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Paper Abstract and Keywords
Presentation 2010-12-03 16:00
Improving the Competitive Ratios of the Seat Reservation Problem
Kazuya 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
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  
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.)
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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 

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