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Paper Abstract and Keywords
Presentation 2014-04-24 15:15
Improved Bounds for Online $k$-Frame Throughput Maximization in Network Switches
Koji Kobayashi (NII), Jun Kawahara (NAIST), Shuichi Miyazaki (Kyoto Univ.) COMP2014-6
Abstract (in Japanese) (See Japanese page) 
(in English) We consider a variant of the online buffer management problem in network switches, called the $k$-frame throughput maximization problem ($k$-FTM). This problem models the situation where a large frame is fragmented into $k$ packets and transmitted through the Internet, and the receiver can reconstruct the frame only if he/she accepts all the $k$ packets. Kesselman et~al. introduced this problem and showed that its competitive ratio is unbounded even when $k=2$. They also introduced a restricted variant of $k$-FTM, called $k$-OFTM. They proposed an online algorithm and showed that its competitive ratio is at most $frac{ 2kB }{ lfloor B/k rfloor } + k$ for any $B ge k$, where $B$ is the size of the buffer. They also presented a lower bound of $frac{ B }{ lfloor 2B/k rfloor } = Omega(k)$ for deterministic online algorithms when $2B geq k$ and $k$ is a power of $2$.

In this paper, we improve upper and lower bounds on the competitive ratio of $k$-OFTM. Our main result is to improve an upper bound of $O(k^{2})$ by Kesselman et~al. to $frac{5B + lfloor B/k rfloor - 4}{lfloor B/2k rfloor} = O(k)$ for $Bgeq 2k$, which matches their lower bound of $Omega(k)$ asymptotically. We also present an improved lower bound of $frac{2B}{lfloor {B/(k-1)} rfloor} + 1$ on the competitive ratio of deterministic online algorithms for any $k geq 2$ and any $B geq k-1$, and the first nontrivial lower bound of $k-1$ on the competitive ratio of randomized algorithms for any $k geq 3$ and any $B$.
Keyword (in Japanese) (See Japanese page) 
(in English) Online Problem / Competitive Analysis / Buffer Management / Packet Fragmentation / / / /  
Reference Info. IEICE Tech. Rep., vol. 114, no. 19, COMP2014-6, pp. 37-44, April 2014.
Paper # COMP2014-6 
Date of Issue 2014-04-17 (COMP) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
Copyright
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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 2014-04-24 - 2014-04-24 
Place (in Japanese) (See Japanese page) 
Place (in English) Tohoku University 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2014-04-COMP 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Improved Bounds for Online $k$-Frame Throughput Maximization in Network Switches 
Sub Title (in English)  
Keyword(1) Online Problem  
Keyword(2) Competitive Analysis  
Keyword(3) Buffer Management  
Keyword(4) Packet Fragmentation  
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Keyword(6)  
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1st Author's Name Koji Kobayashi  
1st Author's Affiliation National Institute of Informatics (NII)
2nd Author's Name Jun Kawahara  
2nd Author's Affiliation Nara Institute of Science and Technology (NAIST)
3rd Author's Name Shuichi Miyazaki  
3rd Author's Affiliation Kyoto University (Kyoto Univ.)
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Speaker Author-2 
Date Time 2014-04-24 15:15:00 
Presentation Time 35 minutes 
Registration for COMP 
Paper # COMP2014-6 
Volume (vol) vol.114 
Number (no) no.19 
Page pp.37-44 
#Pages
Date of Issue 2014-04-17 (COMP) 


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