A new characterization of maximal repetitions by Lyndon trees

Hideo Bannai, Tomohiro I, Shunsuke Inenaga, Yuto Nakashima, Masayuki Takeda, Kazuya Tsuruta

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

28 被引用数 (Scopus)

抄録

We give a new characterization of maximal repetitions (or 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 p(n) in a string of length n. Furthermore, we show an upper bound of p(n) < 1.5n, which improves on the best upper bound 1.6n (Crochemore & Hie 2008) that does not rely on computational verification. 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.

本文言語英語
ホスト出版物のタイトルProceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015
出版社Association for Computing Machinery
ページ562-571
ページ数10
January
ISBN(電子版)9781611973747
DOI
出版ステータス出版済み - 2015
イベント26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015 - San Diego, 米国
継続期間: 1 4 20151 6 2015

出版物シリーズ

名前Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
番号January
2015-January

その他

その他26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015
国/地域米国
CitySan Diego
Period1/4/151/6/15

All Science Journal Classification (ASJC) codes

  • ソフトウェア
  • 数学 (全般)

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