author's Affiliation () 9th Author's Name 9th Author's Affiliation () 10th Author's Name 10th Author's Affiliation () 11th Author's Name 11th Author's Affiliation () 12th Author's Name 12th Author's Affiliation () 13th Author's Name 13th Author's Affiliation () 14th Author's Name 14th Author's Affiliation () 15th Author's Name 15th Author's Affiliation () 16th Author's Name 16th Author's Affiliation () 17th Author's Name 17th Author's Affiliation () 18th Author's Name 18th Author's Affiliation () Speaker 1 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