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Paper Abstract and Keywords
Presentation 2013-04-24 11:10
Analysis of the Maximum Sum of Exponents of Runs in Strings
Kazuhiko Kusano, Ryosuke Okuta, Kazuyuki Narisawa, Ayumi Shinohara (Tohoku Univ.) COMP2013-3
Abstract (in Japanese) (See Japanese page) 
(in English) A run in a string is a periodic substring which can not be extendable neither to the left nor right with the same period.
In this paper, we focus on the sum of exponents of runs.
We compute exact values of the maximum sum $sigma_2(n)$ of exponents of runs in a binary string of length $n$, up to $n=57$, by an efficient pruning algorithm.
The current best lower bound for the maximum sum $sigma(n)$ of exponents in a string of length $n$ is $2.03525n$.
We show a new lower bound $2.03696n$, which is discovered by exhaustively searching morphisms generating strings.
Keyword (in Japanese) (See Japanese page) 
(in English) Runs / Repetitions in strings / Exponents of repetitions / / / / /  
Reference Info. IEICE Tech. Rep., vol. 113, no. 14, COMP2013-3, pp. 17-24, April 2013.
Paper # COMP2013-3 
Date of Issue 2013-04-17 (COMP) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
Copyright
and
reproduction		 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 COMP2013-3

Conference Information
Committee COMP  
Conference Date 2013-04-24 - 2013-04-24 
Place (in Japanese) (See Japanese page) 
Place (in English) Kobe University 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2013-04-COMP 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Analysis of the Maximum Sum of Exponents of Runs in Strings 
Sub Title (in English) * 
Keyword(1) Runs  
Keyword(2) Repetitions in strings  
Keyword(3) Exponents of repetitions  
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1st Author's Name Kazuhiko Kusano  
1st Author's Affiliation Tohoku University (Tohoku Univ.)
2nd Author's Name Ryosuke Okuta  
2nd Author's Affiliation Tohoku University (Tohoku Univ.)
3rd Author's Name Kazuyuki Narisawa  
3rd Author's Affiliation Tohoku University (Tohoku Univ.)
4th Author's Name Ayumi Shinohara  
4th Author's Affiliation Tohoku University (Tohoku Univ.)
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Speaker Author-2 
Date Time 2013-04-24 11:10:00 
Presentation Time 35 minutes 
Registration for COMP 
Paper # COMP2013-3 
Volume (vol) vol.113 
Number (no) no.14 
Page pp.17-24 
#Pages 8 
Date of Issue 2013-04-17 (COMP) 

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