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Paper Abstract and Keywords
Presentation 2014-12-05 13:00
[Invited Talk] A new characterization of maximal repetitions by Lyndon trees
Hideo Bannai (Kyushu Univ.), Tomohiro I (TU Dortmund), Shunsuke Inenaga, Yuto Nakashima, Masayuki Takeda, Kazuya Tsuruta (Kyushu Univ.) COMP2014-35
Abstract (in Japanese) (See Japanese page) 
(in English) A run is a maximal periodic sub-interval of a string, that is at least as long as twice its smallest period. Runs are important characteristics of strings since they essentially capture all consecutive repeats of a substring in a string. In this talk, we introduce a new characterization of runs in strings using a tree defined on recursive standard factorizations of Lyndon words, called the Lyndon tree. The characterization leads to a remarkably simple novel proof of the linearity of the maximum number of runs $rho(n)$ in a string of length $n$, as well as the best known upper bound for $rho(n)$. The proof also gives rise to a new, conceptually simple linear-time algorithm for computing all the runs in a string. A notable characteristic of our algorithm is that, unlike all existing linear-time algorithms, it does not utilize the Lempel-Ziv factorization of the string.
Keyword (in Japanese) (See Japanese page) 
(in English) runs / Lyndon Tree / / / / / /  
Reference Info. IEICE Tech. Rep., vol. 114, no. 352, COMP2014-35, pp. 21-21, Dec. 2014.
Paper # COMP2014-35 
Date of Issue 2014-11-28 (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)
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Conference Information
Committee COMP  
Conference Date 2014-12-05 - 2014-12-05 
Place (in Japanese) (See Japanese page) 
Place (in English) Sojo University 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2014-12-COMP 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) A new characterization of maximal repetitions by Lyndon trees 
Sub Title (in English)  
Keyword(1) runs  
Keyword(2) Lyndon Tree  
1st Author's Name Hideo Bannai  
1st Author's Affiliation Kyushu University (Kyushu Univ.)
2nd Author's Name Tomohiro I  
2nd Author's Affiliation Technical University of Dortmund (TU Dortmund)
3rd Author's Name Shunsuke Inenaga  
3rd Author's Affiliation Kyushu University (Kyushu Univ.)
4th Author's Name Yuto Nakashima  
4th Author's Affiliation Kyushu University (Kyushu Univ.)
5th Author's Name Masayuki Takeda  
5th Author's Affiliation Kyushu University (Kyushu Univ.)
6th Author's Name Kazuya Tsuruta  
6th Author's Affiliation Kyushu University (Kyushu Univ.)
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Date Time 2014-12-05 13:00:00 
Presentation Time 40 
Registration for COMP 
Paper # IEICE-COMP2014-35 
Volume (vol) IEICE-114 
Number (no) no.352 
Page p.21 
#Pages IEICE-1 
Date of Issue IEICE-COMP-2014-11-28 

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