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 Paper Abstract and Keywords Presentation 2010-12-03 16:00 Improving the Competitive Ratios of the Seat Reservation ProblemKazuya Okamoto, Shuichi Miyazaki (Kyoto Univ.) COMP2010-45 Abstract (in Japanese) (See Japanese page) (in English) In the seat reservation problem, there are $k$ stations, $s_{1}$ through $s_{k}$, and one train with $n$ seats departing from the station $s_{1}$ and arriving at the station $s_{k}$. Each passenger orders a ticket from station $s_{i}$ to station $s_{j}$ ($1 \leq i < j \leq k$) by specifying $i$ and $j$. The task of an online algorithm is to assign one of $n$ seats to each passenger online, i.e., without knowing future requests. The purpose of the problem is to maximize the total price of the sold tickets. There are two models, the unit price problem and the proportional price problem, depending on the pricing policy of tickets. In this paper, we improve upper and lower bounds on the competitive ratios for both models: For the unit price problem, we give an upper bound of $\frac{4}{k-2\sqrt{k-1}+4}$, which improves the previous bound of $\frac{8}{k+5}$. We also give an upper bound of $\frac{2}{k-2\sqrt{k-1}+2}$ for the competitive ratio of Worst-Fit algorithm, which improves the previous bound of $\frac{4}{k-1}$. For the proportional price problem, we give upper and lower bounds of $\frac{3+\sqrt{13}}{k-1+\sqrt{13}} (\simeq \frac{6.6}{k+2.6})$ and $\frac{2}{k-1}$, respectively, on the competitive ratio, which improves the previous bounds of $\frac{4+2\sqrt{13}}{k+3+2\sqrt{13}} (\simeq \frac{11.2}{k+10.2})$ and $\frac{1}{k-1}$, respectively. Keyword (in Japanese) (See Japanese page) (in English) the seat reservation problem / online problem / online algorithms / competitive analysis / / / / Reference Info. IEICE Tech. Rep., vol. 110, no. 325, COMP2010-45, pp. 45-51, Dec. 2010. Paper # COMP2010-45 Date of Issue 2010-11-26 (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 COMP2010-45

 Conference Information Committee COMP Conference Date 2010-12-03 - 2010-12-03 Place (in Japanese) (See Japanese page) Place (in English) Kyutech Plaza, Kyushu Institute of Technology Topics (in Japanese) (See Japanese page) Topics (in English) Paper Information Registration To COMP Conference Code 2010-12-COMP Language Japanese Title (in Japanese) (See Japanese page) Sub Title (in Japanese) (See Japanese page) Title (in English) Improving the Competitive Ratios of the Seat Reservation Problem Sub Title (in English) Keyword(1) the seat reservation problem Keyword(2) online problem Keyword(3) online algorithms Keyword(4) competitive analysis Keyword(5) Keyword(6) Keyword(7) Keyword(8) 1st Author's Name Kazuya Okamoto 1st Author's Affiliation Kyoto University (Kyoto Univ.) 2nd Author's Name Shuichi Miyazaki 2nd Author's Affiliation Kyoto University (Kyoto Univ.) 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 2010-12-03 16:00:00 Presentation Time 35 Registration for COMP Paper # IEICE-COMP2010-45 Volume (vol) IEICE-110 Number (no) no.325 Page pp.45-51 #Pages IEICE-7 Date of Issue IEICE-COMP-2010-11-26