Paper Abstract and Keywords 
Presentation 
20101203 16:00
Improving the Competitive Ratios of the Seat Reservation Problem Kazuya Okamoto, Shuichi Miyazaki (Kyoto Univ.) COMP201045 
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 $\frac{4}{k2\sqrt{k1}+4}$, which
improves the previous bound of $\frac{8}{k+5}$. We also give an upper
bound of $\frac{2}{k2\sqrt{k1}+2}$ for the competitive ratio of
WorstFit algorithm, which improves the previous bound of
$\frac{4}{k1}$. For the proportional price problem, we give upper
and lower bounds of $\frac{3+\sqrt{13}}{k1+\sqrt{13}} (\simeq
\frac{6.6}{k+2.6})$ and $\frac{2}{k1}$, 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
$\frac{1}{k1}$, 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, COMP201045, pp. 4551, Dec. 2010. 
Paper # 
COMP201045 
Date of Issue 
20101126 (COMP) 
ISSN 
Print edition: ISSN 09135685 Online edition: ISSN 24326380 
Copyright and reproduction 
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COMP201045 
Conference Information 
Committee 
COMP 
Conference Date 
20101203  20101203 
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 
201012COMP 
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.) 
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Speaker 
1 
Date Time 
20101203 16:00:00 
Presentation Time 
35 
Registration for 
COMP 
Paper # 
IEICECOMP201045 
Volume (vol) 
IEICE110 
Number (no) 
no.325 
Page 
pp.4551 
#Pages 
IEICE7 
Date of Issue 
IEICECOMP20101126 
