TY - GEN

T1 - A new characterization of maximal repetitions by Lyndon trees

AU - Bannai, Hideo

AU - I, Tomohiro

AU - Inenaga, Shunsuke

AU - Nakashima, Yuto

AU - Takeda, Masayuki

AU - Tsuruta, Kazuya

N1 - Publisher Copyright:
Copyright © 2015 by the Society for Industrial and Applied Mathmatics.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84938221386&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84938221386&partnerID=8YFLogxK

U2 - 10.1137/1.9781611973730.38

DO - 10.1137/1.9781611973730.38

M3 - Conference contribution

AN - SCOPUS:84938221386

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 562

EP - 571

BT - Proceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015

PB - Association for Computing Machinery

T2 - 26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015

Y2 - 4 January 2015 through 6 January 2015

ER -