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| 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 |
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| 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 | |
| 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 | COMP2014-35 |
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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 |
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| 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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| Speaker | Author-1 |
| Date Time | 2014-12-05 13:00:00 |
| Presentation Time | 40 minutes |
| Registration for | COMP |
| Paper # | COMP2014-35 |
| Volume (vol) | vol.114 |
| Number (no) | no.352 |
| Page | p.21 |
| #Pages | 1 |
| Date of Issue | 2014-11-28 (COMP) |
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