A new characterization of maximal repetitions by Lyndon trees

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

25 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationProceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015
PublisherAssociation for Computing Machinery
Pages562-571
Number of pages10
EditionJanuary
ISBN (Electronic)9781611973747
DOIs
Publication statusPublished - 2015
Event26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015 - San Diego, United States
Duration: Jan 4 2015Jan 6 2015

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
NumberJanuary
Volume2015-January

Other

Other26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015
CountryUnited States
CitySan Diego
Period1/4/151/6/15

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

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